787 research outputs found
The Biedenharn Approach to Relativistic Coulomb-type Problems
The approach developped by Biedeharn in the sixties for the relativistic
Coulomb problem is reviewed and applied to various physical problems.Comment: 16 pages, 4 figure
Brane-Induced Gravity's Shocks
We construct exact gravitational field solutions for a relativistic particle
localized on a tensional brane in brane-induced gravity. They are a
generalization of gravitational shock waves in 4D de Sitter space. We provide
the metrics for both the normal branch and the self-inflating branch DGP
braneworlds, and compare them to the 4D Einstein gravity solution and to the
case when gravity resides only in the 5D bulk, without any brane-localized
curvature terms. At short distances the wave profile looks the same as in four
dimensions. The corrections appear only far from the source, where they differ
from the long distance corrections in 4D de Sitter space. We also discover a
new non-perturbative channel for energy emission into the bulk from the
self-inflating branch, when gravity is modified at the de Sitter radius.Comment: 4 pages, revtex4; v4: a sign error corrected; the correction
tantamount to swapping normal and self-inflating branch solutions; the only
significant change is that the spectacular new instability is on the
self-inflating branch in the limit of vanishing brane tension; more details
available in hep-th/050203
Electronic structure and optical properties of quantum confined lead-salt nanowires
In the framework of four-band envelope-function formalism, developed earlier
for spherical semiconductor nanocrystals, we study the electronic structure and
optical properties of quantum-confined lead-salt (PbSe and PbS) nanowires (NWs)
with a strong coupling between the conduction and the valence bands. We derive
spatial quantization equations, and calculate numerically energy levels of
spatially quantized states of a transverse electron motion in the plane
perpendicular to the NW axis, and electronic subbands developed due to a free
longitudinal motion along the NW axis. Using explicit expressions for
eigenfunctions of the electronic states, we also derive analytical expressions
for matrix elements of optical transitions and study selection rules for
interband absorption.
Next we study a two-particle problem with a conventional long-range Coulomb
interaction and an interparticle coupling via medium polarization. The obtained
results show that due to a large magnitude of the high-frequency dielectric
permittivity of PbSe material, and hence, a high dielectric NW/vacuum contrast,
the effective coupling via medium polarization significantly exceeds the
effective direct Coulomb coupling at all interparticle separations along the NW
axis. Furthermore, the strong coupling via medium polarization results in a
bound state of the longitudinal motion of the lowest-energy electron-hole pair
(a longitudinal exciton), while fast transverse motions of charge carriers
remain independent of each other.Comment: Some misprints and mistakes are correcte
Non-Volkov solutions for a charge in a plane wave
We focus our attention, once again, on the Klein--Gordon and Dirac equations
with a plane-wave field. We recall that for the first time a set of solutions
of these equations was found by Volkov. The Volkov solutions are widely used in
calculations of quantum effects with electrons and other elementary particles
in laser beams. We demonstrate that one can construct sets of solutions which
differ from the Volkov solutions and which may be useful in physical
applications. For this purpose, we show that the transversal charge motion in a
plane wave can be mapped by a special transformation to transversal free
particle motion. This allows us to find new sets of solutions where the
transversal motion is characterized by quantum numbers different from Volkov's
(in the Volkov solutions this motion is characterized by the transversal
momentum). In particular, we construct solutions with semiclassical transversal
charge motion (transversal squeezed coherent states). In addition, we
demonstrate how the plane-wave field can be eliminated from the transversal
charge motion in a more complicated case of the so-called combined
electromagnetic field (a combination of a plane-wave field and constant
colinear electric and magnetic fields). Thus, we find new sets of solutions of
the Klein--Gordon and Dirac equations with the combined electromagnetic field.Comment: LaTex file, 14 page
The Fate of the Initial State Fluctuations in Heavy Ion Collisions. III The Second Act of Hydrodynamics
Hydrodynamical description of the "Little Bang" in heavy ion collisions is
surprisingly successful, mostly due to the very small viscosity of the
Quark-Gluon plasma. In this paper we systematically study the propagation of
small perturbations, also treated hydrodynamically. We start with a number of
known techniques allowing for analytic calculation of the propagation of small
perturbations on top of the expanding fireball. The simplest approximation is
the "geometric acoustics", which substitutes the wave equation by mechanical
equations for the propagating "phonons". Next we turn to the case in which
variables can be separated, in which case one can obtain not only the eikonal
phases but also amplitudes of the perturbation. Finally, we focus on the so
called Gubser flow, a particular conformal analytic solution for the fireball
expansion, on top of which one can derive closed equations for small
perturbations. Perfect hydrodynamics allows all variables to be separated and
all equations to be solved in terms of known special functions. We can thus
collect the analytical expression for all the harmonics and reconstruct the
complete Green function of the problem. In the viscous case the equations still
allow for variable separation, but one of the equations has to be solved
numerically. We still can collect all the harmonics and show real-time
perturbation evolution, observing viscosity-induced changes in the spectra and
the correlation functions of secondaries. We end up by comparing the calculated
angular shape of the correlation function to the STAR experimental data, and
find, for sufficiently large viscosity, a surprisingly good agreement.Comment: The paper was changed after PRC referee report. It was resubmitted in
this for
Phase transitions in one dimension and less
Phase transitions can occur in one-dimensional classical statistical
mechanics at non-zero temperature when the number of components N of the spin
is infinite. We show how to solve such magnets in one dimension for any N, and
how the phase transition develops at N = infinity. We discuss SU(N) and Sp(N)
magnets, where the transition is second-order. In the new high-temperature
phase, the correlation length is zero. We also show that for the SU(N) magnet
on exactly three sites with periodic boundary conditions, the transition
becomes first order.Comment: 16 pages, 1 figur
Excitonic gap, phase transition, and quantum Hall effect in graphene
We suggest that physics underlying the recently observed removal of
sublattice and spin degeneracies in graphene in a strong magnetic field
describes a phase transition connected with the generation of an excitonic gap.
The experimental form of the Hall conductivity is reproduced and the main
characteristics of the dynamics are described. Predictions of the behavior of
the gap as a function of temperature and a gate voltage are made.Comment: Revtex4, 10 pages, 4 figures, text essentially extended, one figure
and references added; v3: to match PRB versio
Electromagnetic field near cosmic string
The retarded Green function of the electromagnetic field in spacetime of a
straight thin cosmic string is found. It splits into a geodesic part
(corresponding to the propagation along null rays) and to the field scattered
on the string. With help of the Green function the electric and magnetic fields
of simple sources are constructed. It is shown that these sources are
influenced by the cosmic string through a self-interaction with their field.
The distant field of static sources is studied and it is found that it has a
different multipole structure than in Minkowski spacetime. On the other hand,
the string suppresses the electric and magnetic field of distant sources--the
field is expelled from regions near the string.Comment: 12 pages, 8 figures (low-resolution figures; for the version with
high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers/), v2: two
references added, typos correcte
Decoherence in QED at finite temperature
We consider a wave packet of a charged particle passing through a cavity
filled with photons at temperature T and investigate its localization and
interference properties. It is shown that the wave packet becomes localized and
the interference disappears with an exponential speed after a sufficiently long
path through the cavity.Comment: Latex, 10 page
Lattice Boltzmann method with self-consistent thermo-hydrodynamic equilibria
Lattice kinetic equations incorporating the effects of external/internal
force fields via a shift of the local fields in the local equilibria, are
placed within the framework of continuum kinetic theory. The mathematical
treatment reveals that, in order to be consistent with the correct
thermo-hydrodynamical description, temperature must also be shifted, besides
momentum. New perspectives for the formulation of thermo-hydrodynamic lattice
kinetic models of non-ideal fluids are then envisaged. It is also shown that on
the lattice, the definition of the macroscopic temperature requires the
inclusion of new terms directly related to discrete effects. The theoretical
treatment is tested against a controlled case with a non ideal equation of
state.Comment: 10 pages, 1 figur
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