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Starting from the formal expressions of the hydrodynamical (or ``local'') quantities employed in the applications of Clifford Algebras to quantum mechanics, we introduce --in terms of the ordinary tensorial framework-- a new definition for…

This thesis is dedicated to explore the feasibility of numerical calculations in the $\epsilon$--regime of QCD for the extraction of physical information. We apply two formulations of the Ginsparg-Wilson fermions the Neuberger operator and…

We use the Dyson-Wyld diagrammatic technique to analyze the infinite series for the correlation functions of the velocity in the hydrodynamic turbulence. We demonstrate the fundamental role played by the triple correlator of the velocity in…

We derive expressions for the vector and tensor components of the spin polarization of massive vector bosons at local thermodynamic equilibrium up to second order in the space-time gradients of the thermodynamic fields pertaining to the…

We address the physical meaning of hydrodynamic approach related with the coarse graining scale in the frame work of variational formulation. We point out that the local thermal equilibrium does not necessarily play a critical role in the…

Wave-like spatial statistics in walking-droplet quantum analogs are typically attributed to spatial or temporal nonlocal wave effects. We show instead that such behavior arises generically from the low-dimensional nonlinear dynamics of an…

Acoustic fields effect steady transport of suspended particles by rectifying the inertia of primary oscillations. We develop a fully analytic theory that relates this steady particle motion to incident oscillatory (acoustic) flow and the…

We present results on the connection between the vorticity equation and the shape of the single-point vorticity PDF. The statistical framework for these observations is cast in form of conditional averages. The numerical evaluation of these…

Using the supersymmetry approach, we study spectral statistical properties of a two-dimensional quantum particle subject to a non-uniform magnetic field. We focus mainly on the problem of regularisation of the field theory. Our analysis…

New time dependent Wigner functions for the quantum harmonic oscillator have been obtained in this work. The Moyal equation for the harmonic oscillator has been presented as the wave equation of a 2D membrane in the phase plane. The values…

We study the statistical properties of helicity in direct numerical simulations of fully developed homogeneous and isotropic turbulence and in a class of turbulence shell models. We consider correlation functions based on combinations of…

We consider the experimental implications of the axial current triangle diagram anomaly in a hydrodynamic description of high density QCD. We propose a signal of an enhanced production of spin-excited hadrons in the direction of the…

Phase space reflection operators lie at the core of the Wigner-Weyl representation of density operators and observables. The role of the corresponding classical reflections is known in the construction of semiclassical approximations to…

We propose an improved quark coalescence model for spin alignment of vector mesons and polarization of baryons by spin density matrix with phase space dependence. The spin density matrix is defined through Wigner functions. Within the model…

The eigenvalues of the matrix structure $X + X^{(0)}$, where $X$ is a random Gaussian Hermitian matrix and $X^{(0)}$ is non-random or random independent of $X$, are closely related to Dyson Brownian motion. Previous works have shown how an…

The quantum states representing classical phase space are given, and these are used to formulate quantum statistical mechanics as a formally exact double perturbation expansion about classical statistical mechanics. One series of quantum…

We derive an analytical expression of a Wigner function that approximately describes the time evolution of the one-dimensional motion of a particle in a nonharmonic potential. Our method involves two exact frame transformations, accounting…

The purpose of the paper is to develop further a projection variational approach in relativistic hydrodynamics. The approach, previously proposed in [gr-qc/9908032], is based on the variation of the vector field and the projection tensor…

The macroscopic hydrodynamic equations are derived for many-body systems in the local-equilibrium approach, using the Schr\"odinger picture of quantum mechanics. In this approach, statistical operators are defined in terms of microscopic…

A model is proposed, according to which the metric tensor field in the standard gravitational Lagrangian is decomposed into a projection (generally - with a non-zero covariant derivative) tensor field, orthogonal to an arbitrary 4-vector…