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ANALYTICAL MECHANICS IN STOCHASTIC DYNAMICS: MOST PROBABLE PATH, LARGE-DEVIATION RATE FUNCTION AND HAMILTON–JACOBI EQUATION [PDF]
International Journal of Modern Physics B, 2012 Analytical (rational) mechanics is the mathematical structure of Newtonian deterministic dynamics developed by D'Alembert, Lagrange, Hamilton, Jacobi, and many other luminaries of applied mathematics. Diffusion as a stochastic process of an overdamped individual particle immersed in a fluid, initiated by Einstein, Smoluchowski, Langevin and Wiener ...
Ge, Hao, Qian, Hong
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The World as a Neural Network [PDF]
Entropy, 2020 We discuss a possibility that the entire universe on its most fundamental level is a neural network. We identify two different types of dynamical degrees of freedom: “trainable” variables (e.g., bias vector or weight matrix) and “hidden” variables (e.g.,
Vitaly Vanchurin
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Mechanics of infinitesimal gyroscopes on helicoid-catenoid deformation family of minimal surfaces [PDF]
Bulletin of the Polish Academy of Sciences: Technical Sciences, 2021 In this paper we explore the mechanics of infinitesimal gyroscopes (test bodies with internal degrees of freedom) moving on an arbitrary member of the helicoid-catenoid family of minimal surfaces.
Vasyl Kovalchuk +2 more
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Diffusion Effect in Quantum Hydrodynamics
Axioms, 2022 In this paper, we introduce (at least formally) a diffusion effect that is based on an axiom postulated by Werner Heisenberg in the early days of quantum mechanics.
Moise Bonilla-Licea +2 more
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Bohm's potential, classical/quantum duality and repulsive gravity
Physics Letters B, 2019 We propose the notion of a classical/quantum duality in the gravitational case (it can be extended to other interactions). By this one means exchanging Bohm's quantum potential for the classical potential VQ↔V in the stationary quantum Hamilton–Jacobi ...
Carlos Castro Perelman
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Representation Formula for Solutions of Eikonal Type Equations
Nonlinear Analysis, 2001 Equations of an eikonal type ones arise in many areas of applications, including optics, fluid mechanics, material sciences, and control theory. This article investigates the representation formula for semiconcave solutions of the boundary problem for ...
Gintautas Gudynas
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Gauge Invariance of Nonlinear Klein-Gordon
Positron, 2013 We have discussed the gauge invariance of nonlinear Klein-Gordon equation which describes the interaction of electromagnetic initially proposed by Hermann Weyl. The construction of nonlinear Klein-Gordon itself is formulated by two classical conservation
T. B. Prayitno
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Derivation of the Schrödinger equation from the Hamilton–Jacobi equation in Feynman's path integral formulation of quantum mechanics [PDF]
European Journal of Physics, 2010 It is shown how the time-dependent Schr dinger equation may be simply derived from the dynamical postulate of Feynman's path integral formulation of quantum mechanics and the Hamilton-Jacobi equation of classical mechanics. Schr dinger's own published derivations of quantum wave equations, the first of which was also based on the Hamilton-Jacobi ...
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Covariant GUP Deformed Hamilton-Jacobi Method
Advances in High Energy Physics, 2017 We first briefly revisit the original Hamilton-Jacobi method and show that the Hamilton-Jacobi equation for the action I of tunneling of a fermionic particle from a charged black hole can be written in the same form of that for a scalar particle.
Benrong Mu, Peng Wang, Haitang Yang
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Известия Иркутского государственного университета: Серия "Математика", 2019 This study is concerned with a system of two nonlinear first order partial differential equations. The right-hand sides of the system contain the squares of the gradients of the unknown functions.
A.A. Kosov +2 more
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