Related papers: Classical probability waves
De Broglie and Bohm formulated a causal quantum mechanics with a phase space density whose integral over momentum reproduces the position probability density of usual statistical quantum theory. We propose a causal quantum theory with a…
The interaction of charged particles, moving in a uniform magnetic field, with a plane-polarized gravitational wave is considered using the Fokker-Planck- Kolmogorov (FPK) approach. By using a stochasticity criterion, we determine the exact…
Quantum phase-space distributions (Wigner functions) for the plane rotator are defined using wave functions expressed in both angle and angular momentum representations, with emphasis on the quantum superposition between the Fourier dual…
We consider the quantum and classical Liouville dynamics of a non-integrable model of two coupled spins. Initially localised quantum states spread exponentially to the system dimension when the classical dynamics are chaotic. The long-time…
A Langevin equation is proposed to describe the transport of overdamped Brownian particles in a periodic rough potential and driven by an unbiased periodic force. The equation can be transformed into the Fokker-Planck equation by using the…
It is well known in classical mechanics that, the frequencies of a periodic system can be obtained rather easily through the action variable, without completely solving the equation of motion. The equivalent quantum action variable…
The Hamilton-Jacobi equation of relativistic quantum mechanics is revisited. The equation is shown to permit solutions in the form of breathers (nondispersive oscillating/spinning solitons), displaying simultaneous particle-like and…
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of…
It is showed that, in general, classical and quantum dispersion relations are different due to the presence of the Bohm potential. There are exact particular solutions of the quantum (wave) theory which obey the classical dispersion…
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
The Fokker-Planck equation has been very useful for studying dynamic behavior of stochastic differential equations driven by Gaussian noises. However, there are both theoretical and empirical reasons to consider similar equations driven by…
At non-zero temperature classical systems exhibit statistical fluctuations of thermodynamic quantities arising from the variation of the system's initial conditions and its interaction with the environment. The fluctuating work, for…
We study the two-dimensional overdamped motion of an active particle whose orientational dynamics is subject to fractional Brownian noise, whereas its position is affected by self-propulsion and Brownian fluctuations. From a Langevin-like…
In this work, I derive the time-dependent probability density function of classical observables using the Hamiltonian mechanics approach, extending the notion of fluctuation theorems for any observables. In particular, the time-dependent…
In classical statistical mechanics, the partition function is defined in phase space. We extend this concept to quantum statistical mechanics using Bohmian trajectories. The quantum partition function in phase space captures the ensemble of…
We present a new hydrodynamic analogy of nonrelativistic quantum particles in potential wells. Similarities between a real variant of the Schr\"odinger equation and gravity-capillary shallow water waves are reported and analyzed. We show…
Maintaining the position that the wave function $\psi$ provides a complete description of state, the traditional formalism of quantum mechanics is augmented by introducing continuous trajectories for particles which are sample paths of a…
We express the probabilistic character associated to the wave function by treating it as a stochastic variable. This is accomplished by means of a stochastic equation for the wave function whose noise changes the phase of the wave function…
This work discusses simple examples how quantum systems are obtained as subsystems of classical statistical systems. For a single qubit with arbitrary Hamiltonian and for the quantum particle in a harmonic potential we provide explicitly…
The correspondence principle states that the quantum system will approach to the classical system in high quantum numbers. Indeed, the average of the probability density distribution reflects a classical-like distribution. However, the…