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:cond-mat/0406267 · Physical Review B

Effect of nonadiabatic switching of dynamic perturbations in one-dimensional Fermi systems

Carlos Naón, Mariano J. Salvay, Marta L. Trobo

Published Nov 15, 2004• 6 citations
arXivHTMLPDF

Abstract

We study a two-dimensional (2D) fermionic quantum-field-theoretical model used to model 1D strongly correlated electrons in the presence of a time-dependent impurity that drives the system out of equilibrium. In contrast to previous investigations, we consider a dynamic barrier switched on at a finite time. We compute the total energy density of the system and establish two well defined regimes in terms of the relationship between the frequency of the time-dependent perturbation $\ensuremath{\Omega}$ and the electron energy $\ensuremath{\omega}$. Finally, we derive a relaxation time ${t}_{R}$ such that for times shorter than ${t}_{R}$ the finite-time switching process is relevant.

DOI
10.1103/physrevb.70.195109

Related papers

Backscattering off a dynamical impurity in one-dimensional Fermi systems: A perturbative computation

Carlos Naón, Mariano J. Salvay

We investigate the problem of backscattering off a time-dependent and spatially extended barrier in a one-dimensional noninteracting electron gas. By performing a perturbative expansion in the backscattering amplitude, we compute the total energy density of the system. We show how the free fermion spectrum and the conductance of the system are affected by the interplay between dynamical and geometrical properties of the impurity.

arXiv:cond-mat/0610374•Physical Review B•Mar 8, 2007•2 citations

Nonperturbative approach to backscattering off a dynamical impurity in one-dimensional Fermi systems

Daniel Gustavo Barci, L. Moriconi, Marco Moriconi +2 more

We investigate the problem of backscattering off a time-dependent impurity in a one-dimensional electron gas. By combining the Schwinger-Keldysh method with an adiabatic approximation in order to deal with the corresponding out of equilibrium Dirac equation, we compute the total energy density (TED) of the system. We show how the free fermion TED is distorted by the backscattering amplitude and the geometry of the impurity.

arXiv:cond-mat/0503395•Physical Review B•Dec 13, 2005•4 citations

Quench dynamics of noninteracting fermions with a delta impurity

Gabriel Gouraud, Pierre Le Doussal, Grégory Schehr

Abstract We study the out-of-equilibrium dynamics of noninteracting fermions in one dimension and in continuum space, in the presence of a delta impurity potential at the origin whose strength g is varied at time t = 0. The system is prepared in its ground state with g = g 0 = +∞, with two different densities and Fermi wave-vectors k L and k R on the two half-spaces x > 0 and x < 0 respectively. It then evolves for t > 0 as an isolated system, with a finite impurity strength g . We compute exactly the time dependent density and current. For a fixed position x and in the large time limit t → ∞, the system reaches a non-equilibrium stationary state (NESS). We obtain analytically the correlation kernel, density, particle current, and energy current in the NESS, and characterize their relaxation, which is algebraic in time. In particular, in the NESS, we show that, away from the impurity, the particle density displays oscillations which are the non-equilibrium analog of the Friedel oscillations. In the regime of ‘rays’, x / t = ξ fixed with x , t → ∞, we compute the same quantities and observe the emergence of two light cones, associated to the Fermi velocities k L and k R in the initial state. Interestingly, we find non trivial quantum correlations between two opposite rays with velocities ξ and − ξ which we compute explicitly. We extend to a continuum setting and to a correlated initial state the analytical methods developed in a recent work of Ljubotina, Sotiriadis and Prosen, in the context of a discrete fermionic chain with an impurity. We also generalize our results to an initial state at finite temperature, recovering, via explicit calculations, some predictions of conformal field theory in the low energy limit.

arXiv:2202.04871•Journal of Physics A Mathematical and Theoretical•Jul 25, 2022•12 citations

Out-of-equilibrium density dynamics of a quenched fermionic system

S. Porta, Filippo Maria Gambetta, Fabio Cavaliere +2 more

Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional fermionic system with open boundaries and subject to a finite duration quench of the interparticle interaction. We provide analytical and asymptotic solutions to the unitary time evolution of the system, showing that both switching on and switching off the quench ramp create light-cone perturbations in the density. The post-quench dynamics is strongly affected by the interference between these two perturbations. In particular, we find that the discrepancy between the time-dependent density and the one obtained by a generalized Gibbs ensemble picture vanishes with an oscillatory behavior as a function of the quench duration, with local minima corresponding to a perfect overlap of the two light-cone perturbations. For adiabatic quenches, we also obtain a similar behavior in the approach of the generalized Gibbs ensemble density towards the one associated with the ground state of the final Hamiltonian.

arXiv:1606.02997•Physical review. B./Physical review. B•Aug 12, 2016•27 citations

Stationary time correlations for fermions after a quench in the presence of an impurity

Gabriel Gouraud, Pierre Le Doussal, Grégory Schehr

Abstract We consider the quench dynamics of non-interacting fermions in one dimension in the presence of a finite-size impurity at the origin. This impurity is characterized by general momentum-dependent reflection and transmission coefficients which are changed from to at time t = 0. The initial state is at equilibrium with such that the system is cut in two independent halves with , , respectively, to the right and to the left of the impurity. We obtain the exact large time limit of the multi-time correlations. These correlations become time translationally invariant, and are non-zero in two different regimes: i) for where the system reaches a non-equilibrium steady state (NESS), ii) for , i.e. , the ray regime. For a repulsive impurity these correlations are independent of , , while in the presence of bound states they oscillate and memory effects persist. We show that these nontrivial relaxational properties can be retrieved in a simple manner from the large time behaviour of the single particle wave functions.

arXiv:2211.15447•Europhysics Letters (EPL)•Apr 20, 2023•8 citations

Nonequilibrium dynamical cluster theory

Naoto Tsuji, Peter Barmettler, Hideo Aoki +1 more

We study the effect of spatially nonlocal correlations on the nonequilibrium dynamics of interacting fermions by constructing the nonequilibrium dynamical cluster theory, a cluster generalization of the nonequilibrium dynamical mean-field theory (DMFT). The formalism is applied to interaction quenches in the Hubbard model in one and two dimensions, and the results are compared with data from single-site DMFT, the time-dependent density matrix renormalization group, and lattice perturbation theory. Both in one and two dimensions the double occupancy quickly thermalizes, while the momentum distribution relaxes only on much longer time scales. For the two-dimensional square lattice we find a strongly momentum-dependent evolution of the momentum distribution around the Fermi energy, with a much faster relaxation near the momenta $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ than near $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$. This result is interpreted as reflecting the momentum-anisotropic quasiparticle lifetime of the marginal Fermi liquid. The method is further applied to the two-dimensional Hubbard model driven by a dc electric field, where the damping of the Bloch oscillation of the current is found to be less effective than predicted by DMFT and lattice perturbation theory.

arXiv:1307.5946•Physical Review B•Aug 11, 2014•34 citations
We study a two-dimensional (2D) fermionic quantum-field-theoretical model used to model 1D strongly correlated electrons in the presence of a time-dependent impurity that drives the system out of equilibrium. In contrast to previous investigations, we consider a dynamic barrier switched on at a finite time. We compute the total energy density of the system and establish two well defined regimes in terms of the relationship between the frequency of the time-dependent perturbation \ensuremathΩ\ensuremath{\Omega}\ensuremathΩ and the electron energy \ensuremathω\ensuremath{\omega}\ensuremathω. Finally, we derive a relaxation time tR{t}_{R}tR​ such that for times shorter than tR{t}_{R}tR​ the finite-time switching process is relevant.
Abstract We study the out-of-equilibrium dynamics of noninteracting fermions in one dimension and in continuum space, in the presence of a delta impurity potential at the origin whose strength g is varied at time t = 0. The system is prepared in its ground state with g = g 0 = +∞, with two different densities and Fermi wave-vectors k L and k R on the two half-spaces x > 0 and x < 0 respectively. It then evolves for t > 0 as an isolated system, with a finite impurity strength g . We compute exactly the time dependent density and current. For a fixed position x and in the large time limit t → ∞, the system reaches a non-equilibrium stationary state (NESS). We obtain analytically the correlation kernel, density, particle current, and energy current in the NESS, and characterize their relaxation, which is algebraic in time. In particular, in the NESS, we show that, away from the impurity, the particle density displays oscillations which are the non-equilibrium analog of the Friedel oscillations. In the regime of ‘rays’, x / t = ξ fixed with x , t → ∞, we compute the same quantities and observe the emergence of two light cones, associated to the Fermi velocities k L and k R in the initial state. Interestingly, we find non trivial quantum correlations between two opposite rays with velocities ξ and − ξ which we compute explicitly. We extend to a continuum setting and to a correlated initial state the analytical methods developed in a recent work of Ljubotina, Sotiriadis and Prosen, in the context of a discrete fermionic chain with an impurity. We also generalize our results to an initial state at finite temperature, recovering, via explicit calculations, some predictions of conformal field theory in the low energy limit.
Using a Luttinger liquid theory we investigate the time evolution of the particle density of a one-dimensional fermionic system with open boundaries and subject to a finite duration quench of the interparticle interaction. We provide analytical and asymptotic solutions to the unitary time evolution of the system, showing that both switching on and switching off the quench ramp create light-cone perturbations in the density. The post-quench dynamics is strongly affected by the interference between these two perturbations. In particular, we find that the discrepancy between the time-dependent density and the one obtained by a generalized Gibbs ensemble picture vanishes with an oscillatory behavior as a function of the quench duration, with local minima corresponding to a perfect overlap of the two light-cone perturbations. For adiabatic quenches, we also obtain a similar behavior in the approach of the generalized Gibbs ensemble density towards the one associated with the ground state of the final Hamiltonian.
Abstract We consider the quench dynamics of non-interacting fermions in one dimension in the presence of a finite-size impurity at the origin. This impurity is characterized by general momentum-dependent reflection and transmission coefficients which are changed from to at time t = 0. The initial state is at equilibrium with such that the system is cut in two independent halves with , , respectively, to the right and to the left of the impurity. We obtain the exact large time limit of the multi-time correlations. These correlations become time translationally invariant, and are non-zero in two different regimes: i) for where the system reaches a non-equilibrium steady state (NESS), ii) for , i.e. , the ray regime. For a repulsive impurity these correlations are independent of , , while in the presence of bound states they oscillate and memory effects persist. We show that these nontrivial relaxational properties can be retrieved in a simple manner from the large time behaviour of the single particle wave functions.
We study the effect of spatially nonlocal correlations on the nonequilibrium dynamics of interacting fermions by constructing the nonequilibrium dynamical cluster theory, a cluster generalization of the nonequilibrium dynamical mean-field theory (DMFT). The formalism is applied to interaction quenches in the Hubbard model in one and two dimensions, and the results are compared with data from single-site DMFT, the time-dependent density matrix renormalization group, and lattice perturbation theory. Both in one and two dimensions the double occupancy quickly thermalizes, while the momentum distribution relaxes only on much longer time scales. For the two-dimensional square lattice we find a strongly momentum-dependent evolution of the momentum distribution around the Fermi energy, with a much faster relaxation near the momenta $(0,\ensuremath{\pi})$ and $(\ensuremath{\pi},0)$ than near $(\ensuremath{\pi}/2,\ensuremath{\pi}/2)$. This result is interpreted as reflecting the momentum-anisotropic quasiparticle lifetime of the marginal Fermi liquid. The method is further applied to the two-dimensional Hubbard model driven by a dc electric field, where the damping of the Bloch oscillation of the current is found to be less effective than predicted by DMFT and lattice perturbation theory.