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arXiv:2609.26548 · Physical Review A

Magnetic tuning of quantum backflow: Schrödinger vs Pauli system

Tomasz Radozycki

quant-phSubmitted Sep 22, 2026• Announced Sep 23, 2026• 0 citations
arXivHTMLPDF

Abstract

Probability backflow is investigated for charged spin-$1/2$ particles in a uniform magnetic field within the lowest-Landau-level approximation. While single-mode Landau states exhibit only weak and non-robust backflow, it is shown that two-mode interference gives rise to negative probability flux in both the Schrödinger and Pauli formulations. In the Pauli case, orbital and spin contributions to the probability current are explicitly separated, revealing an additional interference mechanism. The external magnetic field is found to act as a tunable control parameter, simultaneously controlling the spatial overlap of orbitals and the spin dynamics. In the two-mode regime, a resonance between orbital mismatch and spin precession leads to an enhancement of backflow. Finite spatial resolution is shown not to suppress the effect within realistic coarse-graining. These results establish magnetic-field-controlled quantum backflow in Landau systems as an accessible interference phenomenon.

Journal reference
Phys. Rev. A 114, 032216(2026)
DOI
10.1103/3jq6-ql82

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Probability backflow is investigated for charged spin-1/21/21/2 particles in a uniform magnetic field within the lowest-Landau-level approximation. While single-mode Landau states exhibit only weak and non-robust backflow, it is shown that two-mode interference gives rise to negative probability flux in both the Schrödinger and Pauli formulations. In the Pauli case, orbital and spin contributions to the probability current are explicitly separated, revealing an additional interference mechanism. The external magnetic field is found to act as a tunable control parameter, simultaneously controlling the spatial overlap of orbitals and the spin dynamics. In the two-mode regime, a resonance between orbital mismatch and spin precession leads to an enhancement of backflow. Finite spatial resolution is shown not to suppress the effect within realistic coarse-graining. These results establish magnetic-field-controlled quantum backflow in Landau systems as an accessible interference phenomenon.
We show that quantum backflow in spin-12\tfrac{1}{2}21​ systems within the Pauli framework can arise from spin-dependent contributions to the probability current. We construct explicit two-mode states in which the orbital current reduces to a uniform drift, so that no interference between longitudinal momentum components is present in this sector. In such configurations, backflow is generated entirely by spinor structure, which induces time-dependent modulations of the local current leading to flux reversal, while the longitudinal momentum distribution remains strictly supported on positive momenta. We derive analytical conditions for backflow in terms of spinor and momentum parameters, allowing direct control of the effect via internal degrees of freedom. We further analyze spatial coarse-graining, showing exponential suppression of interference and a qualitatively different scaling of orbital and spin contributions, with spin-induced backflow remaining robust in regimes where orbital effects are strongly suppressed.
Abstract Landau–Zener–Stückelberg interferometry is extensively investigated in a 3D heterostructure magnetic quantum wire. Local magnetic fields are used to coherently manipulate and control a qubit’s quantum state. For our numerical calculations, a parabolic confinement is assumed. Energy eigenvalues, non-adiabatic and adiabatic transition probabilities are calculated from the diabatic and adiabatic bases for two-level systems. Here, we show that the spatial crossing between interspin levels becomes a spatial anticrossing if the two spin states are coupled by external fields, and that consequently, due to the spin dependence of the harmonic confinement, it will undergo Landau–Zener–Stückelberg interference. It is shown that the system undergoes nonadiabatic Landau–Zener dynamics for a strong confinement in a strong external field, whereas a weak external field induces adiabatic Landau–Zener transition dynamics. Our system allows the coupling strength between the level states at the anti(crossing) point to be modulated. This system allows one to tune the wire’s parabolic confinement potential using experimentally accessible parameters.
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.
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 the maximal amount of backflow has been found to be bounded. Quantum backflow exhibits dramatically different features in two-dimensional systems that, in contrast to the one-dimensional case, allow for degenerate energy eigenstates. Here we investigate the case of a charged particle that is confined to move on a finite disk punctured at the center and that is pierced through the center, and normally to the disk, by a magnetic flux line. We demonstrate that quantum backflow can be unbounded (in a certain sense), which makes this system a promising physical platform regarding the yet-to-be-performed experimental observation of this fundamental quantum phenomenon.
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 put forward a new, "experiment-friendly" formulation of quantum backflow that aims at extending the notion of quantum backflow to situations in which the particle's state may have both positive and negative momenta. Here, we investigate how the experiment-friendly formulation of quantum backflow compares to the standard one when applied to a free particle in a positive-momentum state. We show that the two formulations are not always compatible. We further identify a parametric regime in which the two formulations appear to be in qualitative agreement with one another.
It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.