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  • 1.
    Albeverio, S.
    et al.
    BiBoS Research Center.
    Haake, F.
    Fachbereich Physik, Universität-GH Essen.
    Kurasov, Pavel
    Luleå tekniska universitet.
    Kus, M.
    Fachbereich Physik, Universität-GH Essen.
    Šeba, P.
    Nuclear Physics Institute, Czech Academy of Sciences.
    S-matrix, resonances, and wave functions for transport through billiards with leads1996In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 37, no 10, p. 4888-4903Article in journal (Refereed)
    Abstract [en]

    For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator

  • 2.
    Alho, Artur
    et al.
    Technical University of Lisbon, Portugal.
    Uggla, Claes
    Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Engineering and Physics (from 2013).
    Global dynamics and inflationary center manifold and slow-roll approximants2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 1, article id 012502Article in journal (Refereed)
    Abstract [en]

    We consider the familiar problem of a minimally coupled scalar field with quadratic potential in flat Friedmann-Lemaître-Robertson-Walker cosmology to illustrate a number of techniques and tools, which can be applied to a wide range of scalar field potentials and problems in, e.g., modified gravity. We present a global and regular dynamical systems description that yields a global understanding of the solution space, including asymptotic features. We introduce dynamical systems techniques such as center manifold expansions and use Padé approximants to obtain improved approximations for the “attractor solution” at early times. We also show that future asymptotic behavior is associated with a limit cycle, which shows that manifest self-similarity is asymptotically broken toward the future and gives approximate expressions for this behavior. We then combine these results to obtain global approximations for the attractor solution, which, e.g., might be used in the context of global measures. In addition, we elucidate the connection between slow-roll based approximations and the attractor solution, and compare these approximations with the center manifold based approximants.

  • 3.
    Alhulaimi, Bassemah
    et al.
    Dalhousie University, Halifax, Canada .
    Coley, Alan
    Dalhousie University, Halifax, Canada .
    Sandin, Patrik
    Dalhousie University, Halifax, Canada; Max-Planck-Institut für Gravitationsphysik (Albert-Einstein-Institut), Potsdam, Germany.
    Anisotropic Einstein-aether cosmological models2013In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 54, no 4Article in journal (Refereed)
    Abstract [en]

    We investigate a class of spatially anisotropic cosmological models in Einstein-aether theory with a scalar field in which the self-interaction potential depends on the timelike aether vector field through the expansion and shear scalars. We derive the evolution equations in terms of expansion-normalized variables, which reduce to a dynamical system. We study the local stability of the equilibrium points of the dynamical system corresponding to physically realistic solutions, and find that there are always ranges of values of the parameters of the models for which there exists an inflationary attractor. © 2013 AIP Publishing LLC.

  • 4.
    Andersson, Fredrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Edgar, SB
    Linkoping Univ, Dept Math, S-58183 Linkoping, Sweden.
    Spin coefficients as Lanczos scalars: Underlying spinor relations2000In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 41, no 5, p. 2990-3001Article in journal (Refereed)
    Abstract [en]

    It has been conjectured by Lopez-Bonilla and co-workers that there is some linear relationship between the NP spin coefficients and the Lanczos scalars, and examples have been given for a number of different classes of space-times. We show that in each of those examples a Lanczos potential can be defined in a very simple way directly from the spinor dyad. Although some of these examples seem to have no deeper geometric meaning, we emphasize that there are structural links between Lanczos potential and spin coefficients which we highlight in some other examples. In particular we show that the direct identification of Lanczos potentials with spin coefficients is possible for some important classes of space-times while the direct identification of Lanczos potentials with the properly weighted spin coefficients is also possible for several important classes of space-times. In both of these cases we obtain the necessary and sufficient conditions on the spin coefficients for such identifications to be possible, which enables us to test space-times directly. (C) 2000 American Institute of Physics. [S0022-2488(00)03104-2].

  • 5.
    Andersson, Ole
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Heydari, Hoshang
    Stockholm University, Faculty of Science, Department of Physics.
    Geometric uncertainty relation for mixed quantum states2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 4, p. 042110-Article in journal (Refereed)
    Abstract [en]

    In this paper we use symplectic reduction in an Uhlmann bundle to construct a principal fiber bundle over a general space of unitarily equivalent mixed quantum states. The bundle, which generalizes the Hopf bundle for pure states, gives in a canonical way rise to a Riemannian metric and a symplectic structure on the base space. With these we derive a geometric uncertainty relation for observables acting on quantum systems in mixed states. We also give a geometric proof of the classical Robertson-Schrodinger uncertainty relation, and we compare the two. They turn out not to be equivalent, because of the multiple dimensions of the gauge group for general mixed states. We give examples of observables for which the geometric relation provides a stronger estimate than that of Robertson and Schrodinger, and vice versa.

  • 6.
    Arnlind, Joakim
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Curvature and geometric modules of noncommutative spheres and tori2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 4, p. 041705-Article in journal (Refereed)
    Abstract [en]

    When considered as submanifolds of Euclidean space, the Riemannian geometry of the round sphere and the Clifford torus may be formulated in terms of Poisson algebraic expressions involving the embedding coordinates, and a central object is the projection operator, projecting tangent vectors in the ambient space onto the tangent space of the submanifold. In this note, we point out that there exist noncommutative analogues of these projection operators, which implies a very natural definition of noncommutative tangent spaces as particular projective modules. These modules carry an induced connection from Euclidean space, and we compute its scalar curvature.

  • 7.
    Arnlind, Joakim
    Department of Mathematics, Royal Institute of Technology, S-100 44 Stockholm, Sweden .
    Representation theory of C  -algebras for a higher-order class of spheres and tori2008In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, p. 053502-1-053502-13, article id 053502Article in journal (Refereed)
    Abstract [en]

    We construct C  -algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of “loop” and “string” representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras, we introduce the “Hénon algebras,” for which the dynamical map is a generalized Hénon map, and give an example where irreducible representations of all dimensions exist.

  • 8.
    Arnlind, Joakim
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Representation theory of C-algebras for a higher order class of spheres and tori2008In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 49, no 5, p. 053502-1-053502-13Article in journal (Refereed)
    Abstract [en]

    We construct C-algebras for a class of surfaces that are inverse images of certain polynomials of arbitrary degree. By using the directed graph associated with a matrix, the representation theory can be understood in terms of "loop" and "string" representations, which are closely related to the dynamics of an iterated map in the plane. As a particular class of algebras, we introduce the "Henon algebras," for which the dynamical map is a generalized Henon map, and give an example where irreducible representations of all dimensions exist.

  • 9.
    Arnlind, Joakim
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, The Institute of Technology.
    Grosse, Harald
    Mathematical Physics, Austria .
    Deformed noncommutative tori2012In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 53, no 7, p. 073505-Article in journal (Refereed)
    Abstract [en]

    We recall a construction of non-commutative algebras related to a one-parameter family of (deformed) spheres and tori, and show that in the case of tori, the *-algebras can be completed into C*-algebras isomorphic to the standard non-commutative torus. As the former was constructed in the context of matrix (or fuzzy) geometries, it provides an important link to the framework of non-commutative geometry, and opens up for a concrete way to study deformations of non-commutative tori. Furthermore, we show how the well-known fuzzy sphere and fuzzy torus can be obtained as formal scaling limits of finite-dimensional representations of the deformed algebras, and their projective modules are described together with connections of constant curvature.

  • 10.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, Laboratoire de Mathématiques, Informatique et Applications, 4, rue des Frères Lumière F-68093 Mulhouse, France .
    Silvestrov, Sergei
    Mälardalen University, Division of Applied Mathematics, The School of Education, Culture and Communication, Box 883, 721 23 Västerås, Sweden och Centre for Mathematical Sciences, Lund University, Box 118, 221 00 Lund, Sweden .
    Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, article id 123502Article in journal (Refereed)
    Abstract [en]

    As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions.

  • 11.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, Lab. de Mathématiques Informatique et Applications, 4, rue des Frères Lumière, F-68093 Mulhouse, France.
    Silvestrov, Sergei
    Mälardalen University, School of Education, Culture and Communication.
    Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 12, p. 123502-Article in journal (Refereed)
    Abstract [en]

    As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]

  • 12.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Am Mühlenberg 1, D-14476 Golm, Germany.
    Makhlouf, Abdenacer
    Laboratoire de Mathématiques, Informatique et Applications, Université de Haute Alsace, 4, rue des Frères Lumière, F-68093 Mulhouse, France .
    Silvestrov, Sergei
    Centre for Mathematical Sciences, Lund University, Box 118, SE-221 00 Lund, Sweden .
    Ternary Hom–Nambu–Lie algebras induced by Hom–Lie algebras2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, p. 043515-1-043515-11, article id 43515Article in journal (Refereed)
    Abstract [en]

    The need to consider n  -ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n  -ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n  -Lie structures) constructed from the binary multiplication of a Hom–Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom–Nambu–Lie algebras obtained using this construction.

  • 13.
    Arnlind, Joakim
    et al.
    Max Planck Institute for Gravitational Physics (AEI), Germany.
    Makhlouf, Abdenacer
    Université de Haute Alsace, France .
    Silvestrov, Sergei
    Lund University, Sweden.
    Ternary Hom-Nambu-Lie algebras induced by Hom-Lie algebras2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 4, p. 043515-11Article in journal (Refereed)
    Abstract [en]

    The need to consider n-ary algebraic structures, generalizing Lie and Poisson algebras, has become increasingly important in physics, and it should therefore be of interest to study the mathematical concepts related to n-ary algebras. The purpose of this paper is to investigate ternary multiplications (as deformations of n-Lie structures) constructed from the binary multiplication of a Hom-Lie algebra, a linear twisting map, and a trace function satisfying certain compatibility conditions. We show that the relation between the kernels of the twisting maps and the trace function plays an important role in this context and provide examples of Hom-Nambu-Lie algebras obtained using this construction.

  • 14.
    Ataguema, H.
    et al.
    Universit́e de Haute Alsace, France .
    Makhlouf, A.
    Universit́e de Haute Alsace, France .
    Silvestrov, S. D.
    Lund University.
    Generalization of n-ary Nambu algebras and beyond2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 8, p. Article number 083501-Article in journal (Refereed)
    Abstract [en]

    The aim of this paper is to introduce n-ary Hom-algebra structures generalizing the n-ary algebras of Lie type including n-ary Nambu algebras, n-ary Nambu-Lie algebras and n-ary Lie algebras, and n-ary algebras of associative type including n-ary totally associative and n-ary partially associative algebras. We provide examples of the new structures and present some properties and construction theorems. We describe the general method allowing one to obtain an n-ary Hom-algebra structure starting from an n-ary algebra and an n-ary algebra endomorphism. Several examples are derived using this process. Also we initiate investigation of classification problems for algebraic structures introduced in the article and describe all ternary three-dimensional Hom-Nambu-Lie structures with diagonal homomorphism.

  • 15.
    Atai, Farrokh
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics.
    Deformed Calogero-Sutherland model and fractional quantum Hall effect2017In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 1, article id 011902Article in journal (Refereed)
    Abstract [en]

    The deformed Calogero-Sutherland (CS) model is a quantum integrable system with arbitrary numbers of two types of particles and reducing to the standard CS model in special cases. We show that a known collective field description of the CS model, which is based on conformal field theory (CFT), is actually a collective field description of the deformed CS model. This provides a natural application of the deformed CS model in Wen's effective field theory of the fractional quantum Hall effect (FQHE), with the two kinds of particles corresponding to electrons and quasi-hole excitations. In particular, we use known mathematical results about super-Jack polynomials to obtain simple explicit formulas for the orthonormal CFT basis proposed by van Elburg and Schoutens in the context of the FQHE.

  • 16. Bach, V.
    et al.
    Frohlich, J.
    Jonsson, B. Lars G.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Bogolubov-Hartree-Fock mean field theory for neutron stars and other systems with attractive interactions2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 10Article in journal (Refereed)
    Abstract [en]

    A simplification of the Bogolubov-Hartree-Fock theory, which is a natural generalization of the traditional Hartree-Fock theory, is derived. This simplification allows to express the pairing interaction in terms of the one-particle density matrix for systems interacting by attractive pair potentials, such as the Newtonian gravitational potential.

  • 17.
    Basarab-Horwath, Peter
    et al.
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Gungor, F.
    Istanbul Technical University, Turkey.
    Linearizability for third order evolution equations2017In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 8, article id 081507Article in journal (Refereed)
    Abstract [en]

    The problem of linearization for third order evolution equations is considered. Criteria for testing equations for linearity are presented. A class of linearizable equations depending on arbitrary functions is obtained by requiring presence of an infinite-dimensional symmetry group. Linearizing transformations for this class are found using symmetry structure and local conservation laws. A number of special cases as examples are discussed. Their transformation to equations within the same class by differential substitutions and connection with KdV and mKdV equations is also reviewed in this framework. Published by AIP Publishing.

  • 18.
    Basarab-Horwath, Peter
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Zhdanov, R.Z.
    Institute of Mathematics, 3 Tereshchenkivska Street, 252004 Kyiv, Ukraine.
    Initial-value problems for evolutionary partial differential equations and higher-order conditional symmetries2001In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 42, no 1, p. 376-389Article in journal (Refereed)
    Abstract [en]

    We suggest a new approach to the problem of dimensional reduction of initial/ boundary value problems for evolution equations in one spatial variable. The approach is based on higher-order (generalized) conditional symmetries of the equations involved. It is shown that reducibility of an initial value problem for an evolution equation to a Cauchy problem for a system of ordinary differential equations can be fully characterized in terms of conditional symmetries which leave invariant the equation in question. We also give some examples of the solution of initial value problems for second- and third-order nonlinear differential equations by reduction by their conditional symmetries. We give a systematic classification of general second-order partial differential equations admitting second-order conditional symmetries, based on Lie's classification of invariant second-order ordinary differential equations. This yields five classes of principally new initial value problems for nonlinear evolution equations which admit no Lie symmetries and are reducible via second-order conditional symmetries. © 2001 American Institute of Physics.

  • 19.
    Bengtsson, Anders
    University of Borås, School of Engineering.
    An Abstract Interface to Higher Spin Field Theory2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 4Article in journal (Refereed)
  • 20.
    Bengtsson, Anders
    University of Borås, School of Engineering.
    Structure of Higher Spin Gauge Interactions2007In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, no 7Article in journal (Refereed)
  • 21.
    Bengtsson, Ingemar
    et al.
    Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden.
    Bruzda, Wojciech
    Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, Kraków, Poland.
    Ericsson, Åsa
    Stockholms Universitet, AlbaNova, Fysikum, Stockholm, Sweden.
    Larsson, Jan-Åke
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Tadej, Wojciech
    Wydział Matematyczno-Przyrodniczy, Szkoła Nauk Ścisłych, Universytet Kardynała Stefana Wyszyńskiego, Warszawa, Poland.
    Zyczkowski, Karol
    Instytut Fizyki im. Smoluchowskiego, Uniwersytet Jagielloński, Kraków, Poland and Centrum Fizyki Teoretycznej, Polska Akademia Nauk, Warszawa, Poland.
    Mutually unbiased bases and Hadamard matrices of order six2007In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, no 5, p. 052106-1-052106-21Article in journal (Refereed)
    Abstract [en]

    We report on a search for mutually unbiased bases (MUBs) in six dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organize our results. Finally, we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.

  • 22.
    Bengtsson, Ingemar
    et al.
    Stockholm University, Faculty of Science, Department of Physics.
    Bruzda, Wojciech
    Ericsson, Åsa
    Stockholm University, Faculty of Science, Department of Physics.
    Larsson, Jan-Åke
    Tadej, Wojciech
    Życzkowski, Karol
    Mutually unbiased bases and Hadamard matrices of order six2007In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, no 5, p. 052106-Article in journal (Refereed)
    Abstract [en]

    We report on a search for mutually unbiased bases (MUBs) in six dimensions. We find only triplets of MUBs, and thus do not come close to the theoretical upper bound 7. However, we point out that the natural habitat for sets of MUBs is the set of all complex Hadamard matrices of the given order, and we introduce a natural notion of distance between bases in Hilbert space. This allows us to draw a detailed map of where in the landscape the MUB triplets are situated. We use available tools, such as the theory of the discrete Fourier transform, to organize our results. Finally, we present some evidence for the conjecture that there exists a four dimensional family of complex Hadamard matrices of order 6. If this conjecture is true the landscape in which one may search for MUBs is much larger than previously thought.

  • 23.
    Birnir, B.
    et al.
    Department of Mathematics, UCSB, Santa Barbara, CA 93106, United States.
    Hou, S.
    Department of Mathematics, Michigan State University, East Lansing, MI 48824, United States.
    Wellander, N.
    Swedish Defence Research Agency, FOI, P.O. Box 1165, SE-581 11 Linkoping, Sweden.
    Derivation of the viscous Moore-Greitzer equation for aeroengine flow2007In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, no 6Article in journal (Refereed)
    Abstract [en]

    The viscous Moore-Greitzer equation modeling the airflow through the compression system in turbomachines, such as a jet engine, is derived using a scaled Navier-Stokes equation. The method utilizes a separation of scale argument based on the different spatial scales in the engine and the different time scales in the flow. The pitch and size of the rotor-stator pair of blades provides a small parameter, which is the size of the local cell. The motion of the stator and rotor blades in the compressor produces a very turbulent flow on a fast time scale. The leading order equation, for the fast time and local scales, describes this turbulent flow. The next order equations produce an axisymmetric swirl and a flow pattern analogous to Rayleigh-B´nard convection rolls in Rayleigh-B´nard convection. On a much larger spatial scale and a slower time scale, there exist modulations of the flow including instabilities called surge and stall. A higher order equation, in the small parameter, describes these global flow modulations, when averaged over the small (local) spatial scales, the fast time scale, and the time scale of the vortex rotations. Thus a more general system of spatially global, slow time equations is obtained. This system can be solved numerically without any approximations. The viscous Moore-Greitzer equation is obtained when small inertial terms are dropped from these slow time, spatially global equations averaged once more in the axial direction. The new equations are simulated with two different simplifying assumptions and the results are compared with simulations of the viscous Moore-Greitzer equations. © 2007 American Institute of Physics.

  • 24.
    Bjerklöv, Kristian
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Positive Lyapunov exponents for continuous quasiperiodic Schrodinger equations2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 2Article in journal (Refereed)
    Abstract [en]

    We prove that the continuous one-dimensional Schrodinger equation with an analytic quasi-periodic potential has positive Lyapunov exponents in the bottom of the spectrum for large couplings.

  • 25.
    Blennow, Mattias
    et al.
    KTH, Superseded Departments, Physics.
    Ohlsson, Tommy
    KTH, Superseded Departments, Physics.
    Exact series solution to the two flavor neutrino oscillation problem in matter2004In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 45, no 11, p. 4053-4063Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a real nonlinear differential equation for the two flavor neutrino oscillation problem in matter with an arbitrary density profile. We also present an exact series solution to this nonlinear differential equation. In addition, we investigate numerically the convergence of this solution for different matter density profiles such as constant and linear profiles as well as the Preliminary Reference Earth Model describing the Earth's matter density profile. Finally, we discuss other methods used for solving the neutrino flavor evolution problem.

  • 26. Boscain, Ugo
    et al.
    Grönberg, Fredrik
    KTH, School of Engineering Sciences (SCI), Physics.
    Long, Ruixing
    Rabitz, Herschel
    Minimal time trajectories for two-level quantum systems with two bounded controls2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 6, p. 062106-Article in journal (Refereed)
    Abstract [en]

    In this paper we consider the minimum time population transfer problem for a two level quantum system driven by two external fields with bounded amplitude. The controls are modeled as real functions and we do not use the Rotating Wave Approximation. After projection on the Bloch sphere, we treat the time-optimal control problem with techniques of optimal synthesis on 2D manifolds. Based on the Pontryagin Maximum Principle, we characterize a restricted set of candidate optimal trajectories. Properties on this set, crucial for complete optimal synthesis, are illustrated by numerical simulations. Furthermore, when the two controls have the same bound and this bound is small with respect to the difference of the two energy levels, we get a complete optimal synthesis up to a small neighborhood of the antipodal point of the initial condition.

  • 27.
    Boscain, Ugo
    et al.
    CMAP Ecole Polytech, CNRS, Palaiseau, France.;INRIA Saclay, Team GECO, Saclay, France..
    Grönberg, Fredrik
    KTH, School of Engineering Sciences (SCI), Physics, Physics of Medical Imaging. Linköping Univ, Dept Elect Engn ISY, Linkoping, Sweden..
    Long, Ruixing
    Gen Motors Canada, Oshawa, ON, Canada..
    Rabitz, Herschel
    Princeton Univ, Dept Chem, Princeton, NJ 08544 USA..
    Minimal time trajectories for two-level quantum systems with two bounded controls (vol 55, 062106, 2014)2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 8, article id 089901Article in journal (Refereed)
  • 28. Calogero, F.
    et al.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Goldfishing by gauge theory2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 8Article in journal (Refereed)
    Abstract [en]

    A new solvable many-body problem of goldfish type is identified and used to revisit the connection between two different approaches to solvable dynamical systems. An isochronous variant of this model is identified and investigated. Alternative versions of these models are presented. The behavior of the alternative isochronous model near its equilibrium configurations is investigated, and a remarkable Diophantine result, as well as related Diophantine conjectures, are thereby obtained.

  • 29.
    Cappiello, Marco
    et al.
    Universtiy of Torino, Italy.
    Schulz, René
    Leibniz Universität Hannover, Germany.
    Wahlberg, Patrik
    Linnaeus University, Faculty of Technology, Department of Mathematics.
    Conormal distributions in the Shubin calculus of pseudodifferential operators2018In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 2, article id 021502Article in journal (Refereed)
    Abstract [en]

    We characterize the Schwartz kernels of pseudodifferential operators of Shubin type by means of a Fourier-Bros-Iagolnitzer transform. Based on this, we introduce as a generalization a new class of tempered distributions called Shubin conormal distributions. We study their transformation behavior, normal forms, and microlocal properties.

  • 30.
    Carillo, Sandra
    et al.
    Sapienza Università di Roma, Rome, Italy.
    Lo Schiavo, Mauro
    Sapienza Università di Roma, Rome, Italy.
    Porten, Egmont
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Uniwersytet Jana Kochanowskiego W Kielcach, Kielce, Poland.
    Schiebold, Cornelia
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Mathematics and Science Education. Uniwersytet Jana Kochanowskiego W Kielcach, Kielce, Poland.
    A novel noncommutative KdV-type equation, its recursion operator, and solitons2018In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 59, no 4, article id 043501Article in journal (Refereed)
    Abstract [en]

    A noncommutative KdV-type equation is introduced extending the Bäcklund chart in Carillo et al. [Symmetry Integrability Geom.: Methods Appl. 12, 087 (2016)]. This equation, called meta-mKdV here, is linked by Cole-Hopf transformations to the two noncommutative versions of the mKdV equations listed in Olver and Sokolov [Commun. Math. Phys. 193, 245 (1998), Theorem 3.6]. For this meta-mKdV, and its mirror counterpart, recursion operators, hierarchies, and an explicit solution class are derived. 

  • 31.
    Carillo, Sandra
    et al.
    Univ Roma La Sapienza, Dipartimento Sci Base & Applicate Ingn, Sez Matemat, Rome, Italy .
    Schiebold, Cornelia
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Matrix Korteweg-de Vries and modified Korteweg-de Vries hierarchies: Noncommutative soliton solutions2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 5, p. Art. no. 053507-Article in journal (Refereed)
    Abstract [en]

    The present work continues work on KdV-type hierarchies presented by S. Carillo and C. Schiebold ["Noncommutative Korteweg-de Vries and modified Korteweg-de Vries hierarchies via recursion methods," J. Math. Phys. 50, 073510 (2009)]. General solution formulas for the KdV and mKdV hierarchies are derived by means of Banach space techniques both in the scalar and matrix case. A detailed analysis is given of solitons, breathers, their countable superpositions as well as of multisoliton solutions for the matrix hierarchies. (C) 2011 American Institute of Physics. [doi:10.1063/1.3576185]

  • 32.
    Carillo, Sandra
    et al.
    Universita Roma La Sapienza.
    Schiebold, Cornelia
    Mid Sweden University, Faculty of Science, Technology and Media, Department of Natural Sciences, Engineering and Mathematics.
    Noncommutative Korteweg-de Vries and modified Korteweg-de Vries hierarchies via recursion methods2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 7, article id 073510Article in journal (Refereed)
    Abstract [en]

    Here, noncommutative hierarchies of nonlinear equations are studied. They represent a generalization to the operator level of corresponding hierarchies of scalar equations, which can be obtained from the operator ones via a suitable projection. A key tool is the application of Baumlcklund transformations to relate different operator-valued hierarchies. Indeed, in the case when hierarchies in 1+1-dimensions are considered, a "Baumlcklund chart" depicts links relating, in particular, the Korteweg-de Vries (KdV) to the modified KdV (mKdV) hierarchy. Notably, analogous links connect the hierarchies of operator equations. The main result is the construction of an operator soliton solution depending on an infinite-dimensional parameter. To start with, the potential KdV hierarchy is considered. Then Baumlcklund transformations are exploited to derive solution formulas in the case of KdV and mKdV hierarchies. It is remarked that hierarchies of matrix equations, of any dimension, are also incorporated in the present framework.

  • 33. De Sole, A.
    et al.
    Hekmati, Pedram
    School of Mathematical Sciences, University of Adelaide.
    Kac, Victor G.
    Calculus structure on the Lie conformal algebra complex and the variational complex2011In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 52, no 5Article in journal (Refereed)
    Abstract [en]

    We construct a calculus structure on the Lie conformal algebra cochain complex. By restricting to degree one chains, we recover the structure of a g-complex introduced in [A. De Sole and V. G. Kac, Commun. Math. Phys. 292, 667 (2009)]. A special case of this construction is the variational calculus, for which we provide explicit formulas.

  • 34. Dejak, S. I.
    et al.
    Jonsson, B. Lars G.
    KTH, School of Electrical Engineering (EES), Electromagnetic Engineering.
    Long-time dynamics of variable coefficient modified Korteweg-de Vries solitary waves2006In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 47, no 7Article in journal (Refereed)
    Abstract [en]

    We study the long-time behavior of solutions to the Korteweg-de Vries-type equation partial derivative(t)u=-partial derivative(x)(partial derivative(2)(x)u+f(u)-b(t,x)u), with initial conditions close to a stable, b=0 solitary wave. The coefficient b is a bounded and slowly varying function, and f is a nonlinearity. For a restricted class of nonlinearities, we prove that for long time intervals, such solutions have the form of the solitary wave, whose center and scale evolve according to a certain dynamical law involving the function b(t,x), plus an H-1(R)-small fluctuation. The result is stronger than those previously obtained for general nonlinearities f.

  • 35.
    Edgar, Brian
    Linköping University, The Institute of Technology. Linköping University, Department of Mathematics, Applied Mathematics.
    Necessary and sufficient conditions for n-dimensional conformal Einstein spaces via dimensionally dependent identities2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 1Article in journal (Refereed)
    Abstract [en]

    Listing has recently extended results of Kozameh, Newman, and Tod for fourdimensional space-times and presented a set of necessary and sufficient conditions for a metric to be locally conformally equivalent to an Einstein metric in all semi-Riemannian spaces of dimension n≥4-subject to a nondegeneracy restriction on the Weyl tensor. By exploiting dimensionally dependent identities we demonstrate how to construct two alternative versions of these necessary and sufficient conditions which we believe will be useful in applications. The four-dimensional case is discussed in detail and examples are also given in five and six dimensions.

  • 36.
    Edgar, SB
    et al.
    Linköping University, Department of Mathematics. Linköping University, The Institute of Technology.
    Hoglund, A
    Dimensionally dependent tensor identities by double antisymmetrization2002In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 43, no 1, p. 659-677Article in journal (Refereed)
    Abstract [en]

    Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p greater than or equal ton. We generalize Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrizing over n+1 indices, we establish a very general "master" identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity, in particular we give direct application to Maxwell, Lanczos, Ricci, Bel, and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner. (C) 2002 American Institute of Physics.

  • 37.
    Ekholm, Tomas
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Portmann, Fabian
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    A magnetic contribution to the Hardy inequality2014In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 55, no 2, p. 022101-Article in journal (Refereed)
    Abstract [en]

    We study the quadratic form associated to the kinetic energy operator in the presence of an external magnetic field in d = 3. We show that if the radial component of the magnetic field does not vanish identically, then the classical lower bound given by Hardy is improved by a non-negative potential term depending on properties of the magnetic field.

  • 38.
    Enblom, Alexandra
    Linköping University, Department of Mathematics, Mathematics and Applied Mathematics. Linköping University, Faculty of Science & Engineering.
    Hardy-Carleman type inequalities for Dirac operators2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 10, p. 103503-Article in journal (Refereed)
    Abstract [en]

    General Hardy-Carleman type inequalities for Dirac operators are proved. New inequalities are derived involving particular traditionally used weight functions. In particular, a version of the Agmon inequality and Treve type inequalities is established. The case of a Dirac particle in a (potential) magnetic field is also considered. The methods used are direct and based on quadratic form techniques. (C) 2015 AIP Publishing LLC.

  • 39. Forger, M
    et al.
    Paufler, Cornelius
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Romer, H
    Hamiltonian multivector fields and Poisson forms in multisymplectic field theory2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 11, p. 112903-Article in journal (Refereed)
    Abstract [en]

    We present a general classification of Hamiltonian multivector fields and of Poisson forms on the extended multiphase space appearing in the geometric formulation of first order classical field theories. This is a prerequisite for computing explicit expressions for the Poisson bracket between two Poisson forms.

  • 40. Fredenhagen, Stefan
    et al.
    Hoppe, Jens
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    Hynek, Mariusz
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.).
    The Lorentz anomaly via operator product expansion2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 10, article id 102302Article in journal (Refereed)
    Abstract [en]

    The emergence of a critical dimension is one of the most striking features of string theory. One way to obtain it is by demanding closure of the Lorentz algebra in the light-cone gauge quantisation, as discovered for bosonic strings more than forty years ago. We give a detailed derivation of this classical result based on the operator product expansion on the Lorentzian world-sheet.

  • 41.
    Fuchs, Jürgen
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.
    Runkel, Ingo
    Germany.
    Schweigert, Christoph
    Germany.
    Twenty-five years of two-dimensional rational conformal field theory2010In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 51, no 1Article in journal (Refereed)
  • 42.
    Gordon, James
    et al.
    Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Uppsala University, Sweden; University of British Columbia, Canada .
    Semenoff, Gordon W.
    World-line instantons and the Schwinger effect as a Wentzel-Kramers-Brillouin exact path integral2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 2, article id 22111Article in journal (Refereed)
    Abstract [en]

    A detailed study of the semiclassical expansion of the world line path integral for a charged relativistic particle in a constant external electric field is presented. We show that the Schwinger formula for charged particle pair production is reproduced exactly by the semiclassical expansion around classical instanton solutions when the leading order of fluctuations is taken into account. We prove that all corrections to this leading approximation vanish and that the WKB approximation to the world line path integral is exact. (C) 2015 AIP Publishing LLC.

  • 43.
    Gordon, James
    et al.
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Department of Physics and Astronomy, Theoretical Physics.
    Semenoff, Gordon W.
    World-line instantons and the Schwinger effect as a Wentzel-Kramers-Brillouin exact path integral2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 2, article id 022111Article in journal (Refereed)
    Abstract [en]

    A detailed study of the semiclassical expansion of the world line path integral for a charged relativistic particle in a constant external electric field is presented. We show that the Schwinger formula for charged particle pair production is reproduced exactly by the semiclassical expansion around classical instanton solutions when the leading order of fluctuations is taken into account. We prove that all corrections to this leading approximation vanish and that the WKB approximation to the world line path integral is exact. (C) 2015 AIP Publishing LLC.

  • 44.
    Gordon, James
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Semenoff, Gordon W.
    World-line instantons and the Schwinger effect as a Wentzel-Kramers-Brillouin exact path integral2015In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 2, article id 022111Article in journal (Refereed)
    Abstract [en]

    A detailed study of the semiclassical expansion of the world line path integral for a charged relativistic particle in a constant external electric field is presented. We show that the Schwinger formula for charged particle pair production is reproduced exactly by the semiclassical expansion around classical instanton solutions when the leading order of fluctuations is taken into account. We prove that all corrections to this leading approximation vanish and that the WKB approximation to the world line path integral is exact.

  • 45. Guarnieri, F.
    et al.
    Moon, Woosok
    Stockholm University, Faculty of Science, Department of Mathematics. Stockholm University, Nordic Institute for Theoretical Physics (Nordita). British Antarctic Survey, United Kingdom.
    Wettlaufer, J. S.
    Solution of the Fokker-Planck equation with a logarithmic potential and mixed eigenvalue spectrum2017In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 58, no 9, article id 093301Article in journal (Refereed)
    Abstract [en]

    Motivated by a problem in climate dynamics, we investigate the solution of a Bessel-like process with a negative constant drift, described by a Fokker-Planck equation with a potential V(x) = -[b ln(x) + a x], for b > 0 and a < 0. The problem belongs to a family of Fokker-Planck equations with logarithmic potentials closely related to the Bessel process that has been extensively studied for its applications in physics, biology, and finance. The Bessel-like process we consider can be solved by seeking solutions through an expansion into a complete set of eigenfunctions. The associated imaginary-time Schrodinger equation exhibits a mix of discrete and continuous eigenvalue spectra, corresponding to the quantum Coulomb potential describing the bound states of the hydrogen atom. We present a technique to evaluate the normalization factor of the continuous spectrum of eigenfunctions that relies solely upon their asymptotic behavior. We demonstrate the technique by solving the Brownian motion problem and the Bessel process both with a constant negative drift. We conclude with a comparison to other analytical methods and with numerical solutions.

  • 46.
    Hallnäs, Martin
    et al.
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Langmann, Edwin
    KTH, School of Engineering Sciences (SCI), Theoretical Physics, Mathematical Physics.
    Exact solutions of two complementary one-dimensional quantum many-body systems on the half-line2005In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 46, no 5Article in journal (Refereed)
    Abstract [en]

    We consider two particular one-dimensional quantum many-body systems with local interactions related to the root system C-N. Both models describe identical particles moving on the half-line with nontrivial boundary conditions at the origin, but in the first model the particles interact with the delta interaction while in the second via a particular momentum dependent interaction commonly known as delta-prime interaction. We show that the Bethe ansatz solution of the delta-interaction model is consistent even for the general case where the particles are distinguishable, whereas for the delta-prime interaction it only is consistent and nontrivial in the fermion case. We also establish a duality between the bosonic delta- and the fermionic delta-prime model, and we elaborate on the physical interpretations of these models.

  • 47.
    Hoppe, Jens
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Lundholm, Douglas
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Trzetrzelewski, Maciej
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
    Spin(9) average of SU(N) matrix models2009In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 50, no 4, p. 043510-1-043510-7Article in journal (Refereed)
    Abstract [en]

    We apply a method of group averaging to states and operators appearing in (truncations of) the Spin(9)xSU(N) invariant matrix models. We find that there is an exact correspondence between the standard supersymmetric Hamiltonian and the Spin (9) average of a relatively simple lower-dimensional model.

  • 48.
    Ibragimov, Nail
    et al.
    Blekinge Institute of Technology, Faculty of Engineering, Department of Mathematics and Natural Sciences.
    Gandarias, M.L.
    Galiakberova, L.R.
    Bruzon, M.S.
    Avdonina, E.D.
    Group classification and conservation laws of anisotropic wave equations with a source2016In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 57, no 8, article id 083504Article in journal (Refereed)
    Abstract [en]

    Linear and nonlinear waves in anisotropic media are useful in investigating complex materials in physics, biomechanics, biomedical acoustics, etc. The present paper is devoted to investigation of symmetries and conservation laws for nonlinear anisotropic wave equations with specific external sources when the equations in question are nonlinearly self-adjoint. These equations involve two arbitrary functions. Construction of conservation laws associated with symmetries is based on the generalized conservation theorem for nonlinearly self-adjoint partial differential equations. First we calculate the conservation laws for the basic equation without any restrictions on the arbitrary functions. Then we make the group classification of the basic equation in order to specify all possible values of the arbitrary functions when the equation has additional symmetries and construct the additional conservation laws.

  • 49.
    Ibragimov, Nail H.
    et al.
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Khamitova, Raisa
    Blekinge Institute of Technology, School of Engineering, Department of Mathematics and Science.
    Thidé, Bo
    Conservation laws for the Maxwell-Dirac equations with dual Ohm's law2007In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, no 5Article in journal (Refereed)
    Abstract [en]

    Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov [J. Math. Anal. Appl. 333, 311-320 (2007)], we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and magnetic charges obey linear conductivity laws (dual Ohm's law). We find that this linear system allows for conservation laws which are nonlocal in time. (c) 2007 American Institute of Physics.

  • 50. Ibragimov, Nail H.
    et al.
    Khamitova, Raisa
    Thidé, Bo
    Uppsala University, Disciplinary Domain of Science and Technology, Physics, Swedish Institute of Space Physics, Uppsala Division.
    Conservation laws for the Maxwell-Dirac equations with dual Ohm's law2007In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 48, no 5, p. 053523-Article in journal (Refereed)
    Abstract [en]

    Using a general theorem on conservation laws for arbitrary differential equations proved by Ibragimov [J. Math. Anal. Appl. 333, 311-320 (2007)], we have derived conservation laws for Dirac's symmetrized Maxwell-Lorentz equations under the assumption that both the electric and magnetic charges obey linear conductivity laws (dual Ohm's law). We find that this linear system allows for conservation laws which are nonlocal in time.

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