Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2211.08330 · Journal of Physics A Mathematical and Theoretical

On Landauer–Büttiker formalism from a quantum quench

Oleksandr Gamayun, Yu Zhuravlev, N. Z. Iorgov

Published Apr 5, 2023• 7 citations
arXivHTMLPDF

Abstract

Abstract We study transport in the free fermionic one-dimensional systems subjected to arbitrary local potentials. The bias needed for the transport is modeled by the initial highly non-equilibrium distribution where only half of the system is populated. Additionally to that, the local potential is also suddenly changed when the transport starts. For such a quench protocol we compute the full counting statistics (FCS) of the number of particles in the initially empty part. In the thermodynamic limit, the FCS can be expressed via the Fredholm determinant with the kernel depending on the scattering data and Jost solutions of the pre-quench and the post-quench potentials. We discuss the large-time asymptotic behavior of the obtained determinant and observe that if two or more bound states are present in the spectrum of the post-quench potential the information about the initial state manifests itself in the persistent oscillations of the FCS. On the contrary, when there are no bound states the asymptotic behavior of the FCS is determined solely by the scattering data of the post-quench potential, which for the current (the first moment) is given by the Landauer–Büttiker formalism. The information about the initial state can be observed only in the transient dynamics.

DOI
10.1088/1751-8121/accabf

Related papers

Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains

Oleksandr Gamayun, Oleg Valentinovich Lychkovskiy, Jean-Sébastien Caux

We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.

arXiv:1911.01926•SciPost Physics•Mar 5, 2020•61 citations

Interplay between transport and quantum coherences in free fermionic systems

Tony Jin, Tristan Gautié, Alexandre Krajenbrink +2 more

Abstract We study the quench dynamics in free fermionic systems in the prototypical bipartitioning protocol obtained by joining two semi-infinite subsystems prepared in different states, aiming at understanding the interplay between quantum coherences in space in the initial state and transport properties. Our findings reveal that, under reasonable assumptions, the more correlated the initial state, the slower the transport is. Such statement is first discussed at qualitative level, and then made quantitative by introducing proper measures of correlations and transport ‘speed’. Moreover, it is supported for fermions on a lattice by an exact solution starting from specific initial conditions, and in the continuous case by the explicit solution for a wider class of physically relevant initial states. In particular, for this class of states, we identify a function, that we dub transition map , which takes the value of the stationary current as input and gives the value of correlation as output, in a protocol-independent way. As an aside technical result, in the discrete case, we give an expression of the full counting statistics in terms of a continuous kernel for a general correlated domain wall initial state, thus extending the recent results in Moriya et al (2019 J. Stat. Mech. 2019 063105) on the one-dimensional XX spin chain.

arXiv:2103.13371•Journal of Physics A Mathematical and Theoretical•Aug 25, 2021•17 citations

Exact quantum transport in non-Markovian open Gaussian systems

Guglielmo Pellitteri, Vittorio Giovannetti, Vasco Cavina

We build an exact framework to evaluate heat, energy, and particle transport between Gaussian reservoirs mediated by a quadratic quantum system. By combining full counting statistics with newly developed non-Markovian master equation approaches, we introduce an effective master equation whose solution can be used to generate arbitrary moments of the heat statistics for any number of reservoirs. This theory applies equally to fermionic and bosonic systems, holds at arbitrarily strong coupling, and resolves out-of-equilibrium transient dynamics determined by the system's initial state. In the steady-state, weak-coupling limit, we recover results analogous to those of the well-known Landauer-Büttiker formalism. We conclude our discussion by demonstrating an application of the method to a prototypical fermionic system. Our results uncover a regime of transient negative heat conductance contingent upon the initial system preparation, providing a clear signature of non-trivial out-of-equilibrium dynamics.

quant-pharXiv:2602.21190•Physical review. B./Physical review. B•Feb 25, 2026•0 citations

Full counting statistics for noninteracting fermions: Exact results and the Levitov-Lesovik formula

Kurt Schönhammer

Exact numerical results for the full counting statistics (FCS) for a one-dimensional tight-binding model of noninteracting electrons are presented without using an idealized measuring device. The two initially separate subsystems are connected at $t=0$ and the exact time evolution for the large but finite combined system is obtained numerically via a finite dimensional determinant. Even for surprisingly short times the approximate description of the time evolution with the help of scattering states agrees well with the exact result for the local current matrix elements and the FCS. An additional approximation has to be made to recover the Levitov-Lesovik formula in the limit where the system size becomes infinite and afterwards the long time limit is addressed. The derivation of the Levitov-Lesovik formula is generalized to more general geometries such as a Y junction enclosing a magnetic flux.

arXiv:cond-mat/0701620•Physical Review B•May 21, 2007•123 citations

A hydrodynamic theory for non-equilibrium full counting statistics in one-dimensional quantum systems

Dávid X. Horváth, Benjamin Doyon, Paola Ruggiero

We study the dynamics of charge fluctuations after homogeneous quantum quenches in one-dimensional systems with ballistic transport. For short but macroscopic times where the non-trivial dynamics is largely dominated by long-range correlations, a simple expression for the associated full counting statistics can be obtained by hydrodynamic arguments. This formula links the non-equilibrium charge fluctuation after the quench to the fluctuations of the associated current after a charge-biased inhomogeneous modification of the original quench which corresponds to the paradigmatic partitioning protocol. Under certain assumptions, the fluctuations in the latter case can be expressed by explicit closed form formulas in terms of thermodynamic and hydrodynamic quantities via the Ballistic Fluctuation Theory. In this work, we identify precise physical conditions for the applicability of a fully hydrodynamic theory, and provide a detailed analysis explicitly demonstrating how such conditions are met and how this leads to such hydrodynamic treatment. We discuss these conditions at length in non-relativistic free fermions, where calculations become feasible and allow for cross-checks against exact results. In physically relevant cases, strong long-range correlations can complicate the hydrodynamic picture, but our formula still correctly reproduces the first cumulants.

arXiv:2507.05954•SciPost Physics•Jul 6, 2026•0 citations

Nonequilibrium full counting statistics of multicomponent strongly-interacting quantum gases with defects

Ovidiu I. Pâţu, Oleksandr Gamayun, Cătălin Paşcu Moca

We investigate the full counting statistics of a one-dimensional multicomponent impenetrable gas released from a bipartite state in the presence of a local defect. Spin--charge separation reduces the multivariate generating function to an exact Fredholm determinant whose kernel is built from time-evolved single-particle orbitals. Expressing these orbitals in terms of scattering data gives access to both transient dynamics and the nonequilibrium steady state. We derive the leading long-time asymptotics and identify persistent oscillations in densities and currents caused by multiple bound states at the junction. We argue that interactions between components lead to a linear low-temperature correction to the current, in contrast to the quadratic correction in the single-component case. At equilibrium, we obtain the M-Wright distribution of spin transfer with $t^{1/4}$ scaling.

arXiv:2609.07146•Sep 7, 2026•0 citations
Abstract We study transport in the free fermionic one-dimensional systems subjected to arbitrary local potentials. The bias needed for the transport is modeled by the initial highly non-equilibrium distribution where only half of the system is populated. Additionally to that, the local potential is also suddenly changed when the transport starts. For such a quench protocol we compute the full counting statistics (FCS) of the number of particles in the initially empty part. In the thermodynamic limit, the FCS can be expressed via the Fredholm determinant with the kernel depending on the scattering data and Jost solutions of the pre-quench and the post-quench potentials. We discuss the large-time asymptotic behavior of the obtained determinant and observe that if two or more bound states are present in the spectrum of the post-quench potential the information about the initial state manifests itself in the persistent oscillations of the FCS. On the contrary, when there are no bound states the asymptotic behavior of the FCS is determined solely by the scattering data of the post-quench potential, which for the current (the first moment) is given by the Landauer–Büttiker formalism. The information about the initial state can be observed only in the transient dynamics.
We consider an integrable system of two one-dimensional fermionic chains connected by a link. The hopping constant at the link can be different from that in the bulk. Starting from an initial state in which the left chain is populated while the right is empty, we present time-dependent full counting statistics and the Loschmidt echo in terms of Fredholm determinants. Using this exact representation, we compute the above quantities as well as the current through the link, the shot noise and the entanglement entropy in the large time limit. We find that the physics is strongly affected by the value of the hopping constant at the link. If it is smaller than the hopping constant in the bulk, then a local steady state is established at the link, while in the opposite case all physical quantities studied experience persistent oscillations. In the latter case the frequency of the oscillations is determined by the energy of the bound state and, for the Loschmidt echo, by the bias of chemical potentials.
Abstract We study the quench dynamics in free fermionic systems in the prototypical bipartitioning protocol obtained by joining two semi-infinite subsystems prepared in different states, aiming at understanding the interplay between quantum coherences in space in the initial state and transport properties. Our findings reveal that, under reasonable assumptions, the more correlated the initial state, the slower the transport is. Such statement is first discussed at qualitative level, and then made quantitative by introducing proper measures of correlations and transport ‘speed’. Moreover, it is supported for fermions on a lattice by an exact solution starting from specific initial conditions, and in the continuous case by the explicit solution for a wider class of physically relevant initial states. In particular, for this class of states, we identify a function, that we dub transition map , which takes the value of the stationary current as input and gives the value of correlation as output, in a protocol-independent way. As an aside technical result, in the discrete case, we give an expression of the full counting statistics in terms of a continuous kernel for a general correlated domain wall initial state, thus extending the recent results in Moriya et al (2019 J. Stat. Mech. 2019 063105) on the one-dimensional XX spin chain.
We build an exact framework to evaluate heat, energy, and particle transport between Gaussian reservoirs mediated by a quadratic quantum system. By combining full counting statistics with newly developed non-Markovian master equation approaches, we introduce an effective master equation whose solution can be used to generate arbitrary moments of the heat statistics for any number of reservoirs. This theory applies equally to fermionic and bosonic systems, holds at arbitrarily strong coupling, and resolves out-of-equilibrium transient dynamics determined by the system's initial state. In the steady-state, weak-coupling limit, we recover results analogous to those of the well-known Landauer-Büttiker formalism. We conclude our discussion by demonstrating an application of the method to a prototypical fermionic system. Our results uncover a regime of transient negative heat conductance contingent upon the initial system preparation, providing a clear signature of non-trivial out-of-equilibrium dynamics.
Exact numerical results for the full counting statistics (FCS) for a one-dimensional tight-binding model of noninteracting electrons are presented without using an idealized measuring device. The two initially separate subsystems are connected at t=0t=0t=0 and the exact time evolution for the large but finite combined system is obtained numerically via a finite dimensional determinant. Even for surprisingly short times the approximate description of the time evolution with the help of scattering states agrees well with the exact result for the local current matrix elements and the FCS. An additional approximation has to be made to recover the Levitov-Lesovik formula in the limit where the system size becomes infinite and afterwards the long time limit is addressed. The derivation of the Levitov-Lesovik formula is generalized to more general geometries such as a Y junction enclosing a magnetic flux.
We study the dynamics of charge fluctuations after homogeneous quantum quenches in one-dimensional systems with ballistic transport. For short but macroscopic times where the non-trivial dynamics is largely dominated by long-range correlations, a simple expression for the associated full counting statistics can be obtained by hydrodynamic arguments. This formula links the non-equilibrium charge fluctuation after the quench to the fluctuations of the associated current after a charge-biased inhomogeneous modification of the original quench which corresponds to the paradigmatic partitioning protocol. Under certain assumptions, the fluctuations in the latter case can be expressed by explicit closed form formulas in terms of thermodynamic and hydrodynamic quantities via the Ballistic Fluctuation Theory. In this work, we identify precise physical conditions for the applicability of a fully hydrodynamic theory, and provide a detailed analysis explicitly demonstrating how such conditions are met and how this leads to such hydrodynamic treatment. We discuss these conditions at length in non-relativistic free fermions, where calculations become feasible and allow for cross-checks against exact results. In physically relevant cases, strong long-range correlations can complicate the hydrodynamic picture, but our formula still correctly reproduces the first cumulants.
We investigate the full counting statistics of a one-dimensional multicomponent impenetrable gas released from a bipartite state in the presence of a local defect. Spin--charge separation reduces the multivariate generating function to an exact Fredholm determinant whose kernel is built from time-evolved single-particle orbitals. Expressing these orbitals in terms of scattering data gives access to both transient dynamics and the nonequilibrium steady state. We derive the leading long-time asymptotics and identify persistent oscillations in densities and currents caused by multiple bound states at the junction. We argue that interactions between components lead to a linear low-temperature correction to the current, in contrast to the quadratic correction in the single-component case. At equilibrium, we obtain the M-Wright distribution of spin transfer with t1/4t^{1/4}t1/4 scaling.