Related papers: On the Hamilton-Jacobi method in classical and qua…
Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schroedinger equations in harmonic potentials and nonlinear dynamics in Anti-de Sitter…
Simulation of realistic classical mechanical systems is of great importance to many areas of engineering such as robotics, dynamics of rotating machinery and control theory. In this work, we develop quantum algorithms to estimate quantities…
In this paper, we show how to use canonical perturbation theory for dissipative dynamical systems capable of showing limit cycle oscillations. Thus, our work surmounts the hitherto perceived barrier for canonical perturbation theory that it…
In a previous paper a formalism to analyze the dynamical evolution of classical and quantum probability distributions in terms of their moments was presented. Here the application of this formalism to the system of a particle moving on a…
We map the quantum problem of a free bosonic field in a space-time dependent background into a classical problem. $N$ degrees of freedom of a real field in the quantum theory are mapped into $2N^2$ classical simple harmonic oscillators with…
The geometric framework for the Hamilton-Jacobi theory is used to study this theory in the ambient of higher-order mechanical systems, both in the Lagrangian and Hamiltonian formalisms. Thus, we state the corresponding Hamilton-Jacobi…
We associate the stationary harmonic oscillator with time-dependent systems exhibiting non-Hermiticity by means of point transformations. The new systems are exactly solvable, with all-real spectrum, and transit to the Hermitian…
A new form of quasiclassical space-time dynamics for constrained systems reveals how quantum effects can be derived systematically from canonical quantization of gravitational systems. These quasiclassical methods lead to additional fields,…
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…
I show that the classical Hamilton-Jacobi (H-J) equation can be used as a technique to study quantum mechanical problems. I first show that the the Schr\"odinger equation is just the classical H-J equation, constrained by a condition that…
We discuss an alternative version of non- relativistic Newtonian mechanics in terms of a real Hilbert space mathematical framework. It is demonstrated that the physics of this scheme correspondent with the standard formulation.…
We study the motion of a particle in a particular magnetic field configuration both classically and quantum mechanically. For flux-free radially symmetric magnetic fields defined on circular regions, we establish that particle escape speeds…
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.
This article develops a Hamilton--Jacobi theory for non-conservative classical field theories, with particular emphasis on dissipative systems, in the framework of co-oriented k-contact geometry. We introduce evolution k-contact k-vector…
A basic problem in the relativistic quantum Hamilton-Jacobi theory is to understand whether it may admit superluminal solutions. Here we consider the averaging of the speed on a period of the oscillating term which is similar to Dirac's…
It is shown that it is possible to construct the quantum wave functions for non-separable but integrable two-dimensional Hamiltonian systems, by solving suitable Dirichlet boundary values problems inside and outside the regions spanned by…
In complete analogy with the classical situation (which is briefly reviewed) it is possible to define bi-Hamiltonian descriptions for Quantum systems. We also analyze compatible Hermitian structures in full analogy with compatible Poisson…
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…
We present a general approach to the classical dynamical systems simulation. This approach is based on classical systems extension to quantum states. The proposed theory can be applied to analysis of multiple (including non-Hamiltonian)…