Regensburg 2022 – wissenschaftliches Programm
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QI: Fachverband Quanteninformation
QI 2: Quantum Thermodynamics and Open Quantum Systems
QI 2.5: Vortrag
Montag, 5. September 2022, 10:45–11:00, H9
Quantum trajectories beyond weak coupling — •Brecht Donvil1 and Paolo Muratore Ginanneschi2 — 1Institute for Complex Quantum Systems, Albert-Einstein-Allee 11, D-89069, Ulm — 2University of Helsinki, Department of Mathematics and Statistics P.O. Box 68 FIN-00014, Helsinki, Finland
Master equations are one of the main avenues to study open quantum systems. In situations where the interaction between a dedicated system and its environment is weak, the master equation is of the Lindblad form. In this case, the solution of the master equation can be “unraveled in quantum trajectories” i.e. represented as an average over the realizations of a Markov process in the Hilbert space of the system. Quantum trajectories of this type are both an element of quantum measurement theory as well as a numerical tool for systems in large Hilbert spaces.
In this talk, I show that I show how this procedure can be generalized to arbitrary trace-preserving master equations with time-local dissipation rates. In contrast to the conventional setting, these rates can take also negative values, thus mimicking back-flow of information. Such master equations typically arrive from exactly solvable models or time convoluntionless perturbation theory. The crucial ingredient for our unraveling is to weigh averages by a probability pseudo-measure which we call the “influence martingale”. The influence martingale satisfies a 1d stochastic differential equation enslaved to the ones governing the quantum trajectories. The influence martingale thus extends the existing theory without increasing the computational complexity.