Differential Equation Based Path Integral for System-Bath Dynamics

Abstract

We propose the differential equation based path integral (DEBPI) method to simulate the real-time evolution of open quantum systems. In this method, a system of partial differential equations is derived based on the continuation of a classical numerical method called iterative quasi-adiabatic propagator path integral (i-QuAPI). While the resulting system has infinite equations, we introduce a reasonable closure to obtain a series of finite systems. New numerical schemes can be derived by discretizing these differential equations. It is numerically verified that in certain cases, by selecting appropriate systems and applying suitable numerical schemes, the memory cost required in the i-QuAPI method can be significantly reduced.

29 pages, 9 figures

References in corpus (9)

• Real-time path integral approach to nonequilibrium many-body quantum system
• Diagrammatic Monte Carlo simulation of non-equilibrium systems
• Iterative real-time path integral approach to nonequilibrium quantum transport
• Completely Positive Post-Markovian Master Equation via a Measurement Approach
• Exact master equations for the non-Markovian decay of a qubit
• Inchworm Monte Carlo for exact non-adiabatic dynamics I. Theory and algorithms
• Inchworm Monte Carlo for exact non-adiabatic dynamics II. Benchmarks and comparison with established methods
• Initial System-Environment Correlations via the Transfer Tensor Method
• Inclusion-Exclusion Principle for Open Quantum Systems with Bosonic Bath

Cited by in corpus (5)

• The Bold-Thin-Bold Diagrammatic Monte Carlo Method for Open Quantum Systems
• Tree-based Implementation of the Small Matrix Path Integral for System-Bath Dynamics
• Real-Time Simulation of Open Quantum Spin Chains with Inchworm Method
• Solving Caldeira-Leggett Model by Inchworm Method with Frozen Gaussian Approximation
• Simulation of Spin Chains with off-diagonal Coupling Using Inchworm Method