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The Quantum Hamilton–Jacobi Equation and the Link Between Classical and Quantum Mechanics
Quanta, 2022 We study how the classical Hamilton's principal and characteristic functions are generated from the solutions of the quantum Hamilton–Jacobi equation.
Mario Fusco Girard
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Hamilton-Jacobi Theory for Degenerate Lagrangian Systems with Holonomic and Nonholonomic Constraints [PDF]
, 2012 We extend Hamilton-Jacobi theory to Lagrange-Dirac (or implicit Lagrangian) systems, a generalized formulation of Lagrangian mechanics that can incorporate degenerate Lagrangians as well as holonomic and nonholonomic constraints.
Abraham R. +18 more
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Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole
European Physical Journal C: Particles and Fields, 2017 In curved space-time, the Hamilton–Jacobi equation is a semi-classical particle equation of motion, which plays an important role in the research of black hole physics.
Guo-Ping Li +3 more
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A junction condition by specified homogenization and application to traffic lights [PDF]
, 2015 Given a coercive Hamiltonian which is quasi-convex with respect to the gradient variable and periodic with respect to time and space at least "far away from the origin", we consider the solution of the Cauchy problem of the corresponding Hamilton-Jacobi ...
Galise, Giulio +2 more
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A kinetic eikonal equation [PDF]
, 2012 We analyse the linear kinetic transport equation with a BGK relaxation operator. We study the large scale hyperbolic limit $(t,x)\to (t/\eps,x/\eps)$. We derive a new type of limiting Hamilton-Jacobi equation, which is analogous to the classical eikonal ...
Bouin, Emeric, Calvez, Vincent
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Hypercontractivity of Hamilton–Jacobi equations
Journal de Mathématiques Pures et Appliquées, 2001 Using the equivalence of logarithmic Sobolev inequalities and hypercontractivity of the associated heat semigroup proved by \textit{L. Gross} [Am. J. Math. 97(1975), 1061--1083 (1976; Zbl 0318.46049)], the authors show that logarithmic Sobolev inequalities are similarly related to hypercontractivity of the solutions of Hamilton-Jacobi equations.
Bobkov, Sergey G +2 more
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Hamilton Jacobi Equations with Obstacles [PDF]
Archive for Rational Mechanics and Analysis, 2010 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
De Lellis, Camillo, Robyr, R
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Advances in High Energy Physics, 2016 Based on semiclassical tunneling method, we focus on charged fermions tunneling from higher-dimensional Reissner-Nordström black hole. We first simplify the Dirac equation by semiclassical approximation, and then a semiclassical Hamilton-Jacobi equation ...
ShuZheng Yang, Dan Wen, Kai Lin
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Quantization of Hamiltonian and non-Hamiltonian systems
Communications in Analysis and Mechanics, 2023 The quantization process was always tightly connected to the Hamiltonian formulation of classical mechanics. For non-Hamiltonian systems, traditional quantization algorithms turn out to be unsuitable. Numerous attempts to quantize non-Hamiltonian systems
Sergey A. Rashkovskiy
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