A random phase approximation study of one-dimensional fermions after a
  quantum quench

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Abstract

The effect of interactions on a system of fermions that are in a non-equilibrium steady state due to a quantum quench is studied employing the random-phase-approximation (RPA). As a result of the quench, the distribution function of the fermions is highly broadened. This gives rise to an enhanced particle-hole spectrum and over-damped collective modes for attractive interactions between fermions. On the other hand, for repulsive interactions, an undamped mode above the particle-hole continuum survives. The sensitivity of the result on the nature of the non-equilibrium steady state is explored by also considering a quench that produces a current carrying steady-state.

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Relaxation in a Completely Integrable Many-Body Quantum System: An Ab Initio Study of the Dynamics of the Highly Excited States of Lattice Hard-Core Bosons

Marcos Rigol, Vanja Dunjko, Maxim Olshanii … (2006)

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such state are. We confirm the relaxation hypothesis through a thorough ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which having already been observed in the recent experiment on the non-equilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita, T. Wenger, D. S. Weiss, Nature (London) 440, 900 (2006)].

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Time-dependence of correlation functions following a quantum quench

John Cardy, Pasquale Calabrese (2006)

We show that the time-dependence of correlation functions in an extended quantum system in d dimensions, which is prepared in the ground state of some hamiltonian and then evolves without dissipation according to some other hamiltonian, may be extracted using methods of boundary critical phenomena in d+1 dimensions. For d=1 particularly powerful results are available using conformal field theory. These are checked against those available from solvable models. They may be explained in terms of a picture, valid more generally, whereby quasiparticles, entangled over regions of the order of the correlation length in the initial state, then propagate classically through the system.

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Quantum Quench in the Transverse Field Ising Chain

Pasquale Calabrese, Fabian Essler, Maurizio Fagotti (2011)

We consider the time evolution of observables in the transverse field Ising chain (TFIC) after a sudden quench of the magnetic field. We provide exact analytical results for the asymptotic time and distance dependence of one- and two-point correlation functions of the order parameter. We employ two complementary approaches based on asymptotic evaluations of determinants and form-factor sums. We prove that the stationary value of the two-point correlation function is not thermal, but can be described by a generalized Gibbs ensemble (GGE). The approach to the stationary state can also be understood in terms of a GGE. We present a conjecture on how these results generalize to particular quenches in other integrable models.