Eur. Phys. J. B (2017) 90: 74
https://doi.org/10.1140/epjb/e2017-80009-8

Regular Article

On the quantum CTRW approach^*

Centro Atómico Bariloche, CNEA, Instituto Balseiro, Universidad Nacional de Cuyo, and CONICET, 8400 Bariloche, Argentina

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

Received: 4 January 2017
Received in final form: 13 February 2017
Published online: 17 April 2017

Abstract

The concept of continuous-time random walk is generalized into the quantum approach using a completely positive map. This approach introduces in a phenomenological way the concept of disorder in the transport problem of a quantum open system. If the waiting-time of the continuous-time renewal approach is exponential we recover a semigroup for a dissipative quantum walk. Two models of non-Markovian evolution have been solved considering different types of waiting-time functions.