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Search Results (1,379)

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Keywords = symmetry theory

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12 pages, 4475 KiB  
Article
High-Q Resonances Induced by Toroidal Dipole Bound States in the Continuum in Terahertz Metasurfaces
by Lincheng Guo and Yachen Gao
Crystals 2025, 15(1), 96; https://doi.org/10.3390/cryst15010096 - 20 Jan 2025
Viewed by 221
Abstract
The radiation mode of the interaction between electromagnetic waves and materials has always been a research hotspot in nanophotonics, and bound states in the continuum (BICs) belong to one of the nonradiative modes. Owing to their high-quality factor characteristics, BICs are extensively employed [...] Read more.
The radiation mode of the interaction between electromagnetic waves and materials has always been a research hotspot in nanophotonics, and bound states in the continuum (BICs) belong to one of the nonradiative modes. Owing to their high-quality factor characteristics, BICs are extensively employed in nonlinear harmonic generators and sensors. Here, the influence of structural parameters on radiation modes has been systematically analyzed using band theory; the mechanisms of quasi-BIC mode and BIC mode were also analyzed through multipole decomposition of scattered power and near-field distribution. Notably, this study presents the discovery that the toroidal dipole-BIC (TD-BIC) arises from the interference and cancellation of electric and toroidal dipoles. The research results indicate that the structure, which supports symmetry-protected BICs, is sensitive to variations in the concentration of NaCl solution in its surroundings, making it applicable for liquid detection in miniaturized metal sensors. The proposed scheme broadens the applicability of BIC-based sensors and provides a prospective platform for biological and chemical sensing. Full article
(This article belongs to the Special Issue Organic Photonics: Organic Optical Functional Materials and Devices)
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55 pages, 18951 KiB  
Article
Structured Dynamics in the Algorithmic Agent
by Giulio Ruffini, Francesca Castaldo and Jakub Vohryzek
Entropy 2025, 27(1), 90; https://doi.org/10.3390/e27010090 - 19 Jan 2025
Viewed by 194
Abstract
In the Kolmogorov Theory of Consciousness, algorithmic agents utilize inferred compressive models to track coarse-grained data produced by simplified world models, capturing regularities that structure subjective experience and guide action planning. Here, we study the dynamical aspects of this framework by examining how [...] Read more.
In the Kolmogorov Theory of Consciousness, algorithmic agents utilize inferred compressive models to track coarse-grained data produced by simplified world models, capturing regularities that structure subjective experience and guide action planning. Here, we study the dynamical aspects of this framework by examining how the requirement of tracking natural data drives the structural and dynamical properties of the agent. We first formalize the notion of a generative model using the language of symmetry from group theory, specifically employing Lie pseudogroups to describe the continuous transformations that characterize invariance in natural data. Then, adopting a generic neural network as a proxy for the agent dynamical system and drawing parallels to Noether’s theorem in physics, we demonstrate that data tracking forces the agent to mirror the symmetry properties of the generative world model. This dual constraint on the agent’s constitutive parameters and dynamical repertoire enforces a hierarchical organization consistent with the manifold hypothesis in the neural network. Our findings bridge perspectives from algorithmic information theory (Kolmogorov complexity, compressive modeling), symmetry (group theory), and dynamics (conservation laws, reduced manifolds), offering insights into the neural correlates of agenthood and structured experience in natural systems, as well as the design of artificial intelligence and computational models of the brain. Full article
15 pages, 2686 KiB  
Article
Quantum-Chemical Investigations on the Structure and Stability of Mixed Trimers Containing HC3N in Combination with H2C2 and/or HCN Analyzed by QTAIM, NBO and SAPT Methods
by Andrea Pietropolli Charmet, Paolo Stoppa, Alessandra De Lorenzi and Patrizia Canton
Symmetry 2025, 17(1), 140; https://doi.org/10.3390/sym17010140 - 18 Jan 2025
Viewed by 321
Abstract
The present work deals with the computational study of HC3N··HCN··H2C2-, (HC3N)2··H2C2-, and HC3N··(H2C2 [...] Read more.
The present work deals with the computational study of HC3N··HCN··H2C2-, (HC3N)2··H2C2-, and HC3N··(H2C2)2-mixed trimers. The different equilibrium structures of the different low-lying minima on the corresponding potential energy surface (PES) were accurately determined, and the relative stabilities were computed by extrapolation procedures to the complete basis set limit. For each mixed trimer, the non-covalent interactions ruling the structure of the most stable isomer were analyzed using the QTAIM (Quantum Theory of Atoms in Molecules) approach. Additional insights into these interactions were provided by the Natural Bond Orbital (NBO) and Symmetry-Adapted Perturbation Theory (SAPT) methods. These results can be used to assist further theoretical investigations and experimental studies on the formation of larger molecules potentially relevant in astrochemistry. Full article
(This article belongs to the Special Issue Chemistry: Symmetry/Asymmetry—Feature Papers and Reviews)
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26 pages, 3630 KiB  
Article
Tailoring Spectral Response of Grating-Assisted Co-Directional Couplers with Weighting Techniques and Rational Transfer Functions: Theory and Experiment
by Anatole Lupu
Photonics 2025, 12(1), 73; https://doi.org/10.3390/photonics12010073 - 15 Jan 2025
Viewed by 295
Abstract
This work addresses the tailoring spectral response of grating-assisted co-directional couplers (GADCs) in the context of wavelength filtering for fiber-to-the-home (FTTH) applications. Design methods for spectral response engineering by means of coupling profile apodization-type weighting techniques and also more advanced rational transfer functions [...] Read more.
This work addresses the tailoring spectral response of grating-assisted co-directional couplers (GADCs) in the context of wavelength filtering for fiber-to-the-home (FTTH) applications. Design methods for spectral response engineering by means of coupling profile apodization-type weighting techniques and also more advanced rational transfer functions fitting a predefined spectral window template are presented. Modeling results based on coupled mode theory are then applied for the design and experimental fabrication of InGaAsP/InP GADCs targeting 1.3+/1.3− µm diplexer application in FTTH access networks. The experimental results are found to be in good agreement with the modeling predictions. The design tools presented are quite general and can be easily adapted to other technology platforms, such as silicon photonics for the use of GADCs as add-drop wavelength division multiplexers. The field of parity–time symmetry is another avenue where these types of gain–loss-assisted GADCs as active components are of interest for switching applications, and the design methods presented here may find utility. Full article
(This article belongs to the Special Issue Silicon-Based Integrated Optics: From Design to Applications)
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45 pages, 4574 KiB  
Review
Chiral Effective Model of Cold and Dense Two-Color QCD: The Linear Sigma Model Approach
by Daiki Suenaga
Symmetry 2025, 17(1), 124; https://doi.org/10.3390/sym17010124 - 15 Jan 2025
Viewed by 335
Abstract
This review is devoted to summarizing recent developments of the linear sigma model (LSM) in cold and dense two-color QCD (QC2D), in which lattice simulations are straightforwardly applicable thanks to the disappearance of the sign problem. In QC2D, both [...] Read more.
This review is devoted to summarizing recent developments of the linear sigma model (LSM) in cold and dense two-color QCD (QC2D), in which lattice simulations are straightforwardly applicable thanks to the disappearance of the sign problem. In QC2D, both theoretical and numerical studies derive the presence of the so-called baryon superfluid phase at a sufficiently large chemical potential (μq), where diquark condensates govern the ground state. The hadron mass spectrum simulated in this phase shows that the mass of an iso-singlet (I=0) and 0 state is remarkably reduced, but such a mode cannot be described by the chiral perturbation theory. Motivated by this fact, I have invented a LSM constructed upon the linear representation of chiral symmetry, more precisely Pauli–Gürsey symmetry. It is shown that my LSM successfully reproduces the low-lying hadron mass spectrum in a broad range of μq simulated on the lattice. As applications of the LSM, topological susceptibility and sound velocity in cold and dense QC2D are evaluated to compare with the lattice results. Additionally, the generalized Gell–Mann–Oakes–Renner relation and hardon mass spectrum in the presence of a diquark source are analyzed. I also introduce an extended version of the LSM incorporating spin-1 hadrons. Full article
(This article belongs to the Special Issue Chiral Symmetry, and Restoration in Nuclear Dense Matter)
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10 pages, 216 KiB  
Article
Issues in the Expansion and Contraction of Operators
by Mukhtarbay Otelbaev, Abdukhali Shynybekov and Karlygash Dosmagulova
Symmetry 2025, 17(1), 117; https://doi.org/10.3390/sym17010117 - 14 Jan 2025
Viewed by 284
Abstract
This paper explores fundamental issues in the correct contraction and expansion of operators, with a primary focus on the concept of symmetry within operator theory. Special attention is given to how symmetry influences the behavior of operators, particularly regarding their approximation and convergence [...] Read more.
This paper explores fundamental issues in the correct contraction and expansion of operators, with a primary focus on the concept of symmetry within operator theory. Special attention is given to how symmetry influences the behavior of operators, particularly regarding their approximation and convergence properties. In the domains of quantum mechanics and condensed matter physics, such operators are essential for modeling phenomena like superconductivity, excitons, and surface states. The symmetric properties of operators have a profound impact on the physical interpretations and predictions these models generate. A rigorous analysis is provided regarding the existence of correct contractions and expansions for a specific class of nonlinear operators, demonstrating how symmetry affects the structural integrity of operators under natural conditions. The study presents a comprehensive description of the set of all correct contractions, expansions, and regular expansions, with an application to a third-order nonlinear differential expression. Additionally, a condition for the unique solvability of a Bitsadze–Samarskii-type problem is derived, showcasing how symmetry plays a crucial role in guiding the solution of complex physical models. Furthermore, the paper emphasizes the importance of preserving symmetry in the construction of operators, ensuring the consistency and accuracy of mathematical models. This has significant implications for both theoretical research and practical applications in various fields, including nuclear physics and quantum theory. Full article
(This article belongs to the Section Mathematics)
17 pages, 4522 KiB  
Article
The Temperature-Dependent Tight Binding Theory Modelling of Strain and Composition Effects on the Electronic Structure of CdSe- and ZnSe-Based Core/Shell Quantum Dots
by Derya Malkoç and Hilmi Ünlü
Materials 2025, 18(2), 283; https://doi.org/10.3390/ma18020283 - 10 Jan 2025
Viewed by 360
Abstract
We propose a temperature-dependent optimization procedure for the second-nearest neighbor (2NN) sp3s* tight-binding (TB) theory parameters to calculate the effects of strain, structure dimensions, and alloy composition on the band structure of heterostructure spherical core/shell quantum dots (QDs). We integrate [...] Read more.
We propose a temperature-dependent optimization procedure for the second-nearest neighbor (2NN) sp3s* tight-binding (TB) theory parameters to calculate the effects of strain, structure dimensions, and alloy composition on the band structure of heterostructure spherical core/shell quantum dots (QDs). We integrate the thermoelastic theory of solids with the 2NN sp3s* TB theory to calculate the strain, core and shell dimensions, and composition effects on the band structure of binary/ternary CdSe/Cd(Zn)S and ZnSe/Zn(Cd)S QDs at any temperature. We show that the 2NN sp3s* TB theory with optimized parameters greatly improves the prediction of the energy dispersion curve at and in the vicinity of L and X symmetry points. We further used the optimized 2NN sp3s* TB parameters to calculate the strain, core and shell dimensions, and composition effects on the nanocrystal bandgaps of binary/ternary CdSe/Cd(Zn)S and ZnSe/Zn(Cd)S core/shell QDs. We conclude that the 2NN sp3s* TB theory provides remarkable agreement with the measured nanocrystal bandgaps of CdSe/Cd(Zn)S and ZnSe/Zn(Cd)S QDs and accurately reproduces the energy dispersion curves of the electronic band structure at any temperature. We believe that the proposed optimization procedure makes the 2NN sp3s* TB theory reliable and accurate in the modeling of core/shell QDs for nanoscale devices. Full article
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19 pages, 271 KiB  
Article
Quaternion Fractional Fourier Transform: Bridging Signal Processing and Probability Theory
by Muhammad Adnan Samad, Yuanqing Xia, Saima Siddiqui, Muhammad Younus Bhat, Didar Urynbassarova and Altyn Urynbassarova
Mathematics 2025, 13(2), 195; https://doi.org/10.3390/math13020195 - 9 Jan 2025
Viewed by 355
Abstract
The one-dimensional quaternion fractional Fourier transform (1DQFRFT) introduces a fractional-order parameter that extends traditional Fourier transform techniques, providing new insights into the analysis of quaternion-valued signals. This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as linearity, the [...] Read more.
The one-dimensional quaternion fractional Fourier transform (1DQFRFT) introduces a fractional-order parameter that extends traditional Fourier transform techniques, providing new insights into the analysis of quaternion-valued signals. This paper presents a rigorous theoretical foundation for the 1DQFRFT, examining essential properties such as linearity, the Plancherel theorem, conjugate symmetry, convolution, and a generalized Parseval’s theorem that collectively demonstrate the transform’s analytical power. We further explore the 1DQFRFT’s unique applications to probabilistic methods, particularly for modeling and analyzing stochastic processes within a quaternionic framework. By bridging quaternionic theory with probability, our study opens avenues for advanced applications in signal processing, communications, and applied mathematics, potentially driving significant advancements in these fields. Full article
29 pages, 4960 KiB  
Article
Effective Text Classification Through Supervised Rough Set-Based Term Weighting
by Rasım Çekik
Symmetry 2025, 17(1), 90; https://doi.org/10.3390/sym17010090 - 9 Jan 2025
Viewed by 470
Abstract
This research presents an innovative approach in text mining based on rough set theory. This study fundamentally utilizes the concept of symmetry from rough set theory to construct indiscernibility matrices and model uncertainties in data analysis, ensuring both methodological structure and solution processes [...] Read more.
This research presents an innovative approach in text mining based on rough set theory. This study fundamentally utilizes the concept of symmetry from rough set theory to construct indiscernibility matrices and model uncertainties in data analysis, ensuring both methodological structure and solution processes remain symmetric. The effective management and analysis of large-scale textual data heavily relies on automated text classification technologies. In this context, term weighting plays a crucial role in determining classification performance. Particularly, supervised term weighting methods that utilize class information have emerged as the most effective approaches. However, the optimal representation of class–term relationships remains an area requiring further research. This study proposes the Rough Multivariate Weighting Scheme (RMWS) and presents its mathematical derivative, the Square Root Rough Multivariate Weighting Scheme (SRMWS). The RMWS model employs rough sets to identify information-carrying documents within the document–term–class space and adopts a computational methodology incorporating α, β, and γ coefficients. Moreover, the distribution of the term among classes is again effectively revealed. Comprehensive experimental studies were conducted on three different datasets featuring imbalanced-multiclass, balanced-multiclass, and imbalanced-binary class structures to evaluate the model’s effectiveness. The results show that RMWS and its derivative SRMWS methods outperform existing approaches by exhibiting superior performance on balanced and unbalanced datasets without being affected by class imbalance and number of classes. Furthermore, the SRMWS method is found to be the most effective for SVM and KNN classifiers, while the RMWS method achieves the best results for NB classifiers. These results show that the proposed methods significantly improve the text classification performance. Full article
(This article belongs to the Section Engineering and Materials)
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16 pages, 3366 KiB  
Article
Integrated Design Symmetry Method for Point Meshing Tooth Surfaces Based on Surface Envelope Approximation Theory
by Kaihong Zhou, Sengang Mo and Shu Li
Symmetry 2025, 17(1), 45; https://doi.org/10.3390/sym17010045 - 30 Dec 2024
Viewed by 297
Abstract
Based on the idea of a surface moving frame in differential geometry, a surface envelopment approximation method is proposed for the integrated design of point-contact tooth surfaces. This method utilizes the envelopment characteristic curve of the first tooth surface as the spline curve [...] Read more.
Based on the idea of a surface moving frame in differential geometry, a surface envelopment approximation method is proposed for the integrated design of point-contact tooth surfaces. This method utilizes the envelopment characteristic curve of the first tooth surface as the spline curve and adopts the local structure of the second tooth surface along a predesigned contact path as the surface interpolation condition. Through motion transformation described by the motion invariants of the first tooth surface, a conjugate motion space for the second tooth surface is fully defined by the motion invariants of the first tooth surface. This constitutes the basis of the integrated optimization design space and ensures the global optimization and machinability of the tooth surface design method. Using the experimental data of the point meshing tooth surface loading contact, the gap between the two tooth surfaces during no-load meshing is used as the design target parameter to predict and control the shape and size of the contact area under heavy load and further the symmetry requirements of the tooth surface design. Consequently, a variational inequality model for the global optimal design of the point meshing tooth surface is established. Full article
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16 pages, 8432 KiB  
Article
Evaluating Partitions in Packet Classification with the Asymmetric Metric of Disassortative Modularity
by Jinshui Wang, Yao Xin, Can Lu, Chengjun Jia and Yiming Ding
Symmetry 2025, 17(1), 37; https://doi.org/10.3390/sym17010037 - 28 Dec 2024
Viewed by 390
Abstract
At present, the method of using rule set partitioning technology to assist in constructing multiple decision trees for packet classification has been widely recognized. Rule set partitioning demonstrates a unique symmetry-breaking mechanism, systematically transforming the initial overlapping rule space into a more structured [...] Read more.
At present, the method of using rule set partitioning technology to assist in constructing multiple decision trees for packet classification has been widely recognized. Rule set partitioning demonstrates a unique symmetry-breaking mechanism, systematically transforming the initial overlapping rule space into a more structured and balanced configuration. By separating overlapping rules in the initial stage, this method significantly reduces rule replication within trees, thereby improving the algorithm’s classification performance. The asymmetric characteristics of this partitioning process are particularly noteworthy: through the strategic disruption of the initial rule set’s symmetric distribution, it creates asymmetric subspaces with enhanced computational efficiency. However, existing research lacks standardized metrics for evaluating the effectiveness of rule set partitioning schemes. The purpose of this paper is to investigate the impact of partitioning on algorithm performance. Based on community structure theory, we construct a weighted graph model for rule sets and propose a disassortative modularity metric to evaluate the effectiveness of rule set partitioning. This metric not only examines intra-community connections but also emphasizes the asymmetric connections between communities. By quantifying these structural features, it provides a novel perspective on rule set partitioning strategies. The experimental results demonstrate a significant positive correlation between disassortative modularity and classification throughput. This metric offers valuable guidance for packet classification partitioning techniques, highlighting the practical significance of symmetry and asymmetry in algorithm design. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Embedded Systems)
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21 pages, 4006 KiB  
Review
Strongly Coupled 𝒫𝒯-Symmetric Models in Holography
by Daniel Areán, David Garcia-Fariña and Karl Landsteiner
Entropy 2025, 27(1), 13; https://doi.org/10.3390/e27010013 - 27 Dec 2024
Viewed by 337
Abstract
Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if PT symmetry is respected, and in that case, an equivalent Hermitian description exists via the so-called Dyson map. Generically, PT-symmetric non-Hermitian theories can also [...] Read more.
Non-Hermitian quantum field theories are a promising tool to study open quantum systems. These theories preserve unitarity if PT symmetry is respected, and in that case, an equivalent Hermitian description exists via the so-called Dyson map. Generically, PT-symmetric non-Hermitian theories can also feature phases where PT symmetry is broken and unitarity is lost. We review the construction of holographic duals to strongly coupled PT-symmetric quantum field theories and the study of their phase diagram. We next focus on spacetime-dependent non-Hermitian couplings: non-Hermitian quenches and lattices. They violate the null energy condition in the gravity dual. The lattices realize phases supporting an imaginary current that breaks PT symmetry spontaneously. Remarkably, these non-Hermitian lattices flow to a PT-symmetric fixed point in the IR. Full article
(This article belongs to the Special Issue Quantum Dynamics with Non-hermitian Hamiltonians II)
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17 pages, 3271 KiB  
Article
Experimental and Theoretical Study of Sc2O3 Nanoparticles Under High Pressure
by André Luis de Jesus Pereira, Juan Angel Sans, Rosario Vilaplana, Sudeshna Ray, Prachi Tadge, Armstrong Godoy, Isabela M. Horta, Argemiro S. da Silva-Sobrinho, Plácida Rodríguez-Hernández, Alfonso Muñoz, Catalin Popescu and Francisco J. Manjón
Minerals 2025, 15(1), 21; https://doi.org/10.3390/min15010021 - 27 Dec 2024
Viewed by 390
Abstract
This study investigates the high-pressure structural and vibrational properties of nano-Sc2O3 using a combination of X-ray diffraction, Raman spectroscopy, and theoretical calculations. Nano-Sc2O3 maintains its cubic bixbyite structure up to 26.4 GPa, without evidence of phase transitions, [...] Read more.
This study investigates the high-pressure structural and vibrational properties of nano-Sc2O3 using a combination of X-ray diffraction, Raman spectroscopy, and theoretical calculations. Nano-Sc2O3 maintains its cubic bixbyite structure up to 26.4 GPa, without evidence of phase transitions, contrasting with bulk Sc2O3, which transitions to a monoclinic phase around 25–28 GPa. Raman spectroscopy reveals a pressure-induced blue shift in the vibrational modes, indicating lattice compression, and the absence of new modes confirms the retention of the cubic symmetry. Theoretical predictions using density functional theory (DFT) closely match the experimental data, validating the computational approach we use to model the pressure-dependent vibrational behavior of nano-Sc2O3. Comparisons with previous studies seem to show that the nanoscale material exhibits enhanced structural stability compared to its bulk counterpart, likely due to size effects and surface energy contributions. These findings provide new insights into the behavior of nanomaterials under extreme conditions and highlight the potential applications of nano-Sc2O3 in high-pressure environments. Full article
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15 pages, 3893 KiB  
Article
Correlative Dynamics of Complex Systems: A Multifractal Perspective of Motion Based on SL(2R) Symmetry
by Vlad Ghizdovat, Emanuel Nazaretian, Catalin Gabriel Dumitras, Maricel Agop, Constantin Placinta, Calin Buzea, Cristina Marcela Rusu, Decebal Vasincu and Zoltan Borsos
Symmetry 2025, 17(1), 27; https://doi.org/10.3390/sym17010027 - 27 Dec 2024
Viewed by 327
Abstract
By assimilating any complex system into a multifractal, a new approach for describing the dynamics of such systems is proposed by means of the Multifractal Theory of Motion. In such context, the description of these dynamics is accomplished through continuous and non-differentiable curves [...] Read more.
By assimilating any complex system into a multifractal, a new approach for describing the dynamics of such systems is proposed by means of the Multifractal Theory of Motion. In such context, the description of these dynamics is accomplished through continuous and non-differentiable curves (multifractal curves), giving rise to two scenarios. The first scenario is a Schrödinger-type multifractal scenario, a situation in which the motion laws can be related to the SL(2R) algebra invariant functions. The second scenario is a Madelung-type multifractal scenario, a situation in which if the differentiable and non-differentiable components of the velocity field satisfy a particular restriction, an SL(2R) symmetry can also be highlighted. Moreover, correlative dynamics in either of the two scenarios, based on the same SL(2R) symmetry, can be obtained by Riccati-type gauges, which imply Stoler coherent states. Several cases induced by the SL(2R) symmetry are also analyzed. Full article
(This article belongs to the Special Issue Symmetry in Nonlinear Dynamics)
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25 pages, 3400 KiB  
Article
A Time-(Anti)symmetric Approach to the Double Solution Theory
by Pierre Jamet and Aurélien Drezet
Foundations 2025, 5(1), 1; https://doi.org/10.3390/foundations5010001 - 25 Dec 2024
Viewed by 342
Abstract
In this work, we present a new theoretical approach to interpreting and reproducing quantum mechanics using trajectory-guided wavelets. Inspired by the 1925 work of Louis de Broglie, we demonstrate that pulses composed of a difference between a delayed wave and an advanced wave [...] Read more.
In this work, we present a new theoretical approach to interpreting and reproducing quantum mechanics using trajectory-guided wavelets. Inspired by the 1925 work of Louis de Broglie, we demonstrate that pulses composed of a difference between a delayed wave and an advanced wave (known as antisymmetric waves) are capable of following quantum trajectories predicted by the de Broglie–Bohm theory (also known as Bohmian mechanics). Our theory reproduces the main results of orthodox quantum mechanics and unlike Bohmian theory, is local in the Bell sense. We show that this is linked to the superdeterminism and past–future (anti)symmetry of our theory. Full article
(This article belongs to the Section Physical Sciences)
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