On the effect of decoherence on quantum tunnelling

A Y Klimenko

doi:10.1007/s42452-021-04675-5

Abstract

This work proposes a series of quantum experiments that can, at least in principle, allow for examining microscopic mechanisms associated with decoherence. These experiments can be interpreted as a quantum-mechanical version of non-equilibrium mixing between two volumes separated by a thin interface. One of the principal goals of such experiments is in identifying non-equilibrium conditions when time-symmetric laws give way to time-directional, irreversible processes, which are represented by decoherence at the quantum level. The rate of decoherence is suggested to be examined indirectly, with minimal intrusions—this can be achieved by measuring tunnelling rates that, in turn, are affected by decoherence. Decoherence is understood here as a general process that does not involve any significant exchanges of energy and governed by a particular class of the Kraus operators. The present work analyses different regimes of tunnelling in the presence of decoherence and obtains formulae that link the corresponding rates of tunnelling and decoherence under different conditions. It is shown that the effects on tunnelling of intrinsic decoherence and of decoherence due to unitary interactions with the environment are similar but not the same and can be distinguished in experiments.

Highlights

The goal of this work is to consider experiments that can, at least in principle, examine time-directional quantum effects in an effectively isolated system. Such experiments need to be conducted somewhere at the notional boundary between the microscopic quantum and macroscopic thermodynamic worlds, that is we need to deal with quantum systems that can exhibit some degree of thermodynamic behaviour. This corresponds to persisting decoherence, which is, perhaps, the most fundamental irreversible process that we are aware of—it takes place at the smallest scales, increases entropy [1] and, expectedly, induces various macroscopic effects associated with the thermodynamic arrow of time [2]
This problem represents a quantummechanical version of non-equilibrium mixing between two volumes separated by a thin interface
Among many formulations of tunnelling problems [16,17,18,19,20,21,22], we select one that has a transparent and, at the same time, sufficiently general solution. For this formulation involving quantum tunnelling through a high potential barrier under non-equilibrium conditions, we examine mechanisms that may be responsible for the direction of time

Summary

Introduction

The goal of this work is to consider experiments that can, at least in principle, examine time-directional quantum effects in an effectively isolated system. The present work examines a problem that, at least conceptually, can become an experiment probing the direction of time This problem represents a quantummechanical version of non-equilibrium mixing between two volumes separated by a thin interface. In this quantum version of the classical problem, particles tunnel through the interface and, at the same time, are subject to the omnipresent influence of quantum decoherence, which, presumably, is the fundamental mechanism enacting nonequilibrium, time-directional effects in the macroscopic world [14]

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Discussion

Conclusion