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Interacting fermions and non-equilibrium properties of one-dimensional many-body systems
KTH, School of Engineering Sciences (SCI), Theoretical Physics.ORCID iD: 0000-0003-0011-2937
2016 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Recent experimental progress on ultracold atomic gases have opened up the possibility to simulate many-body systems out of equilibrium. We consider such a system described by the Luttinger model, which is a model of interacting fermions in one spatial dimension.

It is well known that the Luttinger model is exactly solvable using bosonization. This also remains true for certain extensions of the model, e.g., where, in addition, the fermions are coupled to phonons. We give a self-contained account of bosonization, together with complete proofs, and show how this can be used to solve the Luttinger model and the above fermion-phonon model rigorously.

The main focus is on non-equilibrium properties of the Luttinger model. We use the exact solution of the Luttinger model, with non-local interactions, to study the evolution starting from a non-uniform initial state with a position-dependent chemical potential. The system is shown to reach a current-carrying final steady state, in which the universal value of the electrical conductance, known from near-to-equilibrium settings, is recovered. We also study the effects of suddenly changing the interactions and show that the final state has memory of the initial state, which is, e.g., manifested by non- equilibrium exponents in its fermion two-point correlation functions.

Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2016. , 35 p.
Series
TRITA-FYS, ISSN 0280-316X ; 2016:59
National Category
Physical Sciences
Research subject
Physics
Identifiers
URN: urn:nbn:se:kth:diva-193330ISBN: 978-91-7729-089-6 (print)OAI: oai:DiVA.org:kth-193330DiVA: diva2:1010079
Presentation
2016-10-25, sal FB42, AlbaNova, Kungl. Tekniska högskolan, Stockholm, 15:00
Opponent
Supervisors
Note

QC 20161003

Available from: 2016-10-03 Created: 2016-09-30 Last updated: 2016-10-06Bibliographically approved
List of papers
1. Construction by bosonization of a fermion-phonon model
Open this publication in new window or tab >>Construction by bosonization of a fermion-phonon model
2015 (English)In: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 56, no 9, 091902Article in journal (Refereed) Published
Abstract [en]

We discuss an extension of the (massless) Thirring model describing interacting fermions in one dimension which are coupled to phonons and where all interactions are local. This fermion-phonon model can be solved exactly by bosonization.We present a construction and solution of this model which is mathematically rigorous by treating it as a continuum limit of a Luttinger-phonon model. A self-contained account of the mathematical results underlying bosonization is included, together with complete proofs.

National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-175654 (URN)10.1063/1.4930299 (DOI)000362569200020 ()2-s2.0-84941912006 (Scopus ID)
Note

QC 20151023

Available from: 2015-10-23 Created: 2015-10-19 Last updated: 2017-12-01Bibliographically approved
2. Steady states and universal conductance in a quenched Luttinger model
Open this publication in new window or tab >>Steady states and universal conductance in a quenched Luttinger model
2016 (English)In: Communications in Mathematical Physics, ISSN 0010-3616, E-ISSN 1432-0916, 1-32 p.Article in journal (Refereed) Epub ahead of print
Abstract [en]

We obtain exact analytical results for the evolution of a 1+1-dimensional Luttinger model prepared in a domain wall initial state, i.e., a state with different densities on its left and right sides. Such an initial state is modeled as the ground state of a translation invariant Luttinger Hamiltonian (Formula presented.) with short range non-local interaction and different chemical potentials to the left and right of the origin. The system evolves for time t > 0 via a Hamiltonian (Formula presented.) which differs from (Formula presented.) by the strength of the interaction. Asymptotically in time, as (Formula presented.), after taking the thermodynamic limit, the system approaches a translation invariant steady state. This final steady state carries a current I and has an effective chemical potential difference (Formula presented.) between right- (+) and left- (−) moving fermions obtained from the two-point correlation function. Both I and (Formula presented.) depend on (Formula presented.) and (Formula presented.). Only for the case (Formula presented.) does (Formula presented.) equal the difference in the initial left and right chemical potentials. Nevertheless, the Landauer conductance for the final state, (Formula presented.), has a universal value equal to the conductance quantum (Formula presented.) for the spinless case.

Place, publisher, year, edition, pages
Springer-Verlag New York, 2016
National Category
Physical Sciences
Identifiers
urn:nbn:se:kth:diva-193328 (URN)10.1007/s00220-016-2631-x (DOI)000393599800005 ()2-s2.0-84969822488 (Scopus ID)
Note

QC 20161003

Available from: 2016-09-30 Created: 2016-09-30 Last updated: 2017-11-30Bibliographically approved

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