Non-equilibrium Statistical Physics with Application to Disordered Systems

Bath-induced correlations in an infinite-dimensional Hilbert space

“…This picture allows to generalize the description of a QDW into a non-Markovian evolution using the CTRW approach [25,26]. See also a related contribution, in the present issue, for describing completely positive quantum maps in the context of the Renewal theory [27].…”

“…In addition we note that in the lattice the classical random walk solution is P t (s) = e −2Dt I s (2Dt), and from this expression it is simple to get the Gaussian profile in the continuous limit [26].…”

“…We have chosen this interaction Hamiltonian in order to recover the classical master equation for two independent random walk in the case when Ω = 0, for a more extended discussion on this issue see Appendix A in [16,26].…”

“…The quantity T (1) can be interpreted as the one-particle classical random walk return to the origin [26], to see this note that In the inset of Fig.1(b) we plot the correlation T (1,2) (t) showing that there is a time-scale when this quantum correlation reaches a maximum t max D ≡ 2Dt max ≃ 1.9 · · · before the long-time asymptotic regime ∼ 1/t, characterizing the decoherence in the two-particles system.…”

“…A non-Markov extension of the present DQW model can also be introduced using the Continuous-time Random Walk (CTRW) approach introduced by Montroll and Weiss [25,26]. In appendix A a short review on the subject of quantum jumps in presented, this picture can also be related to the random quantum maps approach in the context of the Renewal theory [27].…”