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

- 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 r0(k), t0(k) to r(k), t(k) at time t = 0. The initial state is at equilibrium with t0(k) = 0 such that the system is cut in two independent halves with rR0 (k), rL0 (k), 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 x = O(1) where the system reaches a non-equilibrium steady state (NESS), ii) for x similar to t, i.e., the ray regime. For a repulsive impurity these correlations are independent of rR0 (k), rL0 (k), 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.

Automated summary

This paper investigates the quench dynamics of non-interacting fermions in one dimension with a finite-size impurity at the origin. The impurity is characterized by momentum-dependent reflection and transmission coefficients that change at time t = 0. The initial state is at equilibrium and the system is divided into two independent halves. The exact large time limit of the multi-time correlations is obtained, showing nontrivial relaxational properties related to the behavior of single particle wave functions.