Out of equilibrium density dynamics of a quenched fermionic system

TL;DR

This paper analyzes the non-equilibrium density dynamics of a one-dimensional fermionic system after a finite-duration interaction quench, revealing interference effects and oscillatory convergence to equilibrium states.

Contribution

It provides analytical solutions for the density evolution during finite-time quenches, highlighting the role of light-cone perturbations and their interference.

Findings

Light-cone perturbations are created during quench switching.

Interference between perturbations affects density dynamics.

Oscillatory behavior in the approach to equilibrium states.

Abstract

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 inter-particle 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.