Damped harmonic oscillators in the holomorphic representation

TL;DR

This paper uses quantum dynamical semigroups and the holomorphic representation to derive explicit density matrices for bosonic, fermionic, and supersymmetric oscillators, analyzing their time evolution and symmetry properties.

Contribution

It introduces a novel application of the holomorphic representation to explicitly derive density matrices for various oscillators and explores supersymmetry invariance conditions.

Findings

Explicit density matrices for bosonic and fermionic oscillators derived.

Conditions for supersymmetry invariance in dynamical equations established.

Holomorphic representation effectively describes quantum oscillator dynamics.

Abstract

Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the holomorphic representation. Bosonic and fermionic degrees of freedom are then put together to form a supersymmetric oscillator; the conditions that assure supersymmetry invariance of the corresponding dynamical equations are explicitly derived.