Eur. Phys. J. B (2017) 90: 164
https://doi.org/10.1140/epjb/e2017-80231-4

Regular Article

Bath-induced correlations in an infinite-dimensional Hilbert space^*

¹ Departamento de Física, Universidad Nacional del Comahue, 8300 Neuquén, Argentina
² Centro Atómico Bariloche, CNEA, Instituto Balseiro and CONICET, 8400 Bariloche, Argentina

^a e-mail: marco.nizama@fain.uncoma.edu.ar
^b e-mail: caceres@cab.cnea.gov.ar

Received: 21 April 2017
Received in final form: 28 June 2017
Published online: 4 September 2017

Abstract

Quantum correlations between two free spinless dissipative distinguishable particles (interacting with a thermal bath) are studied analytically using the quantum master equation and tools of quantum information. Bath-induced coherence and correlations in an infinite-dimensional Hilbert space are shown. We show that for temperature T> 0 the time-evolution of the reduced density matrix cannot be written as the direct product of two independent particles. We have found a time-scale that characterizes the time when the bath-induced coherence is maximum before being wiped out by dissipation (purity, relative entropy, spatial dispersion, and mirror correlations are studied). The Wigner function associated to the Wannier lattice (where the dissipative quantum walks move) is studied as an indirect measure of the induced correlations among particles. We have supported the quantum character of the correlations by analyzing the geometric quantum discord.