Related papers: Random Matrices and Quantum Hamilton-Jacobi Method
In this note, we apply canonical quantization to the self-dual particle system describing the motion of poles to a higher rank solution of the KP hierarchy, explicitly determining both the quantum Hamiltonian and the wave function. It is…
In the first paper of this series, I introduced a non-linear, Hamiltonian, generalization of Schroedinger's theory that blocks formation of macroscopic dispersion ("cats"). But that theory was entirely deterministic, and so the origin of…
Standard approach to dynamical random matrix models relies on the description of trajectories of eigenvalues. Using the analogy from optics, based on the duality between the Fermat principle(trajectories) and the Huygens principle…
A general theory of matrix-spherical functions for dual Hopf algebras and right coideal subalgebras is developed. We establish their existence and define their orthogonality relations. When specialized to Kolb and Letzter's quantum…
In this paper, we develop a quantum hydrodynamics (QHD) method for the research of the quantum evolution of a system of spinning particles. We derived the fundamental equation for charged and neutral spinning particles - the energy…
In this paper, we derive a handable expression for the Jacobi process semi group which is given by a bilinear series involving Jacobi polynomials. Our attempt uses a subordination of the considered process by means of a suitable random…
We propose a new way to perform path integrals in quantum mechanics by using a quantum version of Hamilton-Jacobi theory. In classical mechanics, Hamilton-Jacobi theory is a powerful formalism, however, its utility is not explored in…
Within Bohm`s interpretation of quantum mechanics particles follow classical trajectories that are determined by the full solution of the time dependent Schroedinger equation. If this interpretation is consistent it must be possible to…
The question of the representation of quantum stationary partially polarized waves as random superpositions of different polarization ellipses is addressed. To this end, the Bohmian formulation of quantum mechanics is considered and…
We study the dispersion of a particle whose motion dynamics can be described by a forced velocity jump process. To investigate large deviations results, we study the Chapman-Kolmogorov equation of this process in the hyperbolic scaling…
We study a Hamiltonian system of type describing a charged particle resonant interaction with an electromagnetic wave. We consider an ensemble of particles that repeatedly pass through the resonance with the wave, and study evolution of the…
In this paper, we show that the Kirchhoff equations are derived from the Schr\"odinger equation by assuming the wave function to be a polynomial like solution. These Kirchhoff equations describe the evolution of $n$ point vortices in…
The `dynamic' Hubbard Hamiltonian describes interacting fermions on a lattice whose on-site repulsion is modulated by a coupling to a fluctuating bosonic field. We investigate one such model, introduced by Hirsch, using the determinant…
In this paper we apply quantum hydrodynamics (QHD) to study the quantum evolution of a system of spinning particles and particles that have the electric dipole moments EDM in the rotating reference frame. The method presented is based on…
In this paper we propose and analyze a method based on the Riccati transformation for solving the evolutionary Hamilton-Jacobi-Bellman equation arising from the stochastic dynamic optimal allocation problem. We show how the fully nonlinear…
We find explicit solutions of the Heisenberg equations of motion for a quadratic Hamiltonian, describing a generic model of variable media, in the case of multi-parameter squeezed input photon configuration. The corresponding probability…
In quantum experiments the acquisition and representation of basic experimental information is governed by the multinomial probability distribution. There exist unique random variables, whose standard deviation becomes asymptotically…
Exotic stochastic processes are shown to emerge in the quantum evolution of complex systems. Using influence function techniques, we consider the dynamics of a system coupled to a chaotic subsystem described through random matrix theory. We…
It is shown that any function $G(q_{i}, p_{i}, t)$, defined on the extended phase space, defines a one-parameter group of canonical transformations which act on any function $f(q_{i}, t)$, in such a way that if $G$ is a constant of motion…
The analysis of the Helmholtz equation is shown to lead to an exact Hamiltonian system of equations describing in terms of ray trajectories a very wide family of wave-like phenomena (including diffraction and interference) going much beyond…