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arXiv:1910.05179 · Physical Review A

Decay of a quasistable quantum system and quantum backflow

W. van Dijk, F. Masafumi Toyama

Published Nov 4, 2019• 24 citations
arXivHTMLPDF

Abstract

The decay of quasistable quantum systems involves primarily an outgoing probability current density. However, during the transition from exponential to inverse-power-law decay there are time intervals during which this current, although small, is inward. In this paper this inward flow is associated with quantum backflow. Furthermore substantial backflow exists for time-evolving free wave packets which are initially confined in space.

DOI
10.1103/physreva.100.052101

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The decay of quasistable quantum systems involves primarily an outgoing probability current density. However, during the transition from exponential to inverse-power-law decay there are time intervals during which this current, although small, is inward. In this paper this inward flow is associated with quantum backflow. Furthermore substantial backflow exists for time-evolving free wave packets which are initially confined in space.
Results of theoretical studies of the quantum unstable systems caused that there are rather widespread belief that a universal feature of the quantum decay process is the presence of three time regimes of the decay process: the early time (initial) leading to the Quantum Zeno (or Anti Zeno) Effects, “exponential” (or “canonical”) described by the decay law of the exponential form, and late time characterized by the decay law having inverse-power law form. Based on the fundamental principles of the quantum theory we give the proof that there is no time interval in which the survival probability (decay law) could be a decreasing function of time of the purely exponential form but even at the “exponential” regime the decay curve is oscillatory modulated with a smaller or a large amplitude of oscillations depending on parameters of the model considered.
Quantum backflow is a counterintuitive phenomenon in which the probability density of a quantum particle propagates opposite to its momentum. Experimental observation of backflow has remained elusive due to two main challenges: (i) the effect is intrinsically small, with less than 4% of the probability able to flow backward, and (ii) it requires wave packets with a well-defined momentum direction, which are difficult both to prepare and to verify under realistic, noisy conditions. Here, we overcome these challenges by introducing a general formulation of quantum backflow applicable to arbitrary momentum distributions. The framework recovers the standard backflow limit for unidirectional states and identifies general backflow as probability flow exceeding that predicted by the particle's momentum distribution alone. We show that this excess can reach nearly 13%, surpassing the standard backflow bound by more than a factor of three. Furthermore, we extend the framework to the closely related phenomenon of quantum reentry, provide explicit examples of quantum states exhibiting large general backflow and reentry, and discuss the foundational implications of these nonclassical effects. Our results open a pathway toward the experimental observation of quantum backflow in realistic settings.
We present an introduction to the backflow effect in quantum mechanics – the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. We show that the effect is present even for simple states consisting of superpositions of gaussian wave packets, although the size of the effect is small. Inspired by the numerical results of Penz et al, we present a wave function whose current at any time may be computed analytically and which has periods of significant backflow, with a backwards flux equal to about 70 percent of the maximum possible backflow, a dimensionless number c bm ≈ 0.04, discovered by Bracken and Melloy. This number has the unusual property of being independent of ℏ (and also of all other parameters of the model), despite corresponding to a quantum-mechanical effect, and we shed some light on this surprising property by considering the classical limit of backflow. We conclude by discussing a specific measurement model in which backflow may be identified in certain measurable probabilities.
Quantum backflow is the classically forbidden effect pertaining to the fact that a particle with a positive momentum may exhibit a negative probability current at some space-time point. We investigate how this peculiar phenomenon extends to many-particle systems. We give a general formulation of quantum backflow for systems formed of NNN free nonrelativistic structureless particles, either identical or distinguishable. Restricting our attention to bosonic systems where the NNN identical bosons are in the same one-particle state allows us in particular to analytically show that the maximum achievable amount of quantum backflow in this case becomes arbitrarily small for large values of NNN.
We study the phenomenon of quantum backflow in tight-binding systems with complex couplings, considering different boundary conditions and lattice sizes. Backflow is an intrinsically non-classical effect where the density flux associated with a particle described by the superposition of wave functions with, say, positive momentum, acquires negative values. We calculate the superposition of positive momentum states that gives rise to the strongest backflow in the system. We also evaluate the bounds on the total amount of probability that flows in the opposite direction of the particle's momentum.
Abstract Quantum backflow is the unexpected effect that wavepackets consisting of only positive momentum components can apparently move in the negative direction. This is usually described in terms of the backflow constant, which is a dimensionless quantity describing least upper bound on the amount of probability that can flow backwards during a given time interval. Backflow is usually calculated for wavepackets that can be written as a sum of positive momentum plane waves. Here we present a calculation of the backflow constant using the localised free particle hermite wavefunctions where equal weights of positive and negative momentum eigenfunctions occur. The resulting backflow constant is substantially smaller than the accepted value. The reasons for this are discussed and finally we draw conclusions about the calculation of backflow more generally.