Related papers: Random Matrices and Quantum Hamilton-Jacobi Method
Classical random walks and Markov processes are easily described by Hopf algebras. It is also known that groups and Hopf algebras (quantum groups) lead to classical and quantum diffusions. We study here the more primitive notion of a…
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…
A generalization of the Hamilton-Jacobi theory to arbitrary dynamical systems, including non-Hamiltonian ones, is considered. The generalized Hamilton-Jacobi theory is constructed as a theory of ensemble of identical systems moving in the…
Using the Hamilton-Jacobi method, we solve chemical Fokker-Planck equations within the Gaussian approximation and obtain a simple and compact formula for a conditional probability distribution. The formula holds in general transient…
In this article, we consider a set of trial wave-functions denoted by $| Q \right>$ and an associated set of operators $A_\alpha$ which generate transformations connecting those trial states. Using variational principles, we show that we…
The Hawking radiation is considered as a quantum tunneling process, which can be studied in the framework of the Hamilton-Jacobi method. In this study, we present the wave equation for a mass generating massive and charged scalar particle…
We investigate two methods of constructing a solution of the Schr\"{o}dinger equation from the canonical transformation in classical mechanics. One method shows that we can formulate the solution of the Schr\"{o}dinger equation from linear…
In the frame of Hamilton-Jacobi method, the back-reactions of the radiating particles together with the total entropy change of the whole system are investigated. The emission probability from this process is found to be equivalent to the…
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…
We propose that the Schrodinger equation results from applying the classical wave equation to describe the physical system in which subatomic particles play random motion, thereby leading to quantum mechanics. The physical reality described…
Jacobi's method is a well-known algorithm in linear algebra to diagonalize symmetric matrices by successive elementary rotations. We report about the generalization of these elementary rotations towards canonical transformations acting in…
We show that the quantum Hamilton Jacobi approach to a class of quantum mechanical bound state problems and the Gaussian orthogonal ensemble of random matrix theory are equivalent. The Berry connection for both problems is identical to…
The Hamilton-Jacobi equation of classical mechanics is approached as a model reduction of conservative particle mechanics where the velocity degrees-of-freedom are eliminated. This viewpoint allows an extension of the association of the…
Motivated by recent results in random matrix theory we will study the distributions arising from products of complex Gaussian random matrices and truncations of Haar distributed unitary matrices. We introduce an appropriately general class…
We obtain the time-dependent correlation function describing the evolution of a single spin excitation state in a linear spin chain with isotropic nearest-neighbour XY coupling, where the Hamiltonian is related to the Jacobi matrix of a set…
This paper gives a technically elementary treatment of some aspects of Hamilton-Jacobi theory, especially in relation to the calculus of variations. The second half of the paper describes the application to geometric optics, the…
Some recent experiments claim to show that any model in which a quantum state represents mere information about an underlying physical reality of the system must make predictions which contradict those of quantum theory. The present work…
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
We construct a family of Fourier Integral Operators, defined for arbitrary large times, representing a global parametrix for the Schr\"odinger propagator when the potential is quadratic at infinity. This construction is based on the…
In this note, we characterize the solution of a system of elliptic integro-differential equations describing a phe-notypically structured population subject to mutation, selection and migration. Generalizing an approach based on…