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Quantum Hamilton-Jacobi equation [PDF]
Physical Review Letters, 1997 The nontrivial transformation of the phase space path integral measure under certain discretized analogues of canonical transformations is computed. This Jacobian is used to derive a quantum analogue of the Hamilton-Jacobi equation for the generating ...
A. Anderson +24 more
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Generalized Hamilton-Jacobi equations for nonholonomic dynamics [PDF]
Journal of Mathematical Physics, 2004 Employing a suitable nonlinear Lagrange functional, we derive generalized Hamilton-Jacobi equations for dynamical systems subject to linear velocity constraints.
Kosmol P. +7 more
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Optimal Trajectories Associated to a Solution of Contingent Hamilton-Jacobi Equation [PDF]
IEEE Conference on Decision and Control, 1987 In this paper we study the existence of optimal trajectories associated with a generalized solution to Hamilton-Jacobi-Bellman equation arising in optimal control. In general, we cannot expect such solutions to be differentiable.
Frankowska, H.
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On controlled Hamilton and Hamilton–Jacobi differential equations of higher-order [PDF]
Scientific Reports, 2022 In this paper, we investigate the nonlinear dynamics associated with controlled Lagrangians involving higher-order derivatives. More precisely, we establish the controlled higher-order Hamilton ordinary differential equations (ODEs) and Hamilton–Jacobi ...
Savin Treanţă +2 more
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Dynamic programming principle for backward doubly stochastic recursive optimal control problem and sobolev weak solution of the stochastic Hamilton-Jacobi-Bellman equation [PDF]
Fundamental ResearchIn this paper, we investigate a backward doubly stochastic recursive optimal control problem wherein the cost function is expressed as the solution to a backward doubly stochastic differential equation.
Yunhong Li +3 more
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Hamilton–Jacobi equations [PDF]
, 2010 In this chapter we discuss numerical methods for the solution of general Hamilton-Jacobi equations of the form $${\phi _t} + H\left( {\nabla \phi } \right) = 0$$ (5.1) where H can be a function of both space and time. In three spatial dimensions, we can write $${\phi _t} + H\left( {{\phi _x},{\phi _y},{\phi _z}} \right) = 0$$ (5.2 ...
Stanley Osher, Ronald Fedkiw
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Spinning black holes with a separable Hamilton–Jacobi equation from a modified Newman–Janis algorithm [PDF]
The European Physical Journal C, 2020 Obtaining solutions of the Einstein field equations describing spinning compact bodies is typically challenging. The Newman–Janis algorithm provides a procedure to obtain rotating spacetimes from a static, spherically symmetric, seed metric.
H. C. L. Junior +3 more
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The Parisi formula is a Hamilton–Jacobi equation in Wasserstein space
Canadian Journal of Mathematics - Journal Canadien de Mathematiques, 2021 The Parisi formula is a self-contained description of the infinite-volume limit of the free energy of mean-field spin glass models. We showthat this quantity can be recast as the solution of a Hamilton–Jacobi equation in the Wasserstein space of ...
J. Mourrat
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Mathematics in Engineering, 2023 In recent years there has been intense interest in the vanishing discount problem for Hamilton-Jacobi equations. In the case of the scalar equation, B. Ziliotto has recently given an example of the Hamilton-Jacobi equation having non-convex Hamiltonian ...
Hitoshi Ishii
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Hamilton-Jacobi equation for spinning particles near black holes [PDF]
Physical Review D, 2019 A compact stellar-mass object inspiralling onto a massive black hole deviates from geodesic motion due to radiation-reaction forces as well as finite-size effects. Such post-geodesic deviations need to be included with sufficient precision into wave-form
V. Witzany
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