On the time-dependent Aharonov-Bohm effect and the 4-dimensional Stokes theorem

• URL: http://arxiv.org/abs/2406.18046v2
• Date: Sun, 02 Mar 2025 05:08:42 GMT
• Title: On the time-dependent Aharonov-Bohm effect and the 4-dimensional Stokes theorem
• Authors: Masashi Wakamatsu,
• Abstract summary: The time-dependent Aharonov-Bohm (AB) effect considers the situation in which the magnetic flux inside the solenoid changes time-dependently.<n>The difficulty originates from the fact that its theoretical analysis requires line-integrals of the time-dependent vector potential along paths in the 4-dimensional Minkowski space.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The time-dependent Aharonov-Bohm (AB) effect considers the situation in which the magnetic flux inside the solenoid changes time-dependently. Different from the standard AB-effect, the problem is unexpectedly subtle and not easy to solve without any doubt, which is the reason why it is still in a state of unsettlement even theoretically. The difficulty originates from the fact that its theoretical analysis requires line-integrals of the time-dependent vector potential along paths in the 4-dimensional Minkowski space. Owing to the 4-dimensional Stokes theorem, this closed line-integral of the vector potential can be related to the integral of the electric and magnetic fields over the 2-dimensional area, the boundary of which is given by the above-mentioned closed path. The central controversy concerns the success or failure of the claim by Singleton and collaborators based on the 4-dimensional Stokes theorem, which states that the time-dependent part of the AB-phase shift due to the magnetic vector potential is precisely cancelled by the effect of induced electric field generated by the time-variation of the magnetic flux. In the present paper, we carefully reanalyze their cancellation argument by going back to the basic quantum mechanical analysis of the charged particle motion under the presence of the time-dependent external electromagnetic potential combined with more careful treatment of the 4-dimensional Stokes theorem. Careful analysis of the 4-dimensional Stokes theorem shows that the cancellation argument by Singleton et al. is partially correct but their central claim that only the time-independent part of the magnetic field contributes to the AB-phase shift so that there is no time-dependent AB-effect is not justified, thereby supporting likely existence of the time-dependent AB-effect.

Related papers

• Time-dependent adiabatic elimination in matter-wave optics [41.99844472131922]
  We show how the dynamics of a specific subset of states can be separated from the dynamic of the total quantum state.<n>Our formalism allows to perform the adiabatic elimination in such a setting.
  arXiv  Detail & Related papers  (2026-03-02T12:58:57Z)
• Generalized Aharonov-Bohm Effect [7.94562320583783]
  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.
  arXiv  Detail & Related papers  (2026-01-25T02:35:26Z)
• On the role of induced electric field in the time-dependent Aharonov-Bohm effect [0.0]
  The time-dependent Aharonov-Bohm (AB) effect even exists or not has been the subject of long-standing debate.<n>This paper re-investigates the role of the induced electric field with the utmost care.
  arXiv  Detail & Related papers  (2025-11-11T02:46:47Z)
• Time Symmetry, Retrocausality, and Emergent Collapse: The Tlalpan Interpretation of Quantum Mechanics [51.56484100374058]
  The Tlalpan Interpretation (QTI) proposes that the wavefunction collapse is not a primitive, axiomatic rule but an emergent phenomenon.<n>The novelty of QTI lies in its embedding of collapse within the conceptual language of critical phenomena in statistical physics.
  arXiv  Detail & Related papers  (2025-08-25T20:30:56Z)
• The quantum Hall effect under the influence of gravity and inertia: A unified approach [44.99833362998488]
  We examine how both the integer and the fractional quantum Hall effects behave under a combined influence of gravity and inertia. The general Hamiltonian for describing the combined effect of gravity, rotation and inertia on the electrons of a Hall sample is then built and the eigenstates are obtained.
  arXiv  Detail & Related papers  (2024-03-11T18:01:55Z)
• 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)
• Real-time dynamics of false vacuum decay [49.1574468325115]
  We investigate false vacuum decay of a relativistic scalar field in the metastable minimum of an asymmetric double-well potential. We employ the non-perturbative framework of the two-particle irreducible (2PI) quantum effective action at next-to-leading order in a large-N expansion.
  arXiv  Detail & Related papers  (2023-10-06T12:44:48Z)
• Electron Scattering at a Potential Temporal Step Discontinuity [0.27624021966289597]
  We show that the Schrodinger equation cannot account for scattering in this problem. We derive the scattering probabilities, of later forward and backward nature, with the later-backward wave being a relativistic effect.
  arXiv  Detail & Related papers  (2023-07-16T17:33:17Z)
• Adiabatic amplification of energy and magnetic moment of a charged particle after the magnetic field inversion [77.34726150561087]
  We study the evolution of the energy and magnetic moment of a quantum charged particle placed in a homogeneous magnetic field. We show that after a single magnetic field passage through zero value, the famous adiabatic invariant ratio of energy to frequency is reestablished again.
  arXiv  Detail & Related papers  (2023-04-10T00:46:15Z)
• 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)
• Partition of kinetic energy and magnetic moment in dissipative diamagnetism [20.218184785285132]
  We analyze dissipative diamagnetism, arising due to dissipative cyclotron motion in two dimensions, in the light of the quantum counterpart of energy equipartition theorem. The expressions for kinetic energy and magnetic moment are reformulated in the context of superstatistics.
  arXiv  Detail & Related papers  (2022-07-30T08:07:28Z)
• Bound State Formation in Time Dependent Potentials [0.0]
  We study the temporal formation of quantum mechanical bound states within a one-dimensional attractive square-well potential. Our main goal is to study the time scales, in which the bound state is populated and depopulated.
  arXiv  Detail & Related papers  (2022-07-11T14:18:49Z)
• 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)
• New approach to describe two coupled spins in a variable magnetic field [55.41644538483948]
  We describe the evolution of two spins coupled by hyperfine interaction in an external time-dependent magnetic field. We modify the time-dependent Schr"odinger equation through a change of representation. The solution is highly simplified when an adiabatically varying magnetic field perturbs the system.
  arXiv  Detail & Related papers  (2020-11-23T17:29:31Z)
• Probing the coherence of solid-state qubits at avoided crossings [51.805457601192614]
  We study the quantum dynamics of paramagnetic defects interacting with a nuclear spin bath at avoided crossings. The proposed theoretical approach paves the way to designing the coherence properties of spin qubits from first principles.
  arXiv  Detail & Related papers  (2020-10-21T15:37:59Z)
• Three Faces of the Aharonov-Bohm Phase [0.0]
  The Aharonov-Bohm (AB) phase that makes its entry in the above bizarre effect is also deployed to derive the observed magnetic flux quantisation in superconductors. The Dirac result implies that the existence of a single magnetic monopole anywhere in the universe would entail quantisation of the product of a particle's electric charge and the monopole's magnetic charge.
  arXiv  Detail & Related papers  (2020-10-21T13:34:38Z)
• Interference of Clocks: A Quantum Twin Paradox [39.645665748998816]
  Phase of matter waves depends on proper time and is susceptible to special-relativistic (kinematic) and gravitational (redshift) time dilation. It is conceivable that atom interferometers measure general-relativistic time-dilation effects. We show that closed light-pulse interferometers without clock transitions during the pulse sequence are not sensitive to gravitational time dilation in a linear potential.
  arXiv  Detail & Related papers  (2019-05-22T12:30:57Z)

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.