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

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.

Crossing time in the dissipative Landau–Zener quantum dynamics

“…The quasi-adiabatic path integral (QUAPI) [22,[37][38][39][40] was used to obtain numerical exact results for the dissipative Landau Zener dynamics. QUAPI is based on a symmetric Trotter splitting of the short-time propagator K(t k+1 , t k ) (describing time evolution over a time slice δt) for the full Hamiltonian H. The splitting is by construction exact in the limit δt → 0, but introduces a finite Trotter error for a finite time increment, which has to be eliminated by choosing δt small.…”

“…Generally, valid results are achieved by finding convergence while increasing τ mem but at the same time decreasing δt to minimize the Trotter error. For a detailed discussion on how to achieve convergence regarding these two parameters, see [38,40]. We focus here the investigation on convergence with respect to the key quantities of the paper: P LZ and P ES which reflect additionally the long time limit of the driven dynamics.…”

“…A transverse super Ohmic bath, however, exhibits again a much wider crossing time window which renders a numerical exact simulation even at very small system-bath couplings' challenging. We determine the Landau-Zener and the excited-state survival probabilities numerically exact employing the quasi-adiabatic path integral (QUAPI) [22,37,38,40]. We show that at weak coupling, the adiabatic Markovian non-equilibrium Bloch equations (NEQBs) [35,36] indeed can reliably simulate both.…”

Quantendynamik offener Systeme, Trendbericht Theoretische Chemie 2020, Teil 3

“…Der Einfluss der Umgebung auf den Transferprozess durch nichtdiagonale Ankopplung an das Quantensystem dagegen ist weniger untersucht. Die Behandlung nichtdiagonaler System-Bad-Wechselwirkung 28) und die Berücksichtigung mehrerer, nichtkommutierender Bäder 29) bleiben eine Herausforderung für die numerische Beschreibung offener Quantensysteme.…”

Crossing time in the Landau-Zener quantum dynamics in a super Ohmic environment

“…A transverse super Ohmic bath, however, exhibits again a much wider crossing time window which renders a numerical exact simulation even at very small system-bath couplings challenging. We determine the Landau-Zener and the excited state survival probabilities numerically exact employing the quasi adiabatic path integral (QUAPI) [18,[25][26][27]. We show that at weak coupling the adiabatic Markovian non-equilibrium Bloch equations (NEQBs) [28,29] can reliably simulate both.…”