Quantum walks of two interacting particles in a classical environment

Quantum walks (QWs) describe the propagation of a quantum particle over a discrete lattice with equal tunnelling probability between adjacent sites. Two-particle QWs are paradigmatic systems to study the interplay between particle indistinguishability and particle interaction. Here we address the decoherent dynamics of two interacting and indistinguishable particles over a chain with random, time-dependent, tunneling amplitudes. In particular, the hopping amplitudes have been modeled as independent stochastic processes in the form of non-Gaussian random telegraphic noise. Upon tuning the ratio between the time scale of the noise and the walkers’ coupling strength, we may explore very different dynamical regimes. In particular, we show that noise with fast-decaying autocorrelation function may lead to a faster propagation with respect to the noiseless case. On the other hand, in the slow noise regime, the system displays a dynamical Anderson-like localization. Finally, we study the non-Markovian character of the dynamical map in order to relate specific features of the interacting QWs dynamics to the presence of memory effect. [1] Phys. Rev. A 95 (2), 022106 (2017). [2] Comp. Phys. Comm. 215, 235 (2017).