Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function
| Autor: | Iwamoto, Yuki, Tanimura, Yoshitaka |
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| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | J. Comp. Elect. 20, 2091 (2021) |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s10825-021-01754-z |
| Popis: | Discretizing a distribution function in a phase space for an efficient quantum dynamics simulation is a non-trivial challenge, in particular for a case that a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM) most notably by a quantum Fokker-Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we employ a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths. This model is an ideal platform not only for a periodic system but also for a non-periodic system confined by a potential. We then derive the numerically ''exact'' hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. As demonstrations, we numerically integrate the discrete QFPE for a 2D free rotor and harmonic potential systems in a high-temperature Markovian case using a coarse mesh with initial conditions that involve singularity. Comment: 20 pages 5 figures |
| Databáze: | arXiv |
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