Gauge independent description of Aharonov-Bohm Effect
- URL: http://arxiv.org/abs/2209.11091v1
- Date: Thu, 22 Sep 2022 15:23:49 GMT
- Title: Gauge independent description of Aharonov-Bohm Effect
- Authors: Xiang Li, Thors Hans Hansson, and Wei Ku
- Abstract summary: Aharonov-Bohm (AB) effect is a pure quantum effect that implies a measurable phase shift in the wave function for a charged particle.
Classically, such a non-local effect appears to be impossible since the Lorentz force depends on only the magnetic field at the location of the particle.
In quantum mechanics, the Hamiltonian, and thus the Schr"odinger equation, has a local coupling between the current due to the particle, and the electromagnetic vector potential $mathbfA$.
- Score: 3.923738926797954
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: The Aharonov-Bohm (AB) effect is a pure quantum effect that implies a
measurable phase shift in the wave function for a charged particle that
encircles a magnetic flux located in a region \textit{inaccessible} to the
particle. Classically, such a non-local effect appears to be impossible since
the Lorentz force depends on only the magnetic field at the location of the
particle. In quantum mechanics, the Hamiltonian, and thus the Schr\"odinger
equation, has a local coupling between the current due to the particle, and the
electromagnetic vector potential $\mathbf{A}$, which extends to the entire
space beyond the region with finite magnetic field. This has sometimes been
interpreted as meaning that in quantum mechanics $\mathbf{A}$ is in some sense
more "fundamental" than $\mathbf {B}$ in spite of the former being gauge
dependent, and thus unobservable. Here we shall, with a general proof followed
by a few examples, demonstrate that the AB-effect can be fully accounted for by
considering only the gauge invariant $\mathbf{B}$ field, as long as it is
included as part of the quantum action of the entire isolated system. The price
for the gauge invariant formulation is that we must give up locality -- the
AB-phase for the particle will arise from the change in the action for the
$\mathbf{B}$ field in the region inaccessible to the particle.
Related papers
- Magnetization without spin: effective Lagrangian of itinerant electrons [0.0]
The effective Lagrangian at a finite $B$ represents physical effects at $ B neq 0$ properly.
A universal shift of the magnetic field known as Slater-Pauling curve is derived from the effective Lagrangian.
arXiv Detail & Related papers (2024-06-05T10:03:24Z) - Quantum electrodynamics of lossy magnetodielectric samples in vacuum: modified Langevin noise formalism [55.2480439325792]
We analytically derive the modified Langevin noise formalism from the established canonical quantization of the electromagnetic field in macroscopic media.
We prove that each of the two field parts can be expressed in term of particular bosonic operators, which in turn diagonalize the electromagnetic Hamiltonian.
arXiv Detail & Related papers (2024-04-07T14:37:04Z) - A non-hermitean momentum operator for the particle in a box [49.1574468325115]
We show how to construct the corresponding hermitean Hamiltonian for the infinite as well as concrete example.
The resulting Hilbert space can be decomposed into a physical and unphysical subspace.
arXiv Detail & Related papers (2024-03-20T12:51:58Z) - 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) - Small-time controllability for the nonlinear Schr\"odinger equation on
$\mathbb{R}^N$ via bilinear electromagnetic fields [55.2480439325792]
We address the small-time controllability problem for a nonlinear Schr"odinger equation (NLS) on $mathbbRN$ in the presence of magnetic and electric external fields.
In detail, we study when it is possible to control the dynamics of (NLS) as fast as desired via sufficiently large control signals.
arXiv Detail & Related papers (2023-07-28T21:30:44Z) - Aharonov-Bohm effect as a diffusion phenomenon [0.0]
This paper presents a hydrodynamical view of the Aharonov-Bohm effect, using Nelson's formulation of quantum mechanics.
Our aim is to compare our results with other systems and gain a better understanding of the mysteries behind this effect, such as why the motion of a particle is affected in a region where there is no magnetic field.
arXiv Detail & Related papers (2023-07-13T11:03:23Z) - 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) - Aharonov-Bohm effect in phase space [0.0]
We characterize for the first time the Aharonov-Bohm effect within two different formalisms of quantum mechanics.
The aim is to obtain a consistent description of the quantum system by means of the quasiprobability Wigner function.
We study the Aharonov-Bohm effect within them for two specific cases: One determined by a non-zero electric potential, and another determined by a non-zero magnetic vector potential.
arXiv Detail & Related papers (2022-11-23T18:38:58Z) - Spin-1/2 particles under the influence of a uniform magnetic field in
the interior Schwarzschild solution [62.997667081978825]
relativistic wave equation for spin-1/2 particles in the interior Schwarzschild solution in the presence of a uniform magnetic field is obtained.
Results are relevant to the physics of the interior of neutron stars, where both the gravitational and the magnetic fields are very intense.
arXiv Detail & Related papers (2021-11-30T14:46:00Z) - Path integral action in the generalized uncertainty principle framework [0.36832029288386126]
We study the path integral representation of a particle moving in an arbitrary potential using the generalized uncertainty principle (GUP)
First we work out the action of the particle in an arbitrary potential and hence find an upper bound to the velocity of a free particle.
arXiv Detail & Related papers (2021-05-10T13:17:37Z) - 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)
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.