Generalized Aharonov-Bohm Effect

• URL: http://arxiv.org/abs/2601.17659v1
• Date: Sun, 25 Jan 2026 02:35:26 GMT
• Title: Generalized Aharonov-Bohm Effect
• Authors: Shan Gao,
• Abstract summary: Aharonov-Bohm (AB) effect manifesting as a phase shift for a charged particle in field-free regions.<n>We derive the AB phase shift for a time-dependent magnetic vector potential.<n>For non-circular paths, the phase shift depends on both the flux history and path geometry.
• Score: 7.94562320583783
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Aharonov-Bohm (AB) effect highlights the fundamental role of electromagnetic potentials in quantum mechanics, manifesting as a phase shift for a charged particle in field-free regions. While well-established for static magnetic fluxes, the effect's behavior under time-varying fluxes remains an open and debated question. Employing the WKB method, we derive the AB phase shift for a time-dependent magnetic vector potential, demonstrating that for circular paths in the quasistatic regime, it is proportional to the time-averaged enclosed magnetic flux, \(Δφ_{\rm AB} = \frac{1}{T} \int_0^T e Φ(t) \, dt\), with the total phase shift, including kinetic contributions, equaling \(e Φ(0)\). For non-circular paths, the phase shift depends on both the flux history and path geometry, revealing the effect's hybrid nature involving gauge potentials and induced electric fields. We verify the consistency of our gauge choice with Maxwell's equations and discuss the implications for local versus nonlocal interpretations of the AB effect. We also generalize the results to scenarios with nonzero external magnetic fields, where the enclosed flux is through the actual electron paths, and for circular paths of radius $R$, the AB phase shift is also proportional to the time average of the enclosed flux \(Φ_{\rm enc}(R,t)\), with the total phase shift depending only on the initial enclosed flux \(e Φ_{\rm enc}(R,0)\); for general non-circular paths, the external magnetic field affects trajectories and phase accumulation through the Lorentz force, leading to additional path dependence. These findings clarify the role of gauge-dependent potentials and induced fields in the generalized AB effect, offering new theoretical insights and potential applications in quantum technologies.

Related papers

• Real-time collisions of fractional charges in a trapped-ion Jackiw-Rebbi field theory [39.146761527401424]
  We study the effect of back-reaction and quantum fluctuations on the coupled dynamics of the full fermion-boson system.<n>Our results reveal how back-reaction and quantum fluctuations modify the stability and real-time evolution of fractionalized fermions.
  arXiv  Detail & Related papers  (2025-12-08T17:34:53Z)
• Generalised fractional Rabi problem [35.18016233072556]
  Fractional quantum dynamics provides a natural framework to capture nonlocal temporal behavior and memory effects in quantum systems.<n>In this work, we analyze the physical consequences of fractional-order quantum evolution using a Green's function formulation based on the Caputo fractional derivative.<n>We find that even in the absence of external driving, the static Hamiltonian term induces non-trivial spin dynamics with damping features directly linked to the fractional temporal nonlocality.
  arXiv  Detail & Related papers  (2025-10-09T12:51:57Z)
• Generalized Gouy Rotation of Electron Vortex beams in uniform magnetic fields [54.010858975226945]
  The intrinsic rotation of electron vortex beams has been experimentally observed in magnetic fields by breaking the beam's cylindrical symmetry.<n>We introduce and derive the generalized Gouy rotation angle, which links the Gouy phase of an extended Landau state to the experimentally observed angular variation.<n>Our results are, in principle, applicable to any system involving electron vortex beams in uniform magnetic fields.
  arXiv  Detail & Related papers  (2024-07-03T03:29:56Z)
• Gauge invariance of the Aharonov-Bohm effect in a quantum electrodynamics framework [0.0]
  We provide an exact solution for the electromagnetic ground energy due to the interaction of the quantum electromagnetic field with the classical charges and currents. We use first-order perturbation theory to compute an extra change on the electromagnetic ground energy due to the presence of a quantum charged particle.
  arXiv  Detail & Related papers  (2024-05-14T12:20:14Z)
• Spin relaxation in inhomogeneous magnetic fields with depolarizing boundaries [24.03686690579752]
  Field-inhomogeneity-induced relaxation of atomic spins confined in vapor cells with depolarizing walls is studied.<n>In contrast to nuclear spins, such as noble-gas spins, atomic spins in uncoated cells undergo randomization at the boundaries.<n>A deviation in high input-power scenarios arises from pump field attenuation, resulting in a non-uniformly distributed light shift.
  arXiv  Detail & Related papers  (2024-03-13T07:15:50Z)
• Unveiling the Quantum Toroidal Dipole [41.99844472131922]
  We present a complete quantum-mechanical formalism for the TD in a nanostructure.<n>We propose the first spectroscopic method for its direct measurement.<n>This provides a clear experimental blueprint to unveil, measure, and characterize this elusive third multipole moment.
  arXiv  Detail & Related papers  (2024-01-26T13:31:32Z)
• Gauge dependence of the Aharonov-Bohm phase in a quantum electrodynamics framework [0.0]
  The Aharonov-Bohm (AB) phase is usually associated with a line integral of the electromagnetic vector potential generated by an external current source, such as a solenoid. Recent attempts to explain the AB effect through the interaction between a charged particle and an external current, mediated by the exchange of quantum photons, have assumed that the AB phase shift is proportional to the change in interaction energy between the charged particle and the external current source. We critically examine this claim and demonstrate that the phase obtained through this approach is actually gauge-dependent and not an observable for a nonclosed path.
  arXiv  Detail & Related papers  (2023-05-23T12:24:02Z)
• Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $λ\!φ^4$ model [44.99833362998488]
  A quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field. We show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs.
  arXiv  Detail & Related papers  (2023-05-10T12:59:07Z)
• Electrodynamic Aharonov-Bohm effect [0.0]
  We propose an electrodynamic Aharonov-Bohm scheme where a nonzero AB phase difference appears even if the interferometer paths do not enclose a magnetic flux. In the proposal, the current in a solenoid outside the interferometer varies in time while the quantum particle is in a superposition state inside two Faraday cages.
  arXiv  Detail & Related papers  (2023-02-28T13:07:24Z)
• Wave manipulation via delay-engineered periodic potentials [55.41644538483948]
  We discuss the semi-classical transverse trapping of waves by means of an inhomogeneous gauge field. We show that, due to the Kapitza effect, an effective potential proportional to the square of the transverse derivative of the delay arises.
  arXiv  Detail & Related papers  (2022-07-27T11:45:32Z)
• Gauge invariance of the local phase in the Aharonov-Bohm interference: quantum electrodynamic approach [0.0]
  In the Aharonov-Bohm (AB) effect, interference fringes are observed for a charged particle in the absence of the local overlap with the external electromagnetic field. This notion of the apparent nonlocality of the interaction or the significant role of the potential has recently been challenged and are under debate. The quantum electrodynamic approach provides a microscopic picture of the characteristics of the interaction between a charge and an external field.
  arXiv  Detail & Related papers  (2022-06-17T08:31:51Z)
• Shear of the vector potential in the Aharonov-Bohm effect [0.0]
  The Aharonov-Bohm (AB) effect is now largely considered to be a manifestation of geometric phase. We show that a local shear field provides a velocity-dependent, dynamic-phase interaction in the AB effect.
  arXiv  Detail & Related papers  (2021-12-16T21:12:57Z)
• Aharonov-Bohm effect on the generalized Duffin-Kemmer-Petiau oscillator in the Som-Raychaudhuri space-time [30.03335724329084]
  The effect from the parameters of space-time, the frequency of oscillator, the Cornell potential and the magnetic flux on the energy eigenvalues have been analyzed. We find an analogs effect for the bound states from the Aharonov-Bohm effect in our considered system.
  arXiv  Detail & Related papers  (2021-06-23T06:48:42Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.