Publications

Searching for Bloch wave packets with almost definite momentum direction

A. Goussev and G. V. Morozov
Physical Review A 112, 032223 (2025); e-print: arXiv:2504.12489

The motion of a quantum particle in a one-dimensional periodic potential can be described in terms of Bloch wave packets. Like free-particle wave packets, they can propagate without attenuation. Here, we examine this similarity more closely by investigating whether Bloch wave packets can maintain a definite – or nearly definite – momentum direction, a property inherent to free-particle wave packets. This question is particularly relevant to the feasibility of using solid-state-based systems in the search for the first experimental realization of quantum backflow, a quantum interference effect in which a particle’s probability density flows in a direction opposite to its momentum.

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Quantum backflow for two identical particles

M. Barbier and A. Goussev

New Journal of Physics 27, 033011 (2025); e-print: arXiv:2412.07898

Quantum mechanics introduces the possibility for particles to move in a direction opposite to their momentum—a counter-intuitive and classically impossible phenomenon known as quantum backflow. The magnitude of this effect is relatively small, making its experimental observation, which has yet to be achieved, particularly challenging. Here, we investigate the influence of quantum statistics on the maximal backflow attainable for two identical particles confined to a ring. Notably, we demonstrate that the fermionic statistics significantly impedes quantum backflow compared to the bosonic statistics. Our findings suggest that any future experimental realization of quantum backflow should prioritize systems involving bosons rather than fermions.​

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Quantum backflow current in a ring: Optimal bounds and fractality

A. Goussev, F. Quinque, J. Joo, and A. Burbanks

Physical Review A 110, 022216 (2024); e-print: arXiv:2403.18586

The probability density of a quantum particle moving freely within a circular ring can exhibit local flow patterns inconsistent with its angular momentum, a phenomenon known as quantum backflow. In this study, we examine a quantum particle confined to a ring and prepared in a state composed of a fixed (yet arbitrary) number of lowest-energy eigenstates with nonnegative angular momentum. We investigate the time-dependent behavior of the probability current at a specified point along the ring's circumference. We establish precise lower and upper bounds for this probability current, thereby delineating the exact scope of the quantum backflow effect. We also present an analytical expression for a quantum state that yields a record-high backflow probability transfer, reaching over 95% of the theoretical bound. Furthermore, our investigation yields compelling numerical and analytical evidence supporting the conjecture that the current-versus-time function associated with states maximizing backflow probability transfer forms a fractal curve with a dimension of 7/4. The observed fractality may provide a characteristic, experimentally relevant signature of quantum backflow near the probability-transfer bound.

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