A classical analog of the quantum Zeeman effect
- URL: http://arxiv.org/abs/2202.06715v1
- Date: Mon, 14 Feb 2022 14:04:12 GMT
- Title: A classical analog of the quantum Zeeman effect
- Authors: Pierre Jamet, Aur\'elien Drezet
- Abstract summary: We study the contribution of a uniform weak magnetic field on their dynamics.
We are able to recover the splitting of the energy levels of the atom called Zeeman's effect.
Our work, based on the old double solution' theory of de Broglie, shows that a dualistic model involving a particle guided by a scalar field can reproduce the normal Zeeman effect.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We extend a recent classical mechanical analog of Bohr's atom consisting of a
scalar field coupled to a massive point-like particle [P. Jamet, A. Drezet, ``A
mechanical analog of Bohr's atom based on de Broglie's double-solution
approach'', Chaos 31, 103120 (2021)] by adding and studying the contribution of
a uniform weak magnetic field on their dynamics. In doing so, we are able to
recover the splitting of the energy levels of the atom called Zeeman's effect
within the constraints of our model and in agreement with the semiclassical
theory of Sommerfeld. This result is obtained using Larmor's theorem for both
the field and the particle, associating magnetic effects with inertial Coriolis
forces in a rotating frame of reference. Our work, based on the old `double
solution' theory of de Broglie, shows that a dualistic model involving a
particle guided by a scalar field can reproduce the normal Zeeman effect.
Related papers
- 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) - The Unruh effect under the de Broglie-Bohm perspective [0.0]
We use the Schr"odinger picture to obtain the wave functional associated with the Minkowski vacuum in Rindler coordinates.
We compute the power spectra, and we exhibit a very special Bohmian field configuration with remarkable physical properties.
arXiv Detail & Related papers (2023-04-21T14:45:44Z) - Quantum vibrational mode in a cavity confining a massless spinor field [91.3755431537592]
We analyse the reaction of a massless (1+1)-dimensional spinor field to the harmonic motion of one cavity wall.
We demonstrate that the system is able to convert bosons into fermion pairs at the lowest perturbative order.
arXiv Detail & Related papers (2022-09-12T08:21:12Z) - Quantum solitodynamics: Non-linear wave mechanics and pilot-wave theory [0.0]
In 1927 Louis de Broglie proposed an alternative approach to standard quantum mechanics known as the double solution program (DSP)
Our model relies on a relativistic phase harmony' condition locking the phases of the solitonic particle and the guiding wave.
arXiv Detail & Related papers (2022-05-10T07:11:54Z) - Classical analog of qubit logic based on a magnon Bose-Einstein
condensate [52.77024349608834]
We present a classical version of several quantum bit (qubit) functionalities using a two-component magnon Bose-Einstein condensate.
The macroscopic wavefunctions of these two condensates serve as orthonormal basis states that form a system being a classical counterpart of a single qubit.
arXiv Detail & Related papers (2021-11-12T16:14:46Z) - A mechanical analog of Bohr's atom based on de Broglie's double-solution
approach [0.0]
We provide a relativistic model for a classical particle coupled to a scalar wave-field through a holonomic constraint.
This dualistic mechanical analog of the quantum theory is reminiscent of the double-solution approach suggested by de Broglie in 1927.
arXiv Detail & Related papers (2021-06-16T17:53:29Z) - Feynman Functional Integral in the Fokker Theory [62.997667081978825]
equivalence of two formulations of Fokker's quantum theory is proved.
The common basis for the two approaches is the generalized canonical form of Fokker's action.
arXiv Detail & Related papers (2020-11-11T12:10:01Z) - Semi-classical quantisation of magnetic solitons in the anisotropic
Heisenberg quantum chain [21.24186888129542]
We study the structure of semi-classical eigenstates in a weakly-anisotropic quantum Heisenberg spin chain.
Special emphasis is devoted to the simplest types of solutions, describing precessional motion and elliptic magnetisation waves.
arXiv Detail & Related papers (2020-10-14T16:46:11Z) - M\'emoire sur la m\'ecanique quantique et l'approche ondulatoire [0.0]
The aim of this essay is to study the wave mechanics as an alternative to traditional quantum mechanics.
The Copenhagen interpretation has been the subject of much criticism, notably by De Broglie and Einstein.
arXiv Detail & Related papers (2020-08-19T05:50:55Z) - From the open Heisenberg model to the Landau-Lifshitz equation [0.0]
Magnetic systems can be described by the classical Landau-Lifshitz (LL) equation or the fully quantum open Heisenberg model.
We demonstrate that the open Heisenberg model is reduced to a generalized LL equation.
The open dynamic is modeled using spin-boson interactions with a common bosonic reservoir at thermal equilibrium.
arXiv Detail & Related papers (2020-06-28T17:20:59Z) - General quantum-mechanical solution for twisted electrons in a uniform
magnetic field [68.8204255655161]
A theory of twisted (and other structured) paraxial electrons in a uniform magnetic field is developed.
The observable effect of a different behavior of relativistic Laguerre-Gauss beams with opposite directions of the orbital angular momentum penetrating from the free space into a magnetic field is predicted.
arXiv Detail & Related papers (2020-05-13T16:35:10Z)
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.