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Propagation of the Wigner function is studied on two levels of semiclassical propagation, one based on the van-Vleck propagator, the other on phase-space path integration. Leading quantum corrections to the classical Liouville propagator…
Using simple kinematical arguments, we derive the Fokker-Planck equation for diffusion processes in curved spacetimes. In the case of Brownian motion, it coincides with Eckart's relativistic heat equation (albeit in a simpler form), and…
Previously, an explicit solution for the time evolution of the Wigner function was presented in terms of auxiliary phase space coordinates which obey simple equations that are analogous with, but not identical to, the classical equations of…
A {\em propagation-dispersion equation} is derived for the first passage distribution function of a particle moving on a substrate with time delays. The equation is obtained as the continuous limit of the {\em first visit equation}, an…
We propose an extension of the classical variational theory of evolution equations that accounts for dynamics also in possibly non-reflexive and non-separable spaces. The pivoting point is to establish a novel variational structure, based…
We use the free evolution propagator to determine the quantum probability representation (i.e., the general expression of the tomogram) of any one-dimensional system described by a density state. The evolution operator for the considered…
We derive an approximate Gaussian solution of the Lindblad equation in the semiclassical limit, given a general Hamiltonian and linear coupling with the environment. The theory is carried out in the chord representation and describes the…
We present a mathematical formulation of a theory of language change. The theory is evolutionary in nature and has close analogies with theories of population genetics. The mathematical structure we construct similarly has correspondences…
The asymptotic analysis of a linear high-field Wigner-BGK equation is developped by a modified Chapman-Enskog procedure. By an expansion of the unknown Wigner function in powers of the Knudsen number $\epsilon$, evolution equations are…
The Wigner function is known to evolve classically under the exclusive action of a quadratic hamiltonian. If the system does interact with the environment through Lindblad operators that are linear functions of position and momentum, we…
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 present note establishes the self-averaging, radiative transfer limit for the two-frequency Wigner distribution for classical waves in random media. Depending on the ratio of the wavelength to the correlation length the limiting…
The evolution of the non-thermal emission emitted by pulsar wind nebulae is generally calculated using spatially-independent particle transport models. Although useful, these models implicitly assume that the source of non-thermal particles…
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…
We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle…
In the probability representation of the standard quantum mechanics, the explicit expression (and its quasiclassical van-Fleck approximation) for the ``classical'' propagator (transition probability distribution), which completely describes…
The Kompaneets theory of photon kinetic evolution due to the Compton effect in the absence of absorption and emission is extended to the case of the Vlasov plasma wave oscillations. Under the assumption that the electron distribution…
An adaptation of the WKB method in the deformation quantization formalism is presented with the aim to obtain an approximate technique of solving the eigenvalue problem for energy in the phase space quantum approach. A relationship between…
We emphasize the fact the evolution of quantum states in the inverted oscillator (IO) is reduced to classical equations of motion, stressing that the corresponding tunnelling and reflexion coefficients addressed in the literature are…
We consider an evolution equation generalising the viscous Burgers equation supplemented by an initial condition which is a homogeneous random field. We develop a non-linear framework enabling us to show the existence and regularity of…