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

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