Markovianity of an emitter coupled to a structured spin-chain bath

Abstract

We analyze the dynamics of a spin 1/2 subsystem coupled to a spin chain. We simulate numerically the full quantum many-body system for various sets of parameters and initial states of the chain, and characterize the divisibility of the subsystem dynamics, i.e. whether it is Markovian and can be described by a (time dependent) master equation. We identify regimes in which the subsystem admits such Markovian description, despite the many-body setting, and provide insight about why the same is not possible in other regimes. Interestingly, coupling the subsystem at the edge, instead of the center, of the chain gives rise to qualitatively distinct behavior.

Mixing times and cutoffs in open quadratic fermionic systems

“…The most natural next step would be to investigate the mixing properties of systems with a non-trivial steady state, for instance one with long-range order, entanglement [1], or current-carrying [3,35,36]. Another possible direction would be to study whether the present analysis, and in particular the existence of cutoffs, could be extended to non-markovian dynamics such as that governing the evolution of subsystem density matrices in isolated quantum systems after a quantum quench [37,38], or in random quantum circuits [39] (see also [40]). A second direction concerns the relation with other physical observables : even though we have observed in Section 5.3 that the most natural local observables as well as the von Neumann entropy are insensitive to the presence of a cutoff, namely they do not develop a sharp jump as the trace-norm distance to equilibrium does at the mixing times t mix (L), it remains an intriguing question whether the cutoff phenomenon might transpire into other physical quantities.…”

Report on scipost_202004_00049v1

“…The most natural next step would be to investigate the mixing properties of systems with a non-trivial steady state, for instance one with long-range order, entanglement [1], or current-carrying [3,33,34]. Another possible direction would be to study whether the present analysis, and in particular the existence of cutoffs, could be extended to non-markovian dynamics such as that governing the evolution of subsystem density matrices in isolated quantum systems after a quantum quench [35,36], or in random quantum circuits [37] (see also [38]). A second direction concerns the relation with other physical observables : even though we have observed in Section 5.3 that the most natural local observables as well as the von Neumann entropy are insensitive to the presence of a cutoff, namely they do not develop a sharp jump as the trace-norm distance to equilibrium does at the mixing times t mix (L), it remains an intriguing question whether the cutoff phenomenon might transpire into other physical quantities.…”

“…We now move back to our models, which in contrast with product chains cannot be written as a tensor product of independent channels, due to the anticommutation between the operators C ± k in different sectors To get an idea of the difficulties raised by the fermionic nature of the problem, let us look at the gain/loss model, starting with a single momentum sector. A generic initial density matrix can be written in the form (38), where…”

Engineering non-Markovianity from defect-phonon interactions

“…On the one hand, classical noise may arise from random fluctuations in an external field, such as the stochastic noise from magnetic impurities [10,18,19] or the fluctuations in laser intensity [20]. On the other hand, quantum noise may be considered from the interaction with a fermionic [21,22] or bosonic [21,23] bath. The latter has been crucial for explaining fundamental aspects like the radiative decay of an atom [24] or the decay of a radiation field inside a cavity QED [24].…”