Related papers: Hamilton-Jacobi equations for nonsymmetric matrix …

Superpotentials in ${\cal N}=2$ supersymmetric classical mechanics are no more than the Hamilton characteristic function of the Hamilton-Jacobi theory for the associated purely bosonic dynamical system. Modulo a global sign, there are…

We investigate the thermodynamic limit of the exact solution, which is given by an inhomogeneous $T-Q$ relation, of the one-dimensional supersymmetric $t-J$ model with unparallel boundary magnetic fields. It is shown that the contribution…

Found all equivalence classes for electromagnetic potentials and space-time metrics of Stackel spaces, provided that the equations of motion of the classical charged test particles are integrated by the method of complete separation of…

Using large $N$ arguments, we propose a scheme for calculating the two-point eigenvector correlation function for non-normal random matrices in the large $N$ limit. The setting generalizes the quaternionic extension of free probability to…

We study the Hamilton-Jacobi equation f - lambda Hf = h, where H f = e^{-f}Ae^f and where A is an operator that corresponds to a well-posed martingale problem. We identify an operator that gives viscosity solutions to the Hamilton-Jacobi…

We will analyze the constraint structure of the Einstein-Hilbert first-order action in two dimensions using the Hamilton-Jacobi approach. We will be able to find a set of involutive, as well as a set of non-involutive constraints. Using…

Using a matrix approach, we define the free Jacobi process as the limit of the complex Jacobi matrix process. The we derive a free SDE which is analogous to its classical counterpart. To proceed, we prove that fro suitable parameters the…

We compute the complete topological expansion of the formal hermitian two-matrix model. For this, we refine the previously formulated diagrammatic rules for computing the 1/ N expansion of the nonmixed correlation functions and give a new…

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a…

Motivated by the vanishing contact problem, we study in the present paper the convergence of solutions of Hamilton-Jacobi equations depending nonlinearly on the unknown function. Let $H(x,p,u)$ be a continuous Hamiltonian which is strictly…

We consider the problem of approximating the free energy density of a translation-invariant, one-dimensional quantum spin system with finite range. While the complexity of this problem is nontrivial due to its close connection to problems…

The 'n-equivalences' of boundary conditions of lattice models are introduced and it is derived that the models with n-equivalent boundary conditions result in the identical free energy. It is shown that the free energy of the six-vertex…

We present the diagrammatic technique for calculating the free energy of the matrix eigenvalue model (the model with arbitrary power $\beta$ by the Vandermonde determinant) to all orders of 1/N expansion in the case where the limiting…

Free energy calculations based on atomistic Hamiltonians provide microscopic insight into the thermodynamic driving forces of biophysical or condensed matter systems. Many approaches use intermediate Hamiltonians interpolating between the…

In inflation with nonminimal derivative coupling there is not a conformal transformation to the Einstein frame where calculations are straightforward, and thus in order to extract inflationary observables one needs to perform a detailed and…

In this paper, we give random matrix theory approach to the quantum mechanics using the quantum Hamilton-Jacobi formalism. We show that the bound state problems in quantum mechanics are analogous to solving Gaussian unitary ensemble of…

Convex Q-learning is a recent approach to reinforcement learning, motivated by the possibility of a firmer theory for convergence, and the possibility of making use of greater a priori knowledge regarding policy or value function structure.…

A simple method to deal with four dimensional Hamilton-Jacobi equation for null hypersurfaces is introduced. This method allows to find simple geometrical conditions which give rise to the failure of the WKB approximation on curved…

We present a summary of: 1) the non-uniqueness problem of the Hamiltonian and energy operators associated, in any given coordinate system, with the generally-covariant Dirac equation; 2) two different ways to restrict the gauge freedom so…

Building upon work by Matsumoto, we show that the quantum relative entropy with full-rank second argument is determined by four simple axioms: i) Continuity in the first argument, ii) the validity of the data-processing inequality, iii)…