22,712 research outputs found
Approximate solution for Fokker-Planck equation
In this paper, an approximate solution to a specific class of the
Fokker-Planck equation is proposed. The solution is based on the relationship
between the Schr\"{o}dinger type equation with a partially confining and
symmetrical potential. To estimate the accuracy of the solution, a function
error obtained from the original Fokker-Planck equation is suggested. Two
examples, a truncated harmonic potential and non-harmonic polynomial, are
analyzed using the proposed method. For the truncated harmonic potential, the
system behavior as a function of temperature is also discussed.Comment: 12 pages, 8 figure
Three-dimensional quantum electrodynamics as an effective interaction
We obtain a Quantum Electrodynamics in 2+1 dimensions by applying a
Kaluza--Klein type method of dimensional reduction to Quantum Electrodynamics
in 3+1 dimensions rendering the model more realistic to application in
solid-state systems, invariant under translations in one direction. We show
that the model obtained leads to an effective action exhibiting an interesting
phase structure and that the generated Chern--Simons term survives only in the
broken phase.Comment: 10 pages in Plain Te
Magnetism and Electronic Correlations in Quasi-One-Dimensional Compounds
In this contribution on the celebration of the 80th birthday anniversary of
Prof. Ricardo Ferreira, we present a brief survey on the magnetism of
quasi-one-dimensional compounds. This has been a research area of intense
activity particularly since the first experimental announcements of magnetism
in organic and organometallic polymers in the mid 80s. We review experimental
and theoretical achievements on the field, featuring chain systems of
correlated electrons in a special AB2 unit cell structure present in inorganic
and organic compounds
Scaling violation and shadowing corrections at HERA
We study the value of shadowing corrections (SC) in HERA kinematic region in
Glauber - Mueller approach. Since the Glauber - Mueller approach was proven in
perturbative QCD in the double logarithmic approximation (DLA), we develop the
DLA approach for deep inelastic structure function which takes into account the
SC. Our estimates show small SC for in HERA kinematic region while they
turn out to be sizable for the gluon structure function. We compare our
estimates with those for gluon distribution in leading order (LO) and next to
leading order (NLO) in the DGLAP evolution equations.Comment: 9pp,6 figures in eps file
Scalar and Spinor Particles in the Spacetime of a Domain Wall in String Theory
We consider scalar and spinor particles in the spacetime of a domain wall in
the context of low energy effective string theories, such as the generalized
scalar-tensor gravity theories. This class of theories allows for an arbitrary
coupling of the wall and the (gravitational) scalar field. First, we derive the
metric of a wall in the weak-field approximation and we show that it depends on
the wall's surface energy density and on two post-Newtonian parameters. Then,
we solve the Klein-Gordon and the Dirac equations in this spacetime. We obtain
the spectrum of energy eigenvalues and the current density in the scalar and
spinor cases, respectively. We show that these quantities, except in the case
of the energy spectrum for a massless spinor particle, depend on the parameters
that characterize the scalar-tensor domain wall.Comment: LATEX file, 21 pages, revised version to appear in Phys. Rev.
Superintegrability of the Fock-Darwin system
The Fock-Darwin system is analysed from the point of view of its symmetry
properties in the quantum and classical frameworks. The quantum Fock-Darwin
system is known to have two sets of ladder operators, a fact which guarantees
its solvability. We show that for rational values of the quotient of two
relevant frequencies, this system is superintegrable, the quantum symmetries
being responsible for the degeneracy of the energy levels. These symmetries are
of higher order and close a polynomial algebra. In the classical case, the
ladder operators are replaced by ladder functions and the symmetries by
constants of motion. We also prove that the rational classical system is
superintegrable and its trajectories are closed. The constants of motion are
also generators of symmetry transformations in the phase space that have been
integrated for some special cases. These transformations connect different
trajectories with the same energy. The coherent states of the quantum
superintegrable system are found and they reproduce the closed trajectories of
the classical one.Comment: 21 pages,16 figure
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