Quasi-adiabatic path integral approach for quantum systems under the influence of multiple non-commuting fluctuations

TL;DR

This paper extends the quasi-adiabatic path integral method to handle quantum systems influenced by multiple non-commuting environmental fluctuations, enabling more accurate simulations of complex open quantum systems.

Contribution

The authors develop a modified quasi-adiabatic path integral approach that accounts for non-commuting bath operators, expanding the method's applicability to more general quantum noise scenarios.

Findings

Successfully extended the path integral approach for non-commuting baths.

Achieved convergent results consistent with weak coupling analytical solutions.

Demonstrated the method on a two-level system with multiple baths.

Abstract

Quantum systems are typically subject to various environmental noise sources. Treating these environmental disturbances with a system-bath approach beyond weak coupling one must refer to numerical methods as, for example, the numerically exact quasi-adiabatic path integral approach. This approach, however, cannot treat baths which couple to the system via operators, which do not commute. We extend the quasi-adiabatic path integral approach by determining the time discrete influence functional for such non-commuting fluctuations and by modifying the propagation scheme accordingly. We test the extended quasi-adiabatic path integral approach by determining the time evolution of a quantum two-level system coupled to two independent bath via non-commuting operators. We show that convergent results can be obtained and agreement with analytical weak coupling results is achieved in the respective limits.