Related papers: Fractional Particle and Sigma Model
In this paper, we use the fractional calculus to discuss the fractional mechanics, where the time derivative is replaced with the fractional derivative of order $\nu$. We deal with the motion of a body in a resisting medium where the…
We introduce a fractional Kramers equation for a particle interacting with a thermal heat bath and external non-linear force field. For the force free case the velocity damping follows the Mittag-Leffler relaxation and the diffusion is…
We show that Wigner-Leggett-Caldeira equation for Wigner phase space distribution function which describes the quantum Brownian motion of a particle in a force field in a high temerature, Ohmic environment can be identified as a…
We investigate the particle and kinetic-energy densities for a system of $N$ fermions bound in a local (mean-field) potential $V(\bfr)$. We generalize a recently developed semiclassical theory [J. Roccia and M. Brack, Phys. Rev.\ Lett. {\bf…
Following Feynman's treatment of the non-relativistic polaron problem, similar techniques are used to study relativistic field theories: after integrating out the bosonic degrees of freedom the resulting effective action is formulated in…
The physical model of a nonrelativistic quantized Schrodinger's electron (SE) is offered. The behaviour of the SE well spread elementary electric charge had been understood by means of two independent and different in a frequency and size…
The paper reviews some parts of classical potential theory with applications to two dimensional fluid dynamics, in particular vortex motion. Energy and forces within a system of point vortices are similar to those for point charges when the…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
We formulate a finite-size particle numerical model of strongly magnetized plasmas in the drift-kinetic approximation. We use the phase space action as an alternative to previous variational formulations based on Low's Lagrangian or on a…
After a brief review of the definition and properties of the quantum effective Hamiltonian action we describe its renormalization flow by a functional RG equation. This equation can be used for a non-perturbative quantization and study also…
A general algebraic method of quantum corrections evaluation is presented. Quantum corrections to a few classical solutions (kinks and periodic) of Ginzburg-Landau (phi-in-quadro) and Sin-Gordon models are calculated in arbitrary…
A completely Lorentz-invariant Bohmian model has been proposed recently for the case of a system of non-interacting spinless particles, obeying Klein-Gordon equations. It is based on a multi-temporal formalism and on the idea of treating…
Here we review the many aspects and distinct phenomena associated to quantum dynamics on general graph structures. For so, we discuss such class of systems under the energy domain Green's function ($G$) framework. This approach is…
Semiclassical expansions for traces involving Greens functions have two contributions, one from the periodic or recurrent orbits of the classical system and one from the phase space volume, i.e. the paths of infinitesimal length.…
Introducing a set $\{\alpha_i\} \in R$ of fractional exponential powers of focal distances an extension of symmetric Cassini-coordinates on the plane to the asymmetric case is proposed which leads to a new set of fractional generalized…
We compute the partition function and specific heat for a quantum mechanical particle under the influence of a quartic double-well potential non-perturbatively, using the semiclassical method. Near the region of bounded motion in the…
Fractional kinetic theory plays a vital role in describing anomalous diffusion in terms of complex dynamics generating semi-Markovian processes. Recently, the variational principle and associated Levy Ansatz have been proposed in order to…
We consider a model of classical noncommutative particle in an external electromagnetic field. For this model, we prove the existence of generalized gauge transformations. Classical dynamics in Hamiltonian and Lagrangian form is discussed,…
We introduce a new Gaussian process, a generalization of both fractional and subfractional Brownian motions, which could serve as a good model for a larger class of natural phenomena. We study its main stochastic properties and some…
We present the analytical solution in closed form for the semiclassical limit of the quantum mechanical Coulomb Green function in position space in n dimensions. We utilize a projection method which has its roots in Lambert's theorem and…