A novel approach to $ \mathit{q} $-fractional partial differential equations: Unraveling solutions through semi-analytical methods by Khalid K. Ali, Mohamed S. Mohamed, M. Maneea

“…These equations are significant in $ \mathit{q} $-calculus, which has gained attention due to its relevance in engineering applications, particularly in quantum mechanics. In this study, we solve linear and nonlinear $ \mathit{q} $-FPDEs and obtain the closed-form solutions, which confirm the validity of the utilized methods. …”
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From Boole to Leggett-Garg: Epistemology of Bell-Type Inequalities by Karl Hess, Hans De Raedt, Kristel Michielsen

“…In 1985 Leggett and Garg derived a physics related inequality, mathematically identical to Boole’s, that according to them represents a demarcation between macroscopic realism and quantum mechanics. We show that a wide gulf separates the “sense impressions” and corresponding data, as well as the postulates of macroscopic realism, from the mathematical abstractions that are used to derive the inequality of Leggett and Garg. …”
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Shape Invariance of Solvable Schrödinger Equations with the Generalized Hyperbolic Pöschl-Teller Potential by Min Li, Shi-Kun Zhong, Li Dong, Lu-Lin Xiong, Guang Luo

“…First, we introduce briefly the shape invariance and the potential algebra in supersymmetric quantum mechanics. Second, we derive three additive shape invariances, which are related to parameters A and B of the partner potentials with the generalized superpotential, and discuss the eigenfunctions and eigenvalues in detail. …”
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Constraints on Gravitation from Causality and Quantum Consistency by Mark P. Hertzberg

“…We examine the role of consistency with causality and quantum mechanics in determining the properties of gravitation. …”
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An analytical investigation of nonlinear time-fractional Schrödinger and coupled Schrödinger–KdV equations by Yogeshwari F. Patel, Mohammad Izadi

“…This study applies the Fractional Reduced Differential Transform Method (FRDTM) to solve two nonlinear fractional equations: the time-fractional Schrödinger equation (TFSE) and the coupled Schrödinger–KdV (Sch–KdV) equation, which are prominent in quantum mechanics, plasma physics, and wave propagation studies. …”
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Kelsen H. Causality and Retribution / trans. from Engl. А. B. Didikin by А. B. Didikin

“…On the basis of historical and philosophical reconstruction of the philosophical ideas of Heraclitus and Democritus Kelsen traces the evolution of the principle of causality to the present day, including the emergence of new theories in the field of quantum mechanics and mathematics…”
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Two-Party Quantum Private Comparison Protocol Based on Rotational Encryption by Min Hou, Yue Wu

“…By harnessing the principles of quantum mechanics, we ensure robust protection against potential eavesdropping and participant attacks. …”
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Recent Progress on the Description of Relativistic Spin: Vector Model of Spinning Particle and Rotating Body with Gravimagnetic Moment in General Relativity by Alexei A. Deriglazov, Walberto Guzmán Ramírez

“…We describe a number of applications and show how the vector model clarifies some issues presented in theoretical description of a relativistic spin: (A) one-particle relativistic quantum mechanics with positive energies and its relation with the Dirac equation and with relativistic Zitterbewegung; (B) spin-induced noncommutativity and the problem of covariant formalism; (C) three-dimensional acceleration consistent with coordinate-independence of the speed of light in general relativity and rainbow geometry seen by spinning particle; (D) paradoxical behavior of the Mathisson-Papapetrou-Tulczyjew-Dixon equations of a rotating body in ultrarelativistic limit, and equations with improved behavior.…”
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Neutrophil Leukocyte: Combustive Microbicidal Action and Chemiluminescence by Robert C. Allen

“…The necessary principles of particle physics and quantum mechanics are developed and integrated into a fundamental explanation of neutrophil microbicidal metabolism.…”
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PhyICNet: Physics-informed interactive learning convolutional recurrent network for spatiotemporal dynamics by Ruohan Cao, Jin Su, Jinqian Feng, Qin Guo

“…The numerical solution of spatiotemporal partial differential equations (PDEs) using the deep learning method has attracted considerable attention in quantum mechanics, fluid mechanics, and many other natural sciences. …”
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Taming non-analyticities of QFT observables by Thomas W. Grimm, Giovanni Ravazzini, Mick van Vliet

“…Finally, we discuss how the eigenvalues of certain Hamiltonians in quantum mechanics are also definable in ℝ G $$ {\mathbb{R}}_{\mathcal{G}} $$ .…”
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Quantum and Classical Dynamics with Random Permutation Circuits by Bruno Bertini, Katja Klobas, Pavel Kos, Daniel Malz

“…A particularly interesting question concerns the role played by quantum mechanics in this process, i.e., whether thermalization in quantum many-body systems is fundamentally different from that in classical many-body systems and, if so, which of its features are genuinely quantum. …”
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Classical eikonal from Magnus expansion by Joon-Hwi Kim, Jung-Wook Kim, Sungsoo Kim, Sangmin Lee

“…In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. …”
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Lump-type kink wave phenomena of the space-time fractional phi-four equation by Khudhayr A. Rashedi, Musawa Yahya Almusawa, Hassan Almusawa, Tariq S. Alshammari, Adel Almarashi

“…This article examines the space-time fractional phi-four (PF) model which is an improvement of the Klein-Fock-Gordon (KFG) model that is relevant in quantum mechanics, transmission of ultra-short pulses in optical fibers, de Broglie wave duality, and compound particles in spinless relativistic systems. …”
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Structural Predictive Model of Presenilin-2 Protein and Analysis of Structural Effects of Familial Alzheimer’s Disease Mutations by Alejandro Soto-Ospina, Pedronel Araque Marín, Gabriel de Jesús Bedoya, Andrés Villegas Lanau

“…Molecular visualization was carried out with the Chimera 1.14 software, and the theoretical calculation with the hybrid quantum mechanics/molecular mechanics system from the semi-empirical method, with Spartan18 software and an AustinModel1 basis. …”
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Calculation of the molecular properties of five cephalosporins: cephradine, cephalexin, cefadroxil, cefprozil and ceftobiprole by Elso Manuel Cruz Cruz, Eslhey María Sánchez Domínguez

“…<strong><br />Methods:</strong> A theoretical study using quantum mechanics methods to model the structure and electronic properties of the cephalosporins listed above was conducted. …”
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Modulation Instability, Analytical, and Numerical Studies for Integrable Time Fractional Nonlinear Model through Two Explicit Methods by Md. Mamunur Roshid, Mosfiqur Rahman, Mahtab Uddin, Harun Or Roshid

“…The present work deals with the investigation of the time-fractional Klein–Gordon (K-G) model, which has great importance in theoretical physics with applications in various fields, including quantum mechanics and field theory. The main motivation of this work is to analyze modulation instability and soliton solution of the time-fractional K-G model. …”
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Enhanced Lightweight Quantum Key Distribution Protocol for Improved Efficiency and Security by Ashutosh Bhatia, Sainath Bitragunta, Kamlesh Tiwari

“…Quantum Key Distribution (QKD) provides secure communication by leveraging quantum mechanics, with the BB84 protocol being one of its most widely adopted implementations. …”
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Maximal steered coherence in accelerating Unruh–DeWitt detectors by Hong-Wei Li, Yi-Hao Fan, Shu-Ting Shen, Xiao-Jing Yan, Xi-Yun Li, Wei Zhong, Yu-Bo Sheng, Lan Zhou, Ming-Ming Du

“…Abstract Quantum coherence, a fundamental aspect of quantum mechanics, plays a crucial role in various quantum information tasks. …”
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Teaching ideal quantum measurement, from dynamics to interpretation by Allahverdyan, Armen E., Balian, Roger, Nieuwenhuizen, Theo M.

“…This is compatible with the principles of quantum mechanics. Born’s rule then arises from the conservation law for the tested observable; it expresses the frequency of occurrence of the final indications Ai of M in terms of the initial state of S. …”
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