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

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 ${\mathsf{r}}_0(k),{\mathsf{t}}_0(k)$ to $\mathsf{r}(k),\mathsf{t}(k)$ at time $t=0$. The initial state is at equilibrium with ${\mathsf{t}}_0(k)=0$ such that the system is cut in two independent halves with ${\mathsf{r}}_0^R(k)$, ${\mathsf{r}}_0^L(k)$ 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 $x\sim t$, i.e., the ray-regime. For a repulsive impurity these correlations are independent of ${\mathsf{r}}_0^R(k)$, ${\mathsf{r}}_0^L(k)$, 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.

Main text: 7 pages, 3 figures. Supp. Mat.: 31 pages, 4 figures

References in corpus (17)

• Experimental Observation of a Generalized Gibbs Ensemble
• Strongly Correlated Quantum Walks in Optical Lattices
• Full counting statistics in a propagating quantum front and random matrix spectra
• Dynamical Correlations after a Quantum Quench
• Non-interacting fermions at finite temperature in a $d$-dimensional trap: universal correlations
• Random matrices and entanglement entropy of trapped Fermi gases
• Universal front propagation in the quantum Ising chain with domain-wall initial states
• Fredholm determinants, full counting statistics and Loschmidt echo for domain wall profiles in one-dimensional free fermionic chains
• Approximate light cone effects in a non-relativistic quantum field theory after a local quench
• Non-Equilibrium Conformal Field Theories with Impurities
• $Large-scale$ thermalization, prethermalization and impact of the temperature in the quench dynamics of two unequal Luttinger liquids
• Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition
• Quenches in initially coupled Tomonaga-Luttinger Liquids: a conformal field theory approach
• Transport through interacting defects and lack of thermalisation
• Impurities in systems of noninteracting trapped fermions
• Quench dynamics of noninteracting fermions with a delta impurity
• Signature of Generalized Gibbs Ensemble Deviation from Equilibrium: Negative Absorption Induced by a Local Quench

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