Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function

Abstract

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.

20 pages 5 figures

References in corpus (8)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Real-Time and Imaginary-Time Quantum Hierarchal Fokker-Planck Equations
• Analysis of 2D THz-Raman spectroscopy using a non-Markovian Brownian oscillator model with nonlinear system-bath interactions
• Low-Temperature Quantum Fokker-Planck and Smoluchowski Equations and Their Extension to Multistate Systems
• Modeling and analyzing a photo-driven molecular motor system: Ratchet dynamics and non-linear optical spectra
• An approach to quantum transport based on reduced hierarchy equations of motion: Application to a resonant tunneling diode
• Open Quantum Dynamics of a Three-Dimensional Rotor Calculated Using a Rotationally Invariant System-Bath Hamiltonian: Linear and Two-Dimensional Rotational Spectra

Cited by in corpus (3)

• Discretized hierarchical equations of motion in mixed Liouville--Wigner space for two-dimensional vibrational spectroscopies of liquid water
• Collective bath coordinate mapping of "hierarchy" in hierarchical equations of motion
• Autobiography of Yoshitaka Tanimura