1,942 research outputs found
Method of functional integration in the problem of line width of parametric X-ray relativistic electron radiation in a crystal
The coherent and non-coherent scattering effects on "backward" parametric
X-ray radiation by relativistic electrons in a crystal on the basis of the
method of functional integration is investigated. A comparison of contributions
of these effects to parametric X-ray radiation line width has been considered.
It is shown that in a number of cases the major contribution to the line width
of parametric X-ray radiation is made by non-coherent multiple scattering.Comment: 7 pages, LaTeX2e forma
Fractional Generalization of Kac Integral
Generalization of the Kac integral and Kac method for paths measure based on
the Levy distribution has been used to derive fractional diffusion equation.
Application to nonlinear fractional Ginzburg-Landau equation is discussed.Comment: 16 pages, LaTe
Time fractional Schrodinger equation
The Schrodinger equation is considered with the first order time derivative
changed to a Caputo fractional derivative, the time fractional Schrodinger
equation. The resulting Hamiltonian is found to be non-Hermitian and non-local
in time. The resulting wave functions are thus not invariant under time
reversal. The time fractional Schrodinger equation is solved for a free
particle and for a potential well. Probability and the resulting energy levels
are found to increase over time to a limiting value depending on the order of
the time derivative. New identities for the Mittag-Leffler function are also
found and presented in an appendix.Comment: 23 page
Dynamics with Low-Level Fractionality
The notion of fractional dynamics is related to equations of motion with one
or a few terms with derivatives of a fractional order. This type of equation
appears in the description of chaotic dynamics, wave propagation in fractal
media, and field theory. For the fractional linear oscillator the physical
meaning of the derivative of order is dissipation. In systems with
many spacially coupled elements (oscillators) the fractional derivative, along
the space coordinate, corresponds to a long range interaction. We discuss a
method of constructing a solution using an expansion in
with small and positive integer . The method is applied to the
fractional linear and nonlinear oscillators and to fractional Ginzburg-Landau
or parabolic equations.Comment: LaTeX, 24 pages, to be published in Physica
Abelian Landau-Pomeranchuk-Migdal effects
It is shown that the high-energy expansion of the scattering amplitude
calculated from Feynman diagrams factorizes in such a way that it can be
reduced to the eikonalized form up to the terms of inverse power in energy in
accordance with results obtained by solving the Klein-Gordon equation.
Therefore the two approaches when applied to the suppression of the emission of
soft photons by fast charged particles in dense matter should give rise to the
same results. A particular limit of thin targets is briefly discussed.Comment: 14 pages, LATEX, 1 Fig. ps, submitted to Mod. Phys. Lett.
Non-ergodic Intensity Correlation Functions for Blinking Nano Crystals
We investigate the non-ergodic properties of blinking nano-crystals using a
stochastic approach. We calculate the distribution functions of the time
averaged intensity correlation function and show that these distributions are
not delta peaked on the ensemble average correlation function values; instead
they are W or U shaped. Beyond blinking nano-crystals our results describe
non-ergodicity in systems stochastically modeled using the Levy walk framework
for anomalous diffusion, for example certain types of chaotic dynamics,
currents in ion-channel, and single spin dynamics to name a few.Comment: 5 pages, 3 figure
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