Efficient simulation of non-Markovian system-environment interaction

Abstract

In this work, we combine an established method for open quantum systems—the time evolving density matrix using orthogonal polynomials algorithm—with the transfer tensors formalism, a new tool for the analysis, compression and propagation of non-Markovian processes. A compact propagator is generated out of sample trajectories covering the correlation time of the bath. This enables the investigation of previously inaccessible long-time dynamics with linear effort, such as those ensuing from low temperature regimes with arbitrary, possibly highly structured, spectral densities. We briefly introduce both methods, followed by a benchmark to prove viability and combination synergies. Subsequently we illustrate the capabilities of this approach at the hand of specific examples and conclude our analysis by highlighting possible further applications of our method.

Keywords

• open quantum systems
• quantum dissipation
• non-Markovian dynamics
• Nakajima–Zwanzig equation
• density matrix renormalization group