Hierarchical equations of motion: Difference between revisions

Revision as of 12:44, 26 July 2022

Revision as of 12:45, 26 July 2022

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The hierarchical equation of motion for a system in a harmonic Markovian bath is<ref name=Tanimura>{{Citation | last = Tanimura| first = Yoshitaka | year = 1990 | authorlink = Yoshitaka Tanimura |title=Nonperturbative expansion method for a quantum system coupled to a harmonic-oscillator bath | journal = Phys. Rev. A | volume = 41| issue = 12 |pages= 6676–6687 | doi = 10.1103/PhysRevA.41.6676 | pmid = 9903081 | bibcode = 1990PhRvA..41.6676T }}</ref>

:<math> \frac{\partial}{\partial t}{\hat{\rho}}_n = -i (\frac{i}{\hbar}\hat{H}^{\times}_A + n\gamma) \hat{\rho}_n - {1i\over\hbar}\hat{V}^{\times}\hat{\rho}_{n+1} + {in\over\hbar}\hat{\Theta}\hat{\rho}_{n-1}</math>

== Hierarchical equations of motion ==