Open quantum dynamics, Markov processes Part I

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.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.

arXiv:2003.12149Physical Review ASep 8, 20208 citations

Quantum Markov Processes

Luigi Accardi

Springer eBooksJan 1, 19803 citations

Markov approximations encounter map domains: A hazard of open quantum dynamics

Thomas F. Jordan, Anil Shaji, E. C. G. Sudarshan

A Markov approximation in open quantum dynamics can give unphysical results when a map acts on a state that is not in its domain. This is examined here in a simple example, an open quantum dynamics for one qubit in a system of two interacting qubits, for which the map domains have been described quite completely. A time interval is split into two parts and the map from the exact dynamics for the entire interval is replaced by the conjunction of that same map for both parts. If there is any correlation between the two qubits, unphysical results can appear as soon as the map conjunction is used, even for infinitesimal times. If the map is repeated an unlimited number of times, every state is at risk of being taken outside the bounds of physical meaning. Treatment by slippage of initial conditions is discussed.A Markov approximation in open quantum dynamics can give unphysical results when a map acts on a state that is not in its domain. This is examined here in a simple example, an open quantum dynamics for one qubit in a system of two interacting qubits, for which the map domains have been described quite completely. A time interval is split into two parts and the map from the exact dynamics for the entire interval is replaced by the conjunction of that same map for both parts. If there is any correlation between the two qubits, unphysical results can appear as soon as the map conjunction is used, even for infinitesimal times. If the map is repeated an unlimited number of times, every state is at risk of being taken outside the bounds of physical meaning. Treatment by slippage of initial conditions is discussed.

Physical Review AMar 13, 20085 citations

Generated Dynamics of Markov and Quantum Processes

Martin Janßen

Springer eBooksJan 1, 20163 citations

Non-Markovian dynamics of open quantum systems

Carole Addis

Oct 1, 20167 citations

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.