Embedding quantum systems with a non-conserved probability in classical environments

Abstract

Quantum systems with a non-conserved probability can be described by means of non-Hermitian Hamiltonians and non-unitary dynamics. In this paper, the case in which the degrees of freedom can be partitioned in two subsets with light and heavy masses is treated. A classical limit over the heavy coordinates is taken in order to embed the non-unitary dynamics of the subsystem in a classical environment. Such a classical environment, in turn, acts as an additional source of dissipation (or noise), beyond that represented by the non-unitary evolution. The non-Hermitian dynamics of a Heisenberg two-spin chain, with the spins independently coupled to harmonic oscillators, is considered in order to illustrate the formalism.

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• Evolution of a Non-Hermitian Quantum Single-Molecule Junction at Constant Temperature
• Time-Irreversible Quantum-Classical Dynamics of Molecular Models in the Brain
• Phase space formulation of density operator for non-Hermitian Hamiltonians and its application in quantum theory of decay
• Density operator approach to turbulent flows in plasma and atmospheric fluids