A unified stochastic formulation of dissipative quantum dynamics. I. Generalized hierarchical equations
Name
1701.05709.pdf
Size
619.59 KB
Format
Adobe PDF
Checksum (MD5)
ce9e8222841d1d78bcec9451bf89f54c
Author(s)
Hsieh, Chang Yu
Cao, Jianshu
Date Issued
January 2018
Journal
The Journal of Chemical Physics
Publisher
American Institute of Physics (AIP)
Citation
Hsieh, Chang-Yu, and Jianshu Cao. “A Unified Stochastic Formulation of Dissipative Quantum Dynamics. I. Generalized Hierarchical Equations.” The Journal of Chemical Physics, vol. 148, no. 1, Jan. 2018, p. 014103.
Version
Original manuscript
Abstract
We extend a standard stochastic theory to study open quantum systems coupled to a generic quantum environment. We exemplify the general framework by studying a two-level quantum system coupled bilinearly to the three fundamental classes of non-interacting particles: bosons, fermions, and spins. In this unified stochastic approach, the generalized stochastic Liouville equation (SLE) formally captures the exact quantum dissipations when noise variables with appropriate statistics for different bath models are applied. Anharmonic effects of a non-Gaussian bath are precisely encoded in the bath multi-time correlation functions that noise variables have to satisfy. Starting from the SLE, we devise a family of generalized hierarchical equations by averaging out the noise variables and expand bath multi-time correlation functions in a complete basis of orthonormal functions. The general hierarchical equations constitute systems of linear equations that provide numerically exact simulations of quantum dynamics. For bosonic bath models, our general hierarchical equation of motion reduces exactly to an extended version of hierarchical equation of motion which allows efficient simulation for arbitrary spectral densities and temperature regimes. Similar efficiency and flexibility can be achieved for the fermionic bath models within our formalism. The spin bath models can be simulated with two complementary approaches in the present formalism. (I) They can be viewed as an example of non-Gaussian bath models and be directly handled with the general hierarchical equation approach given their multi-time correlation functions. (II) Alternatively, each bath spin can be first mapped onto a pair of fermions and be treated as fermionic environments within the present formalism.
MIT Department
Massachusetts Institute of Technology. Department of Chemistry
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1063/1.5018725
