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Free motion of a quantum particle with the wave function entirely comprised of plane waves with non-negative momenta may be accompanied by negative probability current, an effect called quantum backflow. The effect is weak and fragile, and…

Quantum Physics · Physics 2021-02-25 Arseni Goussev

Quantum backflow is usually understood as a quantum interference phenomenon where probability current of a quantum particle points in the opposite direction to particle's momentum. Here, we quantify the amount of quantum backflow for…

Quantum Physics · Physics 2021-01-13 Marek Miller , Woo Chee Yuan , Rainer Dumke , Tomasz Paterek

Backflow is the phenomenon that the probability current of a quantum particle on the line can flow in the direction opposite to its momentum. In this article, previous investigations of backflow, pertaining to interaction-free dynamics or…

Quantum Physics · Physics 2017-07-24 Henning Bostelmann , Daniela Cadamuro , Gandalf Lechner

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…

Quantum Physics · Physics 2026-03-11 Francisco Ricardo Torres Arvizu , Adrián Ortega , Hernán Larralde

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…

Quantum Physics · Physics 2026-03-03 Tomasz Paterek , Arseni Goussev

Quantum backflow refers to the counterintuitive fact that the probability can flow in the direction opposite to the momentum of a quantum particle. This phenomenon has been seen to be small and fragile for one-dimensional systems, in which…

Quantum Physics · Physics 2025-03-04 Maximilien Barbier , Arseni Goussev , Shashi C. L. Srivastava

Quantum backflow is a counterintuitive effect in which the probability density of a free particle moves in the direction opposite to the particle's momentum. If the particle is electrically charged, then the effect can be viewed as the…

Quantum Physics · Physics 2024-03-05 Arseni Goussev , Jaewoo Joo

It is known that for a non-relativistic quantum particle traveling freely on the $x$-axis, the positional probability can flow in the opposite direction to the particle's velocity. The maximum possible amount of such backflow that can occur…

Quantum Physics · Physics 2016-08-30 A. J. Bracken , J. B. McGuire

We investigate the backflow effect in elementary 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…

Quantum Physics · Physics 2015-06-04 J. M. Yearsley , J J. Halliwell , R. Hartshorn , A. Whitby

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…

Quantum Physics · Physics 2020-09-09 Maximilien Barbier

We present an exhaustive class of states with quantum backflow -- 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. They…

Quantum Physics · Physics 2015-08-13 J. J. Halliwell , E. Gillman , O. Lennon , M. Patel , I. Ramirez

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.…

Quantum Physics · Physics 2015-06-12 J. M. Yearsley , J. J. Halliwell

Quantum backflow is a surprising phenomenon in which a quantum particle, moving in one dimension and with a state of rightwards momentum, can exhibit a net probability transfer to the left-hand half-line over a finite time interval. We…

Quantum Physics · Physics 2025-11-13 Christopher J. Fewster , Harkan J. Kirk-Karakaya

In its standard formulation, quantum backflow is a classically impossible phenomenon in which a free quantum particle in a positive-momentum state exhibits a negative probability current. Recently, Miller et al. [Quantum 5, 379 (2021)] have…

Quantum Physics · Physics 2021-09-08 Maximilien Barbier , Arseni Goussev

We study the quantum backflow problem of a relativistic charged Dirac fermion constrained to move on a ring of radius $R$. Using the relativistic current operator we compute the probability flux through a generic time interval to show…

Quantum Physics · Physics 2023-08-14 Valentin Daniel Paccoia , Orlando Panella , Pinaki Roy

Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…

Quantum Physics · Physics 2017-12-12 Daniela Cadamuro

The decay of quasi-stable quantum system 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…

Quantum Physics · Physics 2019-11-07 Wytse van Dijk , F. Masafumi Toyama

We study the quantum backflow problem in the noncommutative plane. In particular, we have considered a charged particle with and without an oscillator interaction with noncommuting momentum operators and examined angular momentum backflow…

High Energy Physics - Theory · Physics 2020-12-29 V. D. Paccoia , O. Panella , P. Roy

In its original formulation, quantum backflow (QB) is an interference effect that manifests itself as a negative probability transfer for free-particle states comprised of plane waves with only positive momenta. Quantum reentry (QR) is…

Quantum Physics · Physics 2020-08-07 Arseni Goussev

The particle current in a metastable Fermi liquid against a first-order phase transition is calculated at zero temperature. During fluctuations of a droplet of the stable phase, in accordance with the conservation law, not only does an…

Condensed Matter · Physics 2009-10-31 Kei Iida
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