arXiv subjects

Simon Essink

Publications and source records attributed to Simon Essink.

3 recordsLinked to original sources

arXiv2020

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

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.

quant-ph↗

arXiv2019

Transition between dissipatively stabilized helical states

We analyze a $XXZ$ spin-1/2 chain which is driven dissipatively at its boundaries. The dissipative driving is modelled by Lindblad jump operators which only act on both boundary spins. In the limit of large dissipation, we find that the boundary spins are pinned to a certain value and at special values of the interaction anisotropy, the steady states are formed by a rank-2 mixture of helical states with opposite winding numbers. Contrarily to previous stabilization of topological states, these helical states are not protected by a gap in the spectrum of the Lindbladian. By changing the anisotropy, the transition between these steady states takes place via mixed states of higher rank. In particular, crossing the value of zero anisotropy a totally mixed state is found as the steady state. The transition between the different winding numbers via mixed states can be seen in the light of the transitions between different topological states in dissipatively driven systems. The results are obtained developing a perturbation theory in the inverse dissipative coupling strength and using the numerical exact diagonalization and matrix product state methods.

cond-mat.str-el↗

arXiv2018

Effective quantum Zeno dynamics in dissipative quantum systems

We investigate the time evolution of an open quantum system described by a Lindblad master equation with dissipation acting only on a part of the degrees of freedom ${\cal H}_0$ of the system, and targeting a unique dark state in ${\cal H}_0$. We show that, in the Zeno limit of large dissipation, the density matrix of the system traced over the dissipative subspace ${\cal H}_0$, evolves according to another Lindblad dynamics, with renormalized effective Hamiltonian and weak effective dissipation. This behavior is explicitly checked in the case of Heisenberg spin chains with one or both boundary spins strongly coupled to a magnetic reservoir. Moreover, the populations of the eigenstates of the renormalized effective Hamiltonian evolve in time according to a classical Markov dynamics. As a direct application of this result, we propose a computationally-efficient exact method to evaluate the nonequilibrium steady state of a general system in the limit of strong dissipation.

quant-ph↗