Related papers: Classical probability waves
A canonical structure compatible with the action of the Lorentz group can be obtained considering the energy and time as conjugate variables of an extended phase space. Scalar probability waves, describing free relativistic particles, are…
We consider a simple quantum system subjected to a classical random force. Under certain conditions it is shown that the noise-averaged Wigner function of the system follows an integro-differential stochastic Liouville equation. In the…
The problem of classical particle in linear potential is studied by using the formalism of Hilbert space and tomographic probability distribution. The Liouville equation for this problem is solved by finding the density matrix satisfying…
A simple position probability density formulation is presented for the motion of a particle in a spherically symmetric potential. The approach provides an alternative to Newtonian methods for presentation in an elementary course, and…
A study of the non-dissipative Brownian motion in vacuum is presented. The noise source associated to the stochastic process assumed in this work is vacuum fluctuations of some quantum field capable of interact with a massive particle. For…
We consider the motion of a particle governed by a weakly random Hamiltonian flow. We identify temporal and spatial scales on which the particle trajectory converges to a spatial Brownian motion. The main technical issue in the proof is to…
We develop a dynamical theory, based on a system of ordinary differential equations describing the motion of particles which reproduces the results of quantum mechanics. The system generalizes the Hamilton equations of classical mechanics…
A unified form for real and complex wave functions is proposed for the stationary case, and the quantum Hamilton-Jacobi equation is derived in the three-dimensional space. The difficulties which appear in Bohm's theory like the vanishing…
We present a canonical phase space approach to stochastic systems described by Langevin equations driven by white noise. Mapping the associated Fokker-Planck equation to a Hamilton-Jacobi equation in the nonperturbative weak noise limit we…
The functional method to derive the fractional Fokker-Planck equation for probability distribution from the Langevin equation with Levy stable noise is proposed. For the Cauchy stable noise we obtain the exact stationary probability density…
The conditions for observation of the particle coordinates, required by logic of the Special Relativity and filtering the quantum field effects, are described. A general relation between the corresponding density of probability and the wave…
This work presents a selective review of results concerning the mathematical interface between the classical and quantum aspects encountered in problems such as the nuclear mean-field dynamics or quantum Brownian motion. It is shown that…
The two-variable Langevin equations, modeling the Brownian motion of a particle moving in a potential and leading to the Maxwell-Boltzmann distribution of the corresponding Fokker-Planck equation, are shown to give rise to types of…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
We generalize the oscillator model of a particle interacting with a thermal reservoir by introducing arbitrary nonlinear couplings in the particle coordinates.The equilibrium positions of the heat bath oscillators are promoted to space-time…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitudes, Born rule,…
Traditionally, the quantum Brownian motion is described by Fokker-Planck or diffusion equations in terms of quasi-probability distribution functions, e.g., Wigner functions. These often become singular or negative in the full quantum…
A new approach to quantum Markov processes is developed and the corresponding Fokker-Planck equation is derived. The latter is examined to reproduce known results from classical and quantum physics. It was also applied to the phase-space…
The coherence properties of the classical waves are discussed in terms of the Cauchy problem for the wave equation, and of a discrete representation by an ensemble of Hamiltonian systems. Wave quanta are related to specific "action fields",…
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (oscillating/spinning solitons), displaying simultaneous particle-like and wave-like behavior.…