Different routes to the classical limit of backflow

TL;DR

This paper investigates how intrinsic decoherence and dissipative dynamics influence the quantum backflow effect, revealing that backflow diminishes as systems transition towards classical behavior through various theoretical frameworks.

Contribution

It provides a comparative analysis of backflow suppression via intrinsic decoherence models and dissipative dynamics, exploring multiple theoretical approaches to understand the quantum-to-classical transition.

Findings

Backflow is gradually suppressed by intrinsic decoherence.

The route to classicality varies depending on the decoherence mechanism.

Dissipative dynamics from effective Hamiltonians also diminish backflow.

Abstract

Decoherence is a well established process for the emergence of classical mechanics in open quantum systems. However, it can have two different origins or mechanisms depending on the dynamics one is considering, speaking then about intrinsic decoherence for isolated systems and environmental decoherence due to dissipation/fluctuations for open systems. This second mechanism can not be considered for backflow since no thermal fluctuation terms can be added in the formalism in order to keep an important requirement for the occurrence of this effect: only contributions of positive momenta along time should be maintained. The purpose of this work is to analyze the backflow effect in the light of the underlying intrinsic decoherence and the dissipative dynamics. For this goal, we first deal with the Milburn approach where a mean frequency of the unitary evolution steps undergone for the system is assumed. A comparative analysis is carried out in terms of the Lindblad master equation. Second, the so-called quantum-to-classical transition wave equation is analyzed from a linear scaled Schr\"odinger equation which is derived and expressed in terms of a continuous parameter covering from the quantum to the classical regime as well as all in-between dynamical non-classical regimes. This theoretical analysis is inspired by the Wentzel-Kramers-Brillouin approximation. And third, in order to complete our analysis, the transition wave equation formalism is also applied to dissipative backflow within the Caldirola-Kanai approach where the dissipative dynamics comes from an effective Hamiltonian. In all the cases treated here, backflow is gradually suppressed as the intrinsic decoherence process is developing, paying a special attention to the classical limit. The route to classicality is not unique.