Dissipative generation of pure steady states and a gambler's ruin problem

Abstract

We consider an open quantum system, with dissipation applied only to a part of its degrees of freedom, evolving via a quantum Markov dynamics. We demonstrate that, in the Zeno regime of large dissipation, the relaxation of the quantum system towards a pure quantum state is linked to the evolution of a classical Markov process towards a single absorbing state. The rates of the associated classical Markov process are determined by the original quantum dynamics. Extension of this correspondence to absorbing states with internal structure allows us to establish a general criterion for having a Zeno-limit nonequilibrium stationary state of arbitrary finite rank. An application of this criterion is illustrated in the case of an open XXZ spin-1/2 chain dissipatively coupled at its edges to baths with fixed and different polarizations. For this system, we find exact nonequilibrium steady-state solutions of ranks 1 and 2.

Long-Range Coherence and Multiple Steady States in a Lossy Qubit Array

“…(3) with the dissipators ffiffiffiffiffi γ þ pb † 0 and ffiffiffiffiffi γ − pb 0 . Numerically, we find this is the only steady state in each sector [69], up to the largest systems tractable by exact diagonalization. Within the respective eigenspace,ρ η describes an infinite-temperature state with chemical potential μ ¼ lnðγ þ =γ − Þ.…”

Signatures of quantum phases in a dissipative system

“…We also find that for a fixed (α + β), the correlation length ξ (where ξ is −1/slope of the plot of ln |C mn | with |m − n|) is independent of |β − α| when α ̸ = β and ∆ ̸ = 0 (see figures 4(b) and (c)). When α = β, the correlation length is zero (ξ = 0) due to the behavior of correlation function as shown in equation (19).…”

“…While extensively pursued and discussed in the context of few-level systems, quantum optics setups, fairly recently, a huge body of work has been dedicated to their role in dissipative quantum many-body phases of matter [1][2][3][4]. Moreover, recent works have investigated the non-equilibrium steady states of systems evolving under Lindbladian dynamics in the Zeno regime of large dissipation [17][18][19].…”

Dissipative cooling towards phantom Bethe states in boundary-driven XXZ spin chain

“…+ } becomes an adsorbing basin of the Markov process (3) [27] resulting in depopulation of all other states with time, and leading to the NESS of the form…”