English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

This paper considers open quantum systems whose dynamic variables satisfycanonical commutation relations and are governed by MarkovianHudson-Parthasarathy quantum stochastic differential equations driven byexternal bosonic fields. The dependence of the Hamiltonian and the system-fieldcoupling operators on the system variables is represented using the Weylfunctional calculus. This leads to an integro-differential equation (IDE) forthe evolution of the quasi-characteristic function (QCF) which encodes thedynamics of mixed moments of the system variables. Unlike quantum masterequations for reduced density operators, this IDE involves only complex-valuedfunctions on finite-dimensional Euclidean spaces and extends the Wigner-Moyalphase-space approach for quantum stochastic systems. The dynamics of the QCFand the related Wigner quasi-probability density function (QPDF) are discussedin more detail for the case when the coupling operators depend linearly on thesystem variables and the Hamiltonian has a nonquadratic part represented in theWeyl quantization form. For this class of quantum stochastic systems, we alsoconsider an approximate computation of invariant states and discuss thedeviation from Gaussian quantum states in terms of the $\chi^2$-divergence (orthe second-order Renyi relative entropy) applied to the QPDF. The results ofthe paper may find applications to investigating different aspects of themoment stability, relaxation dynamics and invariant states in open quantumsystems.

Evolution of quasi-characteristic functions in quantum stochastic systems with Weyl quantization of energy operators