Related papers: Hamilton-Jacobi equations for nonsymmetric matrix …
We propose a method of free energy calculation for a system of interacting particles arranged in a Bravais lattice. It will be shown how to treat divergences for infinite unbounded systems with "catastrophic" potetntials like Coulomb and…
In this paper, we review the physical concepts of the nonequilibrium techniques for the calculation of free energies applied to magnetic systems using Monte Carlo simulations of different nonequilibrium processes. The methodology allows the…
We consider a spherical spin system with pure 2-spin spherical Sherrington-Kirkpatrick Hamiltonian with ferromagnetic Curie-Weiss interaction. The system shows a two-dimensional phase transition with respect to the temperature and the…
The Hamilton Jacobi Bellman Equation (HJB) provides the globally optimal solution to large classes of control problems. Unfortunately, this generality comes at a price, the calculation of such solutions is typically intractible for systems…
We find the free-energy in the thermodynamic limit of a one dimensional XY model associated to a system of N qubits. The coupling among the sigma_i^z is a long range two bodies random interaction. The randomness in the couplings is the…
It has recently been shown that the Helmholtz free energy difference between two equilibrium configurations of a system may be obtained from an ensemble of finite-time (nonequilibrium) measurements of the work performed in switching an…
We investigate both free energy and complexity of the spherical bipartite spin glass model. We first prove a variational formula in high temperature for the limiting free energy based on the well-known Crisanti-Sommers representation of the…
The free energy is a key quantity of interest in Ising models, but unfortunately, computing it in general is computationally intractable. Two popular (variational) approximation schemes for estimating the free energy of general Ising models…
The proposed method of the free energy calculation is based on the approximation of the energy distribution in the microcanonical ensemble by the Gaussian distribution. We hope that our approach will be effective for the systems with…
Calculating relative free energies is a topic of substantial interest and has many applications including solvation and binding free energies, which are used in computational drug discovery. However, there remain the challenges of accuracy,…
We study a diluted mean-field spin glass model with a quadratic Hamiltonian. Our main result establishes the limiting free energy in terms of an integral of a family of random variables that are the weak limits of the quenched variances of…
An expression is derived for the classical free energy difference between two configurations of a system, in terms of an ensemble of finite-time measurements of the work performed in parametrically switching from one configuration to the…
We study continuous dependence estimates for viscous Hamilton- Jacobi equations defined on a network Gamma. Given two Hamilton-Jacobi equations, we prove an estimate of the C2-norm of the difference between the corresponding solutions in…
A simple modification of the definition of the S-matrix is proposed. It is expected that the divergences related to nonzero self-energies are considerably milder with the modified definition than with the usual one. This conjecture is…
We study the periodic homogenization of convex Hamilton-Jacobi equations on perforated domains with Dirichlet boundary conditions. By analyzing the optimal control representation of the solutions and the properties of the metric function…
We discuss a general procedure for arriving at the Hamilton-Jacobi equation of second-class constrained systems, and illustrate it in terms of a number of examples by explicitely obtaining the respective Hamilton principal function, and…
It is known that the joint limit distribution of independent Wigner matrices satisfies a very special asymptotic independence, called freeness. We study the joint convergence of a few other patterned matrices, providing a framework to…
If an absolute reference frame with respect to time, position, or orientation is missing one can only implement quantum operations which are covariant with respect to the corresponding unitary symmetry group G. Extending observations of…
We consider an infinite horizon control problem for dynamics constrained to remain on a multidimensional junction with entry costs. We derive the associated system of Hamilton-Jacobi equations (HJ), prove the comparison principle and that…
We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the…