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  • 1.
    Berggren, Karl-Fredrik
    et al.
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics . Linköping University, The Institute of Technology.
    Maksimov, Dmitrii N.
    L.V. Kirensky Institute of Physics.
    Sadreev, Almas F.
    Linköping University, Department of Physics, Chemistry and Biology. Linköping University, The Institute of Technology.
    Höhmann, Ruven
    AG Quantenchaos.
    Kuhl, Ulrich
    AG Quantenchaos.
    Stöckmann, Hans-Jürgen
    AG Quantenchaos.
    Quantum stress in chaotic billiards2008In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 77, no 066209Article in journal (Refereed)
    Abstract [en]

    This paper reports on a joint theoretical and experimental study of the Pauli quantum-mechanical stress tensor T(x,y) for open two-dimensional chaotic billiards. In the case of a finite current flow through the system the interior wave function is expressed as =u+iv. With the assumption that u and v are Gaussian random fields we derive analytic expressions for the statistical distributions for the quantum stress tensor components T. The Gaussian random field model is tested for a Sinai billiard with two opposite leads by analyzing the scattering wave functions obtained numerically from the corresponding Schrödinger equation. Two-dimensional quantum billiards may be emulated from planar microwave analogs. Hence we report on microwave measurements for an open two-dimensional cavity and how the quantum stress tensor analog is extracted from the recorded electric field. The agreement with the theoretical predictions for the distributions for T(x,y) is quite satisfactory for small net currents. However, a distinct difference between experiments and theory is observed at higher net flow, which could be explained using a Gaussian random field, where the net current was taken into account by an additional plane wave with a preferential direction and amplitude.

  • 2.
    Berggren, Karl-Fredrik
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics .
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Starikov, Anton
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Crossover from regular to irregular behavior in current flow through open billiards2002In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 66, no 1Article in journal (Refereed)
    Abstract [en]

    We discuss signatures of quantum chaos in terms of distributions of nodal points, saddle points, and streamlines for coherent electron transport through two-dimensional billiards, which are either nominally integrable or chaotic. As typical examples of the two cases we select rectangular and Sinai billiards. We have numerically evaluted distribution functions for nearest distances between nodal points and found that there is a generic form for open chaotic billiards through which a net current is passed. We have also evaluated the distribution functions for nodal points with specific vorticity (winding number) as well as for saddle points. The distributions may be used as signatures of quantum chaos in open systems. All distributions are well reproduced using random complex linear combinations of nearly monochromatic states in nominally closed billiards. In the case of rectangular billiards with simple sharp-cornered leads the distributions have characteristic features related to order among the nodal points. A flaring or rounding of the contact regions may, however, induce a crossover to nodal point distributions and current flow typical for quantum chaos. For an irregular arrangement of nodal points, as for example in the Sinai billiard, the quantum flow lines become very complex and volatile, recalling chaos among classical trajectories. Similarities with percolation are pointed out. ©2002 The American Physical Society.

  • 3. Bulgakov, EN
    et al.
    Exner, P
    Pichugin, KN
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Multiple bound states in scissor-shaped waveguides2002In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 66, no 15Article in journal (Refereed)
    Abstract [en]

    We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle theta. Such a four-terminal junction with a tunable theta can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for theta=90degrees there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of theta in the interval (0,90degrees). Moreover, states which are sufficiently strongly bound exist in pairs with a small energy difference and opposite parities. Finally, we discuss how the bound states transform with increasing theta into quasibound states with a complex wave vector.

  • 4.
    Bulgakov, E.N.
    et al.
    Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation, Astaf'Ev Pedagogical University, 89, Krasnoyarsk, 660049 Lebedeva, Russian Federation.
    Maksimov, D.N.
    Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Electric circuit networks equivalent to chaotic quantum billiards2005In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 71, no 4Article in journal (Refereed)
    Abstract [en]

    We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics. © 2005 The American Physical Society.

  • 5.
    Bulgakov, E.N.
    et al.
    Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany, Kirensky Institute of Physics, 660036 Krasnoyarsk, Russian Federation.
    Rotter, I.
    Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Phase rigidity and avoided level crossings in the complex energy plane2006In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 74, no 5Article in journal (Refereed)
    Abstract [en]

    We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions ?, and define the value r? = (?/?) ?/? that characterizes the phase rigidity of the eigenfunctions ?. In the scenario with avoided level crossings, r? varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of r? is an internal property of an open quantum system. In the literature, the phase rigidity ? of the scattering wave function ?CE is considered. Since ?CE can be represented in the interior of the system by the ?, the phase rigidity ? of the ?CE is related to the r? and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity ? to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant at energies that are determined by the real part of the eigenvalues of the effective Hamiltonian. We illustrate the relation between phase rigidity ? and transmission numerically for small open cavities. © 2006 The American Physical Society.

  • 6.
    Bulgakov, E.N.
    et al.
    Kirensky Institute of Physics-, 660036, Krasnoyarsk, Russian Federation.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Rectangular microwave resonators with magnetic anisotropy. Mapping onto pseudointegrable rhombus2002In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 57, no 2, p. 198-204Article in journal (Refereed)
    Abstract [en]

    A rectangular microwave resonator filled with ferrite with uniaxial magnetic anisotropy is considered. It is shown that this task can be reduced to an empty rhombus resonator with the vertex angle defined by an external magnetic field, provided that the magnetic anisotropy of the ferrite is strong. Therefore, the statistics of eigenfrequencies for TM modes is described by the Brody or semi-Poisson distribution with some exceptional cases.

  • 7.
    Bulgakov, E.N.
    et al.
    Institute of Physics, Russian Academy of Sciences, Krasnoyarsk, 660036, Russian Federation.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Spin polarization in quantum dots by radiation field with circular polarization2001In: JETP Letters: Journal of Experimental And Theoretical Physics Letters, ISSN 0021-3640, E-ISSN 1090-6487, Vol. 73, no 10, p. 505-509Article in journal (Refereed)
    Abstract [en]

    For circular quantum dot (QD), taking into account the Razhba spin-orbit interaction (SOI), an exact energy spectrum is obtained. For a small SOI constant, the eigenfunctions of the QD are found. It is shown that the application of a radiation field with circular polarization removes the Kramers degeneracy of the QD eigenstates. Effective spin polarization of electrons transmitted through the QD owing to a radiation field with circular polarization is demonstrated. © 2001 MAIK "Nauka/Interperiodica".

  • 8. Bulgakov, EN
    et al.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Spin rotation for ballistic electron transmission induced by spin-orbit interaction2002In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 66, no 7Article in journal (Refereed)
    Abstract [en]

    We study spin-dependent electron transmission through one- and two-dimensional curved waveguides and quantum dots with account of spin-orbit interaction. We prove that for a transmission through an arbitrary structure there is no spin polarization provided the electron transmits in an isolated energy subband and only two leads are attached to the structure. In particular there is no spin polarization in the one-dimensional wire, for which a spin-dependent solution is found analytically. The solution demonstrates the spin evolution as dependent on a length of wire. The numerical solution for transmission of electrons through the two-dimensional curved waveguides coincides with the solution for the one-dimensional wire if the energy of electron is within the first energy subband. In the vicinity of edges of the energy subbands there are sharp anomalies of spin flipping.

  • 9.
    Bulgakov, E.N.
    et al.
    Kirensky Institute of Physics, 660036, Krasnoyarsk, Russian Federation, Astaf'ev Krasnoyarsk Pedagogical U., 660049, Lebedeva, 89, Russian Federation.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Statistics of wave functions and currents induced by spin-orbit interaction in chaotic billiards2004In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 70, no 5 2Article in journal (Refereed)
    Abstract [en]

    The statistics of wave functions and currents induced by spin-orbit interaction (SOI) in chaotic billiards were investigated. It was observed that for small constant the current statistics was described by universal current distributions derived for slightly opened chaotic billiards. It was also observed that for SOI both components of the spinor eigenstate were complex random Gaussian fields. It was found that for intermediate values of the statistics of the eigenstates and currents, both were deeply nonuniversal.

  • 10.
    Bulgakov, E.N.
    et al.
    Institute of Physics, Siberian Division, Russian Academy of Sciences, Krasnoyarsk, 660036, Russian Federation.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    The effect of bound states in microwave waveguides on electromagnetic wave propagation2001In: Technical physics, ISSN 1063-7842, E-ISSN 1090-6525, Vol. 46, no 10, p. 1281-1290Article in journal (Refereed)
    Abstract [en]

    The transmission of a TE microwave field with a frequency ? through G, T, and X waveguide junctions filled with a ferromagnetic is considered. These junctions are known to have bound states with below-cut-off frequencies. A probing microwave radiation with a frequency O applied to the scattering region generates magnetic oscillations with frequencies ? + nO (where n = 0, ±1, ±2, ...), which resonantly combine with the bound waveguide states. This effect provides for a new method of studying bound waveguide states and efficiently controlling the transmission of microwave radiation. © 2001 MAIK "Nauka/Interperiodica".

  • 11. Bulgakov, EN
    et al.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Vortex phase diagram of F=1 spinor Bose-Einstein condensates2003In: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 90, no 20Article in journal (Refereed)
    Abstract [en]

    We have calculated the F=1 ground state of a spinor Bose-Einstein condensate trapped harmonic potential with an applied Ioffe-Pitchard magnetic field. The vortex phase diagram is found in the plane spanned by perpendicular and longitudinal magnetic fields. The ferromagnetic condensate has two vortex phases which differ by winding number in the spinor components. The two vortices for the F-z=-1 antiferromagnetic condensate are separated in space. Moreover, we considered an average local spin \[(S) over right arrow]\ to testify to what extent it is parallel to magnetic field (the nonadiabatic effects). We have shown that the effects are important at vortex cores.

  • 12.
    Ishio, H
    et al.
    Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England Nizhny Novgorod State Univ, Dept Radiophys, Nizhnii Novgorod 603600, Russia LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia.
    Saichev, AI
    Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden Univ Bristol, Sch Math, Bristol BS8 1TW, Avon, England Nizhny Novgorod State Univ, Dept Radiophys, Nizhnii Novgorod 603600, Russia LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Berggren, Karl-Fredrik
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics .
    Wave function statistics for ballistic quantum transport through chaotic open billiards: Statistical crossover and coexistence of regular and chaotic waves2001In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 64, no 5, p. art. no.-056208Article in journal (Refereed)
    Abstract [en]

    For ballistic transport through chaotic open billiards, we implement accurate fully quantal calculations of the probability distributions and spatial correlations of the local densities of single-electron wave functions within the cavity. We find wave-statistical behaviors intrinsically different from those in their closed counterparts. Chaotic-scattering wave functions in open systems can be quantitatively interpreted in terms of statistically independent real and imaginary random fields in the same way as for wave-function statistics of closed systems in the time-reversal symmetry-breaking crossover regime. We also discuss perceived statistical deviations, which are attributed to the coexistence of regular and chaotic waves and given analytical explanations.

  • 13. Ishio, H.
    et al.
    Saichev, A.I.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Berggren, Karl-Fredrik
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics .
    Wave function statistics for mesoscopic transport through chaotic open billiards: Time reversibility, space reciprocity breaking and statistical crossover2001In: Computer Physics Communications, ISSN 0010-4655, E-ISSN 1879-2944, Vol. 142, no 1-3, p. 64-70Conference paper (Other academic)
    Abstract [en]

    We investigate the probability distributions and spatial correlations of the local densities of electron wave functions for ballistic transport through mesoscopic chaotic open billiards. By quantitative comparison between our accurate fully-quantal calculations with theoretical expressions, we find wave-statistical behaviors intrinsically different from those in closed systems. It is shown that chaotic-scattering wave functions in open systems can be universally interpreted in terms of statistically independent real and imaginary random fields together with breaking of the endowed space reciprocity, resulting in the same wave function statistics as in the time-reversal symmetry-breaking crossover regime in closed systems. © 2001 Elsevier Science B.V. All rights reserved.

  • 14. Maksimov, Dmitrii N.
    et al.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Bound states in elastic waveguides2006In: PHYSICAL REVIEW E, ISSN 1539-3755, Vol. 74, no 1Article in journal (Refereed)
    Abstract [en]

    We consider numerically the L-, T-, and X-shaped elastic waveguides with the Dirichlet boundary conditions for in-plane deformations (displacements) which obey the vectorial Navier-Cauchy equation. In the X-shaped waveguide we show the existence of a doubly degenerate bound state with frequency below the first symmetrical cutoff frequency, which belongs to the two-dimensional irreducible representation E of symmetry group C-4v. Moreover the next bound state is below the next antisymmetric cutoff frequency. This bound state belongs to the irreducible representation A(2). The T-shaped waveguide has only one bound state while the L-shaped one has no bound states.

  • 15.
    Maksimov, D.N.
    et al.
    Institute of Physics, Russian Academy of Sciences, Krasnoyarsk, 660036, Russian Federation.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Gaussian random waves in elastic media2007In: JETP Letters: Journal of Experimental And Theoretical Physics Letters, ISSN 0021-3640, E-ISSN 1090-6487, Vol. 86, no 9, p. 584-588Article in journal (Refereed)
    Abstract [en]

    Similar to the Berry conjecture of quantum chaos, an elastic analogue which incorporates longitudinal and transverse elastic displacements with corresponding wave vectors is considered. The correlation functions are derived for the amplitudes and intensities of elastic displacements. A comparison to the numerics in a quarter-Bunimovich stadium demonstrates excellent agreement. © 2007 Pleiades Publishing, Ltd.

  • 16.
    Maksimov, D.N.
    et al.
    L.V. Kirensky Institute of Physics, 660036, Krasnoyarsk, Russian Federation.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Phase correlation function of complex random Gaussian fields2007In: Europhysics letters, ISSN 0295-5075, E-ISSN 1286-4854, Vol. 80, no 5Article in journal (Refereed)
    Abstract [en]

    The phase correlation function for the complex random Gaussian field (x)=(x)exp[i(x)] is derived. It is compared to the numerical scattering wave function in the open Sinai billiard. © Europhysics Letters Association.

  • 17.
    Rotter, I.
    et al.
    Max-Planck-Inst. Physik Komplexer S., D-01187 Dresden, Germany.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Avoided level crossings, diabolic points, and branch points in the complex plane in an open double quantum dot2005In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 71, no 3Article in journal (Refereed)
    Abstract [en]

    We study the spectrum of an open double quantum dot as a function of different system parameters in order to receive information on the geometric phases of branch points in the complex plane (BPCP). We relate them to the geometrical phases of the diabolic points (DPs) of the corresponding closed system. The double dot consists of two single dots and a wire connecting them. The two dots and the wire are represented by only a single state each. The spectroscopic values follow from the eigenvalues and eigenfunctions of the Hamiltonian describing the double dot system. They are real when the system is closed, and complex when the system is opened by attaching leads to it. The discrete states as well as the narrow resonance states avoid crossing. The DPs are points within the avoided level crossing scenario of discrete states. At the BPCP, width bifurcation occurs. Here, different Riemann sheets evolve and the levels do not cross anymore. The BPCP are physically meaningful. The DPs are unfolded into two BPCP with different chirality when the system is opened. The geometric phase that arises by encircling the DP in the real plane, is different from the phase that appears by encircling the BPCP. This is found to be true even for a weakly opened system and the two BPCP into which the DP is unfolded. ©2005 The American Physical Society.

  • 18.
    Rotter, I.
    et al.
    Max-Planck-Inst. Phys. Komplexer S., D-01187 Dresden, Germany.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Influence of branch points in the complex plane on the transmission through double quantum dots2004In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 69, no 6 2Article in journal (Refereed)
    Abstract [en]

    The behavior of a simple model was considered that reflected many characteristic features of realistic double quantum dots (QD) with more complicated structure. The system was described in the framework of the S matrix theory by the effective Hamiltonian of the open quantum system. It consisted of the Hamiltonian of the closed system and a term that accounts for the coupling of the states via the continuum of propagating modes in the leads. The results show that the branch points influence strongly the features of transmission through double quantum dots.

  • 19.
    Rotter, I.
    et al.
    Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Singularities caused by coalesced complex eigenvalues of an effective Hamilton operator2007In: International journal of theoretical physics, ISSN 0020-7748, E-ISSN 1572-9575, Vol. 46, no 8, p. 1914-1928Article in journal (Refereed)
    Abstract [en]

    The S matrix theory with use of the effective Hamiltonian is sketched and applied to the description of the transmission through double quantum dots. The effective Hamilton operator is non-hermitian, its eigenvalues are complex, the eigenfunctions are bi-orthogonal. In this theory, singularities occur at points where two (or more) eigenvalues of the effective Hamiltonian coalesce. These points are physically meaningful: they separate the scenario of avoided level crossings from that without any crossings in the complex plane. They are branch points in the complex plane. Their geometrical features are different from those of the diabolic points. © 2007 Springer Science+Business Media, LLC.

  • 20.
    Rotter, I.
    et al.
    Max-Planck-Inst. Phys. Komplexer S., D-01187 Dresden, Germany.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Zeros in single-channel transmission through double quantum dots2005In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 71, no 4Article in journal (Refereed)
    Abstract [en]

    By using a simple model we consider single-channel transmission through a double quantum dot that consists of two single dots coupled by a wire of finite length L. Each of the two single dots is characterized by a few energy levels only, and the wire is assumed to have only one level whose energy depends on the length L. The transmission is described by using 5 matrix theory and the effective non-Hermitian Hamilton operator Heff of the system. The decay widths of the eigenstates of Heff depend strongly on energy. The model explains the origin of the transmission zeros of the double dot that is considered by us. Mostly, they are caused by (destructive) interferences between neighboring levels and are of first order. When, however, both single dots are identical and their transmission zeros are of first order, those of the double dot are of second order. First-order transmission zeros cause phase jumps of the transmission amplitude by p, while there are no phase jumps related to second-order transmission zeros. In this latter case, a phase jump occurs due to the fact that the width of one of the states vanishes when crossing the energy of the transmission zero. The parameter dependence of the widths of the resonance states is determined by the spectral properties of the two single dots. ©2005 The American Physical Society.

  • 21.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Current statistics for transport through rectangular and circular billiards2004In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, ISSN 1539-3755, Vol. 70, no 1 2Article in journal (Refereed)
    Abstract [en]

    The statistics of currents for electron transmission through rectangular and circular billiards was discussed. The statistics was based on fact that the scattering function described a complex Gaussian random field?=u+iv with the correlation dependent on the conductance and measure of the openness of the billiard. For nonresonant transmission the current statistics reveals features of the current channeling interior of the billiard. It was observed that scattering function interior of the billiard could be superposed of the eigenfunctions of the billiard although the coefficients of superposition are not random.

  • 22.
    Sadreev, Almas
    et al.
    Linköping University, Department of Physics, Chemistry and Biology.
    Berggren, Karl-Fredrik
    Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics . Linköping University, The Institute of Technology.
    Current statistics for wave transmission through an open Sinai billiard: Effects of net currents2004In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 70, no 2Article in journal (Refereed)
    Abstract [en]

    Transport through quantum and microwave cavities is studied by analytic and numerical techniques. In particular, we consider the statistics for a finite net probability current (Poynting vector) flowing through an open ballistic Sinai billiard to which two opposite leads/wave guides are attached. We show that if the net probability current is small, the scattering wave function inside the billiard is well approximated by a Gaussian random complex field. In this case, the current statistics are universal and obey simple analytic forms. For larger net currents, these forms still apply over several orders of magnitudes. However, small characteristic deviations appear in the tail regions. Although the focus is on electron and microwave billiards, the analysis is relevant also to other classical wave cavities as, for example, open planar acoustic reverberation rooms, elastic membranes, and water surface waves in irregularly shaped vessels.

  • 23.
    Sadreev, Almas
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Bulgakov, E.N.
    Kirensky Institute of Physics, Krasnoyarsk, 660036, Russian Federation.
    Rotter, I.
    Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany.
    S-matrix formalism of transmission through two quantum billiards coupled by a waveguide2005In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 38, no 49, p. 10647-10661Article in journal (Refereed)
    Abstract [en]

    We consider a system that consists of two single-quantum billiards (QBs) coupled by a waveguide and study the transmission through this system as a function of length and width of the waveguide. To interpret the numerical results for the transmission, we explore a simple model with a small number of states which allows us to consider the problem analytically. The transmission is described in the S-matrix formalism by using the non-Hermitian effective Hamilton operator for the open system. The coupling of the single QBs to the internal waveguide characterizes the 'internal' coupling strength u of the states of the system while that of the system as a whole to the attached leads determines the 'external' coupling strength v of the resonance states via the continuum (waves in the leads). The transmission is resonant for all values of v/u in relation to the effective Hamiltonian. It depends strongly on the ratio v/u via the eigenvalues and eigenfunctions of the effective Hamiltonian. The results obtained are compared qualitatively with those from simulation calculations for larger systems. Most interesting is the existence of resonance states with vanishing widths that may appear at all values of v/u. They cause zeros in the transmission through the double QB due to trapping of the particle in the waveguide. © 2005 IOP Publishing Ltd.

  • 24.
    Sadreev, Almas
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Bulgakov, E.N.
    Institute of Physics, Russian Academy of Sciences, Krasnoyarsk, 660036, Russian Federation.
    Rotter, I.
    Max-Planck-Institut für Physik Komplexer Systeme, D-01187 Dresden, Germany.
    Trapping of an electron in the transmission through two quantum dots coupled by a wire2005In: JETP Letters: Journal of Experimental And Theoretical Physics Letters, ISSN 0021-3640, E-ISSN 1090-6487, Vol. 82, no 8, p. 498-503Article in journal (Refereed)
    Abstract [en]

    We consider single-channel transmission through a double quantum dot that consists of two identical single dots coupled by a wire. The numerical solution for the scattering wave function shows that the resonance width of a few of the states may vanish when the width (or length) of the wire and the energy of the incident particle each take a certain value. In such a case, a particle is trapped inside the wire as the numerical visualization of the scattering wave function shows. To understand these numerical results, we explore a simple model with a small number of states, which allows us to consider the problem analytically. If the eigenenergies of the closed system cross the energies of the transmission zeroes, the wire effectively decouples from the rest of the system and traps the particle. © 2005 Pleiades Publishing, Inc.

  • 25.
    Sadreev, Almas
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Davlet-Kildeev, K.
    Institute of Physics, Academy of Sciences, 660036 Krasnoyarsk, Russian Federation.
    Electron transmission through an ac biased quantum point contact2007In: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 75, no 23Article in journal (Refereed)
    Abstract [en]

    We consider a transmission through the potential relief created by a split gate constriction (quantum point contact). Simultaneously, dc and ac voltages Vup (t) = V0 + V1 cos ?t and Vdw (t) = V0 + V1 cos (?t+?) are applied to the gates. We show numerically that the in-phase ac voltages (?=0) smear the conductance steps of the stationary conductance, while the antiphase ac voltages (?=p) only shift the conductance steps. Moreover, computation of currents in probing wires connected cross to the time-periodic quantum point contact reveals a net current for ? 0,p. This implies that the Schrödinger equation described by the electron transport under the effect of the time-periodic long electrodes is equivalent to the transmission in the crossed effective magnetic and electric fields, where the in-plane magnetic field b~? is directed along the transport axis and the electric field e~? is directed perpendicular to the plane of electron transport. Then the vector e×b gives rise to the galvanomagnetic current directed cross to the electron transport. © 2007 The American Physical Society.

  • 26.
    Sadreev, Almas
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Rotter, I.
    Max-Planck-Inst. Phys. Komplexer S., D-01187 Dresden, Germany.
    S-matrix theory for transmission through billiards in tight-binding approach2003In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 36, no 45, p. 11413-11433Article in journal (Refereed)
    Abstract [en]

    In the tight-binding approximation we consider multi-channel transmission through a billiard coupled to leads. Following Dittos we derive the coupling matrix, the scattering matrix and the effective Hamiltonian, but take into account the energy restriction of the conductance band. The complex eigenvalues of the effective Hamiltonian define the poles of the scattering matrix. For some simple cases, we present exact values for the poles. We derive also the condition for the appearance of double poles.

  • 27.
    Sadreev, Almas
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Sukhinin, Y.V.
    Uvdal, Kajsa
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Sensor Science and Molecular Physics .
    Pohl, A.
    Thermal reduction of activation energy of tricyclohexylphosphine on a rhodium crystal surface2001In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 115, no 20, p. 9513-9518Article in journal (Refereed)
    Abstract [en]

    The activation energy of desorption for TCHP adsorbed on Rh(111) was calculated. Thermal atomic displacements of a semi-infinite metal of the crystal and effects of molecular rotation modes were included in the calculation. The potential versus the molecular distance to the Rh surface was taken as the Morse potential but with parameters fitted to the DFT calculations. The resulting data was analyzed in detail.

  • 28. Saichev, A.I.
    et al.
    Ishio, H.
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Berggren, Karl-Fredrik
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics .
    Statistics of interior current distributions in two-dimensional open chaotic billiards2002In: Journal of Physics A: Mathematical and General, ISSN 0305-4470, E-ISSN 1361-6447, Vol. 35, no 7Article in journal (Refereed)
    Abstract [en]

    The probability current statistics of two-dimensional open chaotic ballistic billiards is studied both analytically and numerically. Assuming that the real and imaginary parts of the scattering wave function are both random Gaussian fields, we find a universal distribution function for the interior probability current. As a by-product we recover previous analytic forms for wave function statistics. The expressions bridge the entire region from GOE to GUE type statistics. Our analytic expressions are verified numerically by explicit quantum mechanical calculations of transport through a Bunimovich billiard.

  • 29.
    Saichev, AL
    et al.
    Nizhny Novgorod Univ, Dept Radiophys, Nizhnii Novgorod 603600, Russia Linkoping Univ, Dept Phys & Measurement Technol, S-58183 Linkoping, Sweden LV Kirenskii Inst Phys, Krasnoyarsk 660036, Russia.
    Berggren, Karl-Fredrik
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Theoretical Physics .
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology.
    Distribution of nearest distances between nodal points for the Berry function in two dimensions2001In: Physical Review E. Statistical, Nonlinear, and Soft Matter Physics: Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, ISSN 1063-651X, E-ISSN 1095-3787, Vol. 64, no 3Article in journal (Refereed)
    Abstract [en]

    According to Berry a wave-chaotic state may be viewed as a superposition of monochromatic plane waves with random phases and amplitudes. Here we consider the distribution of nodal points associated with this state. Using the property that both the real and imaginary parts of the wave function are random Gaussian fields we analyze the correlation function and densities of the nodal points. Using two approaches (the Poisson and Bernoulli) we derive the distribution of nearest neighbor separations. Furthermore the distribution functions for nodal points with specific chirality are found. Comparison is made with results from numerical calculations for the Berry wave function.

  • 30.
    Uvdal, Kajsa
    et al.
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Sensor Science and Molecular Physics .
    Sadreev, Almas
    Linköping University, The Institute of Technology. Linköping University, Department of Physics, Chemistry and Biology, Sensor Science and Molecular Physics .
    Sukhinin, Y
    Thermoactivated desorption of Tricyclohexylphosphine from rhodium2001In: Journal of Chemical Physics, ISSN 0021-9606, E-ISSN 1089-7690, Vol. 115, p. 9513-9519Article in journal (Refereed)
1 - 30 of 30
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