Eur. Phys. J. B (2018) 91: 256
https://doi.org/10.1140/epjb/e2018-90387-x

Regular Article

A non-Markovian approach for two dissipative quantum walks

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

^a e-mail: caceres@cab.cnea.gov.ar

Received: 12 June 2018
Received in final form: 3 August 2018
Published online: 18 October 2018

Abstract

We study the non-Markovian evolution of two free spinless distinguishable particles in a 1D lattice using a completely positive map. The Renewal theory is used to introduce, in a phenomenological way, the concept of disorder in the random time-interventions of the environment. If the waiting-time of the Renewal approach is exponential, we recover a semigroup description for the density matrix. Introducing a non-Poissonian random-time bath-interventions a non-Markovian evolution for the density matrix has been worked out. Under this scenario, we have studied the time evolution of the Quantum Coherence and Negativity measures for local and non-local initial conditions. We show the relevance of the (weak) non-Markovian evolution in calculating short-time correlations, while in the long-time regime a renormalized Markovian evolution appears.