Operator growth in open quantum systems: lessons from the dissipative SYK

Conservation law of operator current in open quantum systems

Quantum control of dissipative systems

We study the effect of dissipation, i.e., uncontrollable interactions of a quantum system with the environment, on one’s ability to control the system. In particular we show that dissipation, although often considered undesirable, opens up unique possibilities for quantum control by removing the constraint of unitary evolution, which restricts the set of reachable states and imposes bounds on t...

Quantum mechanics of dissipative systems.

Quantum dissipation involves both energy relaxation and decoherence, leading toward quantum thermal equilibrium. There are several theoretical prescriptions of quantum dissipation but none of them is simple enough to be treated exactly in real applications. As a result, formulations in different prescriptions are practically used with different approximation schemes. This review examines both t...

From open quantum systems to open quantum maps

In this paper we show that for a class of open quantum systems satisfying a natural dynamical assumption (see §2.2) the study of the resolvent, and hence of scattering, and of resonances, can be reduced, in the semiclassical limit, to the study of open quantum maps, that is of finite dimensional quantizations of canonical relations obtained by truncation of symplectomorphisms derived from the c...

Dissipative tunneling through a parabolic potential in the Lindblad theory of open quantum systems

By using the Lindblad theory for open quantum systems, an analytical expression of the tunneling probability through an inverted parabola is obtained. This penetration probability depends on the environment coefficients. It is shown that the tunneling probability increases with the dissipation and the temperature of the thermal bath. PACS numbers: 03.65.Bz, 05.30.-d, 05.40.Jc (a) e-mail address...