Quantum behavior of general time-dependent quadratic systems linearly coupled to a bath

J. Twamley*

*Corresponding author for this work

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

In this paper we solve for the quantum propagator of a general time-dependent system quadratic in both position and momentum, linearly coupled to an infinite bath of harmonic oscillators. We work in the regime where the quantum optical master equation is valid. We map this master equation to a Schrödinger equation on super-Hilbert space and utilize Lie-algebraic techniques to solve for the dynamics in this space. We then map back to the original Hilbert space to obtain the solution of the quantum dynamics. The Lie-algebraic techniques used are preferable to the standard Wei-Norman methods in that only coupled systems of first-order ordinary differential equations and purely algebraic equations need only be solved. We look at two examples.

Original languageEnglish
Pages (from-to)2627-2633
Number of pages7
JournalPhysical Review A
Volume48
Issue number4
DOIs
Publication statusPublished - 1993
Externally publishedYes

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