Efficient Real-Time Path Integrals for Non-Markovian Spin-Boson Models

Abstract

Strong coupling between a system and its environment leads to the emergence of non-Markovian dynamics, which cannot be described by a time-local master equation. One way to capture such dynamics is to use numerical real-time path integrals, where assuming a finite bath memory time enables manageable simulation scaling. However, by comparing to the exactly soluble independent boson model, we show that the presence of transient negative decay rates in the exact dynamics can result in simulations with unphysical exponential growth of density matrix elements when the finite memory approximation is used. We therefore reformulate this approximation in such a way that the exact dynamics are reproduced identically and then apply our new method to the spin-boson model with superohmic environmental coupling, commonly used to model phonon environments, but which cannot be solved exactly. Our new method allows us to easily access parameter regimes where we find revivals in population dynamics which are due to non-Markovian backflow of information from the bath to the system.

11 pages, 7 figures

References in corpus (13)

• The numerical renormalization group method for quantum impurity systems
• Real-time dynamics in Quantum Impurity Systems: A Time-dependent Numerical Renormalization Group Approach
• Coherence of Nitrogen-Vacancy Electronic Spin Ensembles in Diamond
• The fundamental role of quantized vibrations in coherent light harvesting by cryptophyte algae
• Phonon induced Rabi frequency renormalization of optically driven single InGaAs/GaAs quantum dots
• Observation of non-Markovian dynamics of a single quantum dot in a micropillar cavity
• Equilibrium and non-equilibrium dynamics of the sub-ohmic spin-boson model
• Thermalization and breakdown of thermalization in photon condensates
• Coherent and incoherent dynamics in excitonic energy transfer: correlated fluctuations and off-resonance effects
• Non-Markovian dynamics of double quantum dot charge qubits due to acoustic phonons
• Dephasing-assisted Gain and Loss in Mesoscopic Quantum Systems
• Keldysh meets Lindblad: Correlated Gain and Loss in Higher-Order Perturbation Theory
• Path integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative system

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