Non-Markovian continuous-time quantum walks on lattices with dynamical noise

Abstract

We address the dynamics of continuous-time quantum walks on one-dimensional disordered lattices inducing dynamical noise in the system. Noise is described as time-dependent fluctuations of the tunneling amplitudes between adjacent sites, and attention is focused on non-Gaussian telegraph noise, going beyond the usual assumption of fast Gaussian noise. We observe the emergence of two different dynamical behaviors for the walker, corresponding to two opposite noise regimes: slow noise (i.e. strong coupling with the environment) confines the walker into few lattice nodes, while fast noise (weak coupling) induces a transition between quantum and classical diffusion over the lattice. A phase transition between the two dynamical regimes may be observed by tuning the ratio between the autocorrelation time of the noise and the coupling between the walker and the external environment generating the noise. We also address the non-Markovianity of the quantum map by assessing its memory effects, as well as evaluating the information backflow to the system. Our results suggest that the non-Markovian character of the evolution is linked to the dynamical behavior in the slow noise regime, and that fast noise induces a Markovian dynamics for the walker.

Stochastic quantum Zeno-based detection of noise correlations

“…, and we find the Lindblad-Kossakowski master equation3. In general, the memory kernel can lead to non-Markovian dynamics depending on the structure and time scale of the Hamiltonian, as for example demonstrated for random telegraph noise (RTN) and 1/ f -noise78. Indeed, also a Markovian stochastic process Ω( t ) (as in the case of RTN, where the time correlation is ) can lead to non-Markovian dynamics of the quantum system it is coupled to.…”

“…Therefore, in the last few years several theoretical proposals for the characterization of the environment according to whether it can generate Markovian or non-Markovian dynamics of the system to which it is coupled have been put forward, and a full hierarchy of non-Markovianity6 has been introduced. In particular, it has been shown that classical environments exhibiting time-correlated random fluctuations can lead to non-Markovian quantum dynamics78. The structure of such an environment can be probed by coupling a (typically small, e.g.…”

Quantum correlations of identical particles subject to classical environmental noise

“…Also the effects of static noise (resulting in lattice disorder) could be explored in the case of identical particles-due to their role in phenomena like Anderson localization or the transition from quantum to classical random walks [119][120][121][122]-in order to explore differences, if present, with the distinguishable particle case [66].…”

Efficient quantum transport in a multi-site system combining classical noise and quantum baths

“…Uchiyama et al [17] have analyzed the effect of spatial and temporal correlations on EET in a multi-site model by using a Ornstein-Uhlenbeck noise process to describe the environment, and observe that negative spatial correlation of the noise is the most effective in helping the EET. The effect of RTN on transport via continuous-time quantum walks has been studied on lattices [30,31], also in presence of spatial correlations [32]. Its effect on the non-Markovianity of the dynamics of the spin-boson model has also been considered [33].…”