Dissipative quantum backflow

Abstract

Dissipative backflow is studied in the context of open quantum systems. This theoretical analysis is carried out within two frameworks, the effective time-dependent Hamiltonian due to Caldirola-Kanai (CK) and the Caldeira-Leggett (CL) one where a master equation is used to describe the reduced density matrix in presence of dissipation and temperature of the environment. Two examples are considered, the free evolution of one and two Gaussian wave packets as well as the time evolution under a constant field. Backflow is shown to be reduced with dissipation and temperature but never suppressed. Interestingly enough, quantum backflow is observed when considering both one and two Gaussian wave packets within the CL context. Surprisingly, in both cases, the backflow effect seems to be persistent at long times. Furthermore, the constant force $mg\ge 0$ behaves against backflow. However, the classical limit of this quantum effect within the context of the classical Schrödinger equation is shown to be present. Backflow is also analyzed as an eigenvalue problem in the Caldirola-Kanai framework. In the free propagation case, eigenvalues are independent on mass, Planck constant, friction and its duration but, in the constant force case, eigenvalues depend on a factor which itself is a combination of all of them as well as the force constant.

The interpretation of quantum backflow is not correct in the Caldeira-Leggett framework. See the erratum: https://doi.org/10.1140/epjp/s13360-020-00655-7

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Cited by in corpus (10)

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• Observation of single-photon azimuthal backflow with weak measurement
• On some unexplored decoherence aspects in the Caldeira-Leggett formalism: arrival time distributions, identical particles and diffraction in time
• Different routes to the classical limit of backflow
• Quantum backflow for dissipative two-identical-particle systems
• Quantum backflow for two identical particles
• Quantum backflow current in a ring: Optimal bounds and fractality
• Preparing Quantum Backflow States by Large Momentum Transfer