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

¹ CNRS-Laboratoire de Physique Théorique de l'Ecole Normale Supérieure - 24 rue Lhomond, 75231 Paris Cedex, France
² Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589 - 4 Place Jussieu, 75252 Paris Cedex 05, France

^(a) E-mail: schehr@lpthe.jussieu.fr (corresponding author)

Received: 31 December 2022
Accepted: 17 April 2023

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.