Quantum Dissipative Systems

Daniel F. Walls, Gerard J Milburn

S. Alipour, Dariusz Chruściński, Paolo Facchi A +3 more

Abstract Dynamics and features of quantum systems can be drastically different from classical systems. Dissipation is understood as a general mechanism through which quantum systems may lose part or all of their quantum aspects. Here we discuss a method to analyze behaviors of dissipative quantum systems in an algebraic sense. This method employs a time-dependent product between system’s observables which is induced by the underlying dissipative dynamics. We argue that the long-time limit of the algebra of observables defined with this product yields a contractive algebra which reflects the loss of some quantum features of the dissipative system, and it bears relevant information about irreversibility. We illustrate this result through several examples of dissipation in various Markovian and non-Markovian systems.

Yizhen Huang, Alejandro M. Lobos, Zi Cai

In this paper, we formulate and quantitatively examine the effect of dissipation on topological systems. We use a specific model of Kitaev quantum wire with an onsite Ohmic dissipation and perform a numerically exact method to investigate the effect of dissipation on the topological features of the system (e.g., the Majorana edge mode) at zero temperature. We find that even though the topological phase is robust against weak dissipation as it is supposed to be, it will eventually be destroyed by sufficiently strong dissipation via either a continuous quantum phase transition or a crossover depending on the symmetry of the system. The dissipation-driven quantum criticality has also been discussed.

Paolo Forni, Alain Sarlette

We consider a target quantum system, coupled to an auxiliary quantum system which dissipates rapidly at somewhat adjustable rates. The goal is to minimize the dissipation induced on the target system by this coupling. We use explicit model reduction formulas to express this as a quadratic optimization problem. We prove that maybe counterintuitively, when the auxiliary system dissipates along Hermitian (entropy-increasing) channels, the minimum induced dissipation is reached by maximizing the dissipation rate of the auxiliary system.