An Approach To Quantum Dissipation

J.W. Krol

After completion of our recent work on dissipative quantum hydrodynamics coupled to general relativity we became aware of related results by Turski, who provides a mathematically consistent formulation of dissipation within quantum dynamics. This establishes that dissipation at the quantum level can be treated as a fundamental and well-posed modification rather than a phenomenological artifact. In this article we clarify how this mathematical foundation enables a closed physical framework when combined with a geometric interpretation of dissipation.We argue that dissipation in quantum mechanics enables the formation of localized matter structures, while dissipation into spacetime geometry produces volumetric expansion that dilutes dissipative effects and preserves global consistency.

A. O. Caldeira

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.

Alberto Acevedo, Manuel Berrondo, Jean-François S. Van Huele

Da-Jian Zhang, Hua-Lin Huang, D. M. Tong

It has been found that Markovian quantum dissipative processes, described by the Lindblad equation, may have attractive steady-state manifolds, in which dissipation and decoherence can play a positive role to quantum information processing. In this article, we show that such attractive steady-state manifolds with the same positive features as in Markovian dissipative processes can exist in the non-Markovian dissipative processes. Our finding indicates that the dissipation-assisted schemes implemented in the Markovian systems can be directly generalized to the non-Markovian systems.

E. Celeghini, Mario Rasetti, Giuseppe Vitiello