Adiabatic approximation in the density matrix approach: non-degenerate systems

Abstract

We study the adiabatic limit in the density matrix approach for a quantum system coupled to a weakly dissipative medium. The energy spectrum of the quantum model is supposed to be non-degenerate. In the absence of dissipation, the geometric phases for periodic Hamiltonians obtained previously by M.V. Berry are recovered in the present approach. We determine the necessary condition satisfied by the coefficients of the linear expansion of the non-unitary part of the Liouvillian in order to the imaginary phases acquired by the elements of the density matrix, due to dissipative effects, be geometric. The results derived are model-independent. We apply them to spin 1 2 model coupled to reservoir at thermodynamic equilibrium.

Superradiant Quantum Heat Engine

“…In contrast to energy, which is harvested as work output, coherence is not consumed and it remains within the field. More technically, quantum coherence is determined by the off diagonal elements of the density matrix of the field; and work is harvested in a quantum adiabatic stage, where the off diagonal elements are preserved up to a geometric and dynamic phase factor 37 38 . The diagonal elements, and hence the number of photons, cannot change in accordance with the adiabatic theorem.…”