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State space distribution and dynamical flow for closed and open quantum systems

Author(s)
Dodin, Amro; Willard, Adam P.
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Creative Commons Attribution-Noncommercial-Share Alike http://creativecommons.org/licenses/by-nc-sa/4.0/
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Abstract
We present a general formalism for studying the effects of heterogeneity in open quantum systems. We develop this formalism in the state space of density operators, on which ensembles of quantum states can be conveniently represented by probability distributions. We describe how this representation reduces ambiguity in the definition of quantum ensembles by providing the ability to explicitly separate classical and quantum sources of probabilistic uncertainty. We then derive explicit equations of motion for state space distributions of both open and closed quantum systems and demonstrate that resulting dynamics take a fluid mechanical form analogous to a classical probability fluid on Hamiltonian phase space, thus enabling a straightforward quantum generalization of Liouville's theorem. We illustrate the utility of our formalism by analyzing the dynamics of an open two-level system using the state-space formalism that is shown to be consistent with the derived analytical results.
Date issued
2019-04
URI
https://hdl.handle.net/1721.1/125411
Department
Massachusetts Institute of Technology. Department of Chemistry
Journal
The Journal of chemical physics
Publisher
AIP Publishing
Citation
Dodin, Amro and Adam P. Willard. “State space distribution and dynamical flow for closed and open quantum systems.” The Journal of chemical physics 15 (2019): 064106.
Version: Original manuscript
ISSN
0021-9606

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