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Reconstruction of Quantum Field Equations from Multi-Branch Hamilton–Jacobi Structures
FoundationsWe develop a framework in which quantum field equations are reconstructed from a multi-branch Hamilton–Jacobi structure supplemented by density functionals on configuration space.
Cécile Barbachoux
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Mean Field Game with Delay: A Toy Model
Risks, 2018 We study a toy model of linear-quadratic mean field game with delay. We “lift” the delayed dynamic into an infinite dimensional space, and recast the mean field game system which is made of a forward Kolmogorov equation and a backward ...
Jean-Pierre Fouque, Zhaoyu Zhang
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Hamilton-Jacobi theory applied to Vlasov's equation
, 1966 Solutions of Vlasov's equation are given in terms of the Hamilton-Jacobi function S for the characteristics. Such solutions are appropriate in order to derive equations for macroscopic quantities which are of interest, for instance, in turbulence ...
D. Pfirsch
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Symmetry, Integrability and Geometry: Methods and Applications, 2008 In a previous work the concept of quantum potential is generalized into extended phase space (EPS) for a particle in linear and harmonic potentials.
Sadolah Nasiri, Samira Bahrami
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Optimal investment models with vintage capital: Dynamic Programming approach [PDF]
The Dynamic Programming approach for a family of optimal investment models with vintage capital is here developed. The problem falls into the class of infinite horizon optimal control problems of PDE's with age structure that have been studied in various
Silvia Faggian, Fausto Gozzi
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The Dual Hamilton–Jacobi Equation and the Poincaré Inequality
MathematicsFollowing the equivalence between logarithmic Sobolev inequalities and hypercontractivity shown by L. Gross, and applying the ideas and methods of the work by Bobkov, Gentil and Ledoux, we would like to establish a new connection between the logarithmic ...
Rigao He +3 more
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Envelopes and nonconvex Hamilton–Jacobi equations [PDF]
Calculus of Variations and Partial Differential Equations, 2013 The author derives a new representation formula for viscosity solutions of nonconvex Hamilton-Jacobi PDEs given by \[ \begin{cases} u_{t}(x,t)+H(Du(x,t)) =0, &(x,t)\in \mathbb{R}^{n}\times (0,+\infty)\\ u(x,0) =g(x), &x\in \mathbb{R}^{n}, \end{cases} \] where \( H:\mathbb{R}^{n}\rightarrow \mathbb{R} \) is a smooth nonconvex Hamiltonian and \( g ...
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Electronic Journal of Differential Equations, 2004 In this paper, we study a specific stochastic differential equation depending on a parameter and obtain a representation of its probability density function in terms of Jacobi Functions.
William Margulies, Dean Zes
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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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Parabolic perturbations of Hamilton–Jacobi equations [PDF]
Fundamenta Mathematicae, 1998 Summary: We consider a parabolic perturbation of the Hamilton-Jacobi equation where the potential is periodic in space and time. We show that any solution converges to a limit not depending on initial conditions.
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