相关论文: Generalized Hamilton-Jacobi equations for nonholon…
A generalized Hamilton-Jacobi representation describes microstates of the Schr\"odinger wave function for bound states. At the very points that boundary values are applied to the bound state Schr\"odinger wave function, the generalized…
We continue the study of the homogenization of coercive non-convex Hamilton-Jacobi equations in random media identifying two general classes of Hamiltonians with very distinct behavior. For the first class there is no homogenization in a…
A Green's function method is developed for solving strongly-coupled gravity and matter in the semiclassical limit. In the strong-coupling limit, one assumes that Newton's constant approaches infinity. As a result, one may neglect second…
It is shown that the Benney system is equivalent to a one body classical dynamical problem in which the interaction potential is a functional of the action function. The general solution of this equation is responsible for the general…
In this paper, we study the underlying geometry in the classical Hamilton-Jacobi equation. The proposed formalism is also valid for nonholonomic systems. We first introduce the essential geometric ingredients: a vector bundle, a linear…
A general formalism is developed for constructing modified Hamiltonian dynamical systems which preserve a canonical equilibrium distribution by adding a time evolution equation for a single additional thermostat variable. When such systems…
We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…
The solution with respect to the reduced action of the one-dimensional stationary quantum Hamilton-Jacobi equation is well known in the literature. The extension to higher dimensions in the separated variable case was proposed in…
The 'tHooft-Polyakov monopole is treated as constrained system using the Hamilton-Jacobi method. The set of the Hamilton-Jacobi partial differential equations and the equations of motion are obtained. The quantization of the system is also…
A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One…
The Hamilton-Jacobi problem is revisited bearing in mind the consequences arising from a possible bi-Hamiltonian structure. The problem is formulated on the tangent bundle for Lagrangian systems in order to avoid the bias of the existence…
Here, we study Hamilton-Jacobi-Bellman equations on graphs. These are meant to be the analog of any of the following types of equations in the continuum setting of partial differential and nonlocal integro-differential equations:…
We present the Hamilton-Jakobi method for the classical mechanics with constrains in Grassmann algebra. In the frame of this method the solution for the classical system characterized by the SUSY Lagrangian is obtained.
We present the Hamilton-Jakobi method for the classical mechanics with constrains in Grassmann algebra. In the frame of this method the solution for the classical system characterized by the SUSY Lagrangian is obtained.
We provide a dynamic programming principle for stochastic optimal control problems with expectation constraints. A weak formulation, using test functions and a probabilistic relaxation of the constraint, avoids restrictions related to a…
The link between the treatments of constrained systems with fractional derivatives by using both Hamiltonian and Lagrangian formulations is studied. It is shown that both treatments for systems with linear velocities are equivalent.
This paper provides an introduction to some stochastic models of lattice gases out of equilibrium and a discussion of results of various kinds obtained in recent years. Although these models are different in their microscopic features, a…
The equivalence of the chain method and Hamilton-Jacobi formalism is demonstrated. The stabilization algorithm of Hamilton-Jacobi formalism is clariffied and two examples are presented in details.
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…
In this paper, we introduce Hamilton-Jacobi-Bellman (HJB) equations for Q-functions in continuous time optimal control problems with Lipschitz continuous controls. The standard Q-function used in reinforcement learning is shown to be the…