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100 Years of Quantum Matter Waves: Celebrating the Work of...
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100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: 31 March 2025 | Viewed by 11224

Special Issue Editor

Dr. Aurélien Drezet

E-Mail Website
Guest Editor
Institut NEEL, CNRS and Université Grenoble Alpes, F-38000 Grenoble, France
Interests: quantum matter waves; quantum mechanic; quantum theory; chaos; photonic; nanophotonics

Special Issue Information

Dear Colleagues,

In 1923, Louis de Broglie published the first articles [1–3] theoretically demonstrating how to extend the wave particle duality (discovered by Einstein for photons in 1905) to any material particles, such as electrons, protons or neutrons. This seminal work provided the foundation that paved the way for modern quantum mechanics as developed by Schrodinger, and independently by Heisenberg and subsequently Dirac. Wave mechanics, as it was named by de Broglie, was confirmed by many experiments realized over the years with more and more massive particles such as macromolecules or even Bose–Einstein condensates. At the same time, it is well known that de Broglie was not satisfied with the current form of quantum mechanics. Already in 1927, he proposed two alternative theories: pilot wave theory (rediscovered by David Bohm in 1952) and double-solution theory (where particles are defined as “solitons” solutions of nonlinear wave equations). Like Einstein or Schrodinger (and later John Bell). de Broglie disliked the fact that quantum mechanics is fundamentally indeterministic. Most of all, he wanted a theory where the famous mysteries of quantum mechanics are deciphered and where observers are not playing a central role in the interpretation (i.e., a bit like in classical physics).

For this Symmetry Special Issue celebrating the anniversary of de Broglie’s work, different views of the legacy of his discoveries and ideas would be discussed. Contributions emphasizing the experimental and technological consequences of his work are also welcome. Theoretical and historical works concerning quantum foundations and/or discussing alternative interpretations of quantum mechanics (not necessarily agreeing with the credo of de Broglie) are perfectly suited to this Special Issue. In particular, de Broglie–Bohm like theories (deterministic or stochastic) and models of particles using solitons will be favored. Finally, hydrodynamical or mechanical analogies could be discussed. 

[1] Louis de Broglie, Comptes rendus, Vol. 177, 1923, pp. 507-510
[2] Louis de Broglie, Comptes rendus, Vol. 177, 1923, pp. 548-560
[3] Louis de Broglie, Comptes rendus, Vol. 177, 1923, pp. 630-632

Dr. Aurélien Drezet
Guest Editor

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Keywords

  • quantum matter waves
  • quantum mechanics
  • quantum foundations
  • hydrodynamical
  • mechanical
  • nonlinear wave equations

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Published Papers (6 papers)

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Research

18 pages, 630 KiB  
Article
Rethinking Electron Statistics Rules
by Andras Kovacs and Giorgio Vassallo
Symmetry 2024, 16(9), 1185; https://doi.org/10.3390/sym16091185 - 10 Sep 2024
Viewed by 907
Abstract
The Fermi–Dirac and Bose–Einstein statistics are considered to be key concepts in quantum mechanics, and they are used to explain the occupancy limit of electron orbitals. We investigate the physical origin of these two statistics and uncover that the key determining factor is [...] Read more.
The Fermi–Dirac and Bose–Einstein statistics are considered to be key concepts in quantum mechanics, and they are used to explain the occupancy limit of electron orbitals. We investigate the physical origin of these two statistics and uncover that the key determining factor is whether an individual electron spin is measurable or not. Microscopically, a system with individually measurable electron spins corresponds to the presence of Larmor spin precession in electron–electron interactions, while the non-measurability of individual electron spins corresponds to the absence of Larmor spin precession. Both interaction types are possible, and the favored interaction type is thermodynamically determined. The absence of Larmor spin precession is realized in coherent electron states, and coherent electrons therefore obey Bose–Einstein statistics. Full article
(This article belongs to the Special Issue 100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie)
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12 pages, 11831 KiB  
Article
Revisiting the Two-Dimensional Hydrogen Atom: Azimuthal Wavefunctions for Illustrating s, p, d, and f Orbitals
by Phatlada Sathongpaen, Suphawich Jindanate and Attapon Amthong
Symmetry 2024, 16(9), 1163; https://doi.org/10.3390/sym16091163 - 5 Sep 2024
Cited by 1 | Viewed by 1258
Abstract
The two-dimensional (2D) hydrogen atom is a fundamental atomic model that is important for various technologies based on 2D materials. Here, the atomic model is revisited to enhance understanding of the hydrogen wavefunctions. Unlike in previous studies, we propose an alternative expression of [...] Read more.
The two-dimensional (2D) hydrogen atom is a fundamental atomic model that is important for various technologies based on 2D materials. Here, the atomic model is revisited to enhance understanding of the hydrogen wavefunctions. Unlike in previous studies, we propose an alternative expression of azimuthal wavefunctions, which are the eigenstates of the square of angular momentum and exhibit rotational symmetry. Remarkably, our expression leads to the rotation and oscillation along the azimuthal direction of the probability densities, which do not appear in the conventional wavefunctions. These behaviors are validated by the numerical results obtained through the 2D finite difference approach. Variation in oscillator strengths due to the rotation of wavefunctions is observed in our proposed 2D hydrogen wavefunctions, whereas those due to the conventional wavefunctions remain constant. More importantly, the proposed wavefunctions’ advantage is illustrating the orbital shapes of the planar hydrogen states, whose orientation is labeled here using Cartesian representation for the first time. This study can be applied to visualize the orbital characteristics of the states in quantum confinement with a radial potential. Full article
(This article belongs to the Special Issue 100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie)
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31 pages, 2565 KiB  
Article
Revisiting de Broglie’s Double-Solution Pilot-Wave Theory with a Lorentz-Covariant Lagrangian Framework
by David Darrow and John W. M. Bush
Symmetry 2024, 16(2), 149; https://doi.org/10.3390/sym16020149 - 26 Jan 2024
Cited by 2 | Viewed by 2222
Abstract
The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with [...] Read more.
The relation between de Broglie’s double-solution approach to quantum dynamics and the hydrodynamic pilot-wave system has motivated a number of recent revisitations and extensions of de Broglie’s theory. Building upon these recent developments, we here introduce a rich family of pilot-wave systems, with a view to reformulating and studying de Broglie’s double-solution program in the modern language of classical field theory. Notably, the entire family is local and Lorentz-invariant, follows from a variational principle, and exhibits time-invariant, two-way coupling between particle and pilot-wave field. We first introduce a variational framework for generic pilot-wave systems, including a derivation of particle-wave exchange of Noether currents. We then focus on a particular limit of our system, in which the particle is propelled by the local gradient of its pilot wave. In this case, we see that the Compton-scale oscillations proposed by de Broglie emerge naturally in the form of particle vibrations, and that the vibration modes dynamically adjust to match the Compton frequency in the rest frame of the particle. The underlying field dynamically changes its radiation patterns in order to satisfy the de Broglie relation p=ℏk at the particle’s position, even as the particle momentum p changes. The wave form and frequency thus evolve so as to conform to de Broglie’s harmony of phases, even for unsteady particle motion. We show that the particle is always dressed with a Compton-scale Yukawa wavepacket, independent of its trajectory, and that the associated energy imparts a constant increase to the particle’s inertial mass. Finally, we see that the particle’s wave-induced Compton-scale oscillation gives rise to a classical version of the Heisenberg uncertainty principle. Full article
(This article belongs to the Special Issue 100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie)
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23 pages, 1002 KiB  
Article
de Broglie, General Covariance and a Geometric Background to Quantum Mechanics
by Basil Hiley and Glen Dennis
Symmetry 2024, 16(1), 67; https://doi.org/10.3390/sym16010067 - 4 Jan 2024
Cited by 1 | Viewed by 2231
Abstract
What is striking about de Broglie’s foundational work on wave–particle dualism is the role played by pseudo-Riemannian geometry in his early thinking. While exploring a fully covariant description of the Klein–Gordon equation, he was led to the revolutionary idea that a variable rest [...] Read more.
What is striking about de Broglie’s foundational work on wave–particle dualism is the role played by pseudo-Riemannian geometry in his early thinking. While exploring a fully covariant description of the Klein–Gordon equation, he was led to the revolutionary idea that a variable rest mass was essential. DeWitt later explained that in order to obtain a covariant quantum Hamiltonian, one must supplement the classical Hamiltonian with an additional energy ℏ2Q from which the quantum potential emerges, a potential that Berry has recently shown also arises in classical wave optics. In this paper, we show how these ideas emerge from an essentially geometric structure in which the information normally carried by the wave function is contained within the algebraic description of the geometry itself, within an element of a minimal left ideal. We establish the fundamental importance of conformal symmetry, in which rescaling of the rest mass plays a vital role. Thus, we have the basis for a radically new theory of quantum phenomena based on the process of mass-energy flow. Full article
(This article belongs to the Special Issue 100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie)
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33 pages, 1366 KiB  
Article
Whence Nonlocality? Removing Spooky Action-at-a-Distance from the de Broglie Bohm Pilot-Wave Theory Using a Time-Symmetric Version of the de Broglie Double Solution
by Aurélien Drezet
Symmetry 2024, 16(1), 8; https://doi.org/10.3390/sym16010008 - 19 Dec 2023
Viewed by 1228
Abstract
In this work, we review and extend a version of the old attempt made by Louis de Broglie for interpreting quantum mechanics in realistic terms, namely, the double solution. In this theory, quantum particles are localized waves, i.e., solitons, that are solutions of [...] Read more.
In this work, we review and extend a version of the old attempt made by Louis de Broglie for interpreting quantum mechanics in realistic terms, namely, the double solution. In this theory, quantum particles are localized waves, i.e., solitons, that are solutions of relativistic nonlinear field equations. The theory that we present here is the natural extension of this old work and relies on a strong time-symmetry requiring the presence of advanced and retarded waves converging on particles. Using this method, we are able to justify wave–particle duality and to explain the violations of Bell’s inequalities. Moreover, the theory recovers the predictions of the pilot-wave theory of de Broglie and Bohm, often known as Bohmian mechanics. As a direct consequence, we reinterpret the nonlocal action-at-a-distance in the pilot-wave theory. In the double solution developed here, there is fundamentally no action-at-a-distance but the theory requires a form of superdeterminism driven by time-symmetry. Full article
(This article belongs to the Special Issue 100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie)
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19 pages, 8568 KiB  
Article
Quantum Classical Transition for Mixed States: The Scaled Von Neumann Equation
by S. V. Mousavi and S. Miret-Artés
Symmetry 2023, 15(6), 1184; https://doi.org/10.3390/sym15061184 - 1 Jun 2023
Cited by 3 | Viewed by 1366
Abstract
In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled statistical theory following the [...] Read more.
In this work, we proposed a smooth transition wave equation from a quantum to classical regime in the framework of von Neumann formalism for ensembles and then obtained an equivalent scaled equation. This led us to develop a scaled statistical theory following the well-known Wigner–Moyal approach of quantum mechanics. This scaled nonequilibrium statistical mechanics has in it all the ingredients of the classical and quantum theory described in terms of a continuous parameter displaying all the dynamical regimes in between the two extreme cases. Finally, a simple application of our scaled formalism consisting of reflection from a mirror by computing various quantities, including probability density plots, scaled trajectories, and arrival times, was analyzed. Full article
(This article belongs to the Special Issue 100 Years of Quantum Matter Waves: Celebrating the Work of Louis De Broglie)
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