55 research outputs found
Time correlations in a confined magnetized free-electron gas
The time-dependent pair correlation functions for a degenerate ideal quantum
gas of charged particles in a uniform magnetic field are studied on the basis
of equilibrium statistics. In particular, the influence of a flat hard wall on
the correlations is investigated, both for a perpendicular and a parallel
orientation of the wall with respect to the field. The coherent and incoherent
parts of the time-dependent structure function in position space are determined
from an expansion in terms of the eigenfunctions of the one-particle
Hamiltonian. For the bulk of the system, the intermediate scattering function
and the dynamical structure factor are derived by taking successive Fourier
transforms. In the vicinity of the wall the time-dependent coherent structure
function is found to decay faster than in the bulk. For coinciding positions
near the wall the form of the structure function turns out to be independent of
the orientation of the wall. Numerical results are shown to corroborate these
findings.Comment: 25 pages, 14 figures, to be published in Journal of Physics
Correlations in a confined magnetized free-electron gas
Equilibrium quantum statistical methods are used to study the pair
correlation function for a magnetized free-electron gas in the presence of a
hard wall that is parallel to the field. With the help of a path-integral
technique and a Green function representation the modifications in the
correlation function caused by the wall are determined both for a
non-degenerate and for a completely degenerate gas. In the latter case the
asymptotic behaviour of the correlation function for large position differences
in the direction parallel to the wall and perpendicular to the field, is found
to change from Gaussian in the bulk to algebraic near the wall.Comment: 24 pages, 10 figures, submitted to J. Phys. A: Math. Ge
Spectral properties of distance matrices
Distance matrices are matrices whose elements are the relative distances
between points located on a certain manifold. In all cases considered here all
their eigenvalues except one are non-positive. When the points are uncorrelated
and randomly distributed we investigate the average density of their
eigenvalues and the structure of their eigenfunctions. The spectrum exhibits
delocalized and strongly localized states which possess different power-law
average behaviour. The exponents depend only on the dimensionality of the
manifold.Comment: 31 pages, 9 figure
Random matrix analysis of the QCD sign problem for general topology
Motivated by the important role played by the phase of the fermion
determinant in the investigation of the sign problem in lattice QCD at nonzero
baryon density, we derive an analytical formula for the average phase factor of
the fermion determinant for general topology in the microscopic limit of chiral
random matrix theory at nonzero chemical potential, for both the quenched and
the unquenched case. The formula is a nontrivial extension of the expression
for zero topology derived earlier by Splittorff and Verbaarschot. Our
analytical predictions are verified by detailed numerical random matrix
simulations of the quenched theory.Comment: 33 pages, 9 figures; v2: minor corrections, references added, figures
with increased statistics, as published in JHE
Fractional Klein-Kramers equation for superdiffusive transport: normal versus anomalous time evolution in a differential L{\'e}vy walk model
We introduce a fractional Klein-Kramers equation which describes
sub-ballistic superdiffusion in phase space in the presence of a
space-dependent external force field. This equation defines the differential
L{\'e}vy walk model whose solution is shown to be non-negative. In the velocity
coordinate, the probability density relaxes in Mittag-Leffler fashion towards
the Maxwell distribution whereas in the space coordinate, no stationary
solution exists and the temporal evolution of moments exhibits a competition
between Brownian and anomalous contributions.Comment: 4 pages, REVTe
Fermi-Dirac statistics and the number theory
We relate the Fermi-Dirac statistics of an ideal Fermi gas in a harmonic trap
to partitions of given integers into distinct parts, studied in number theory.
Using methods of quantum statistical physics we derive analytic expressions for
cumulants of the probability distribution of the number of different
partitions.Comment: 7pages, 2 figures, epl.cls, revised versio
A Dialogue of Multipoles: Matched Asymptotic Expansion for Caged Black Holes
No analytic solution is known to date for a black hole in a compact
dimension. We develop an analytic perturbation theory where the small parameter
is the size of the black hole relative to the size of the compact dimension. We
set up a general procedure for an arbitrary order in the perturbation series
based on an asymptotic matched expansion between two coordinate patches: the
near horizon zone and the asymptotic zone. The procedure is ordinary
perturbation expansion in each zone, where additionally some boundary data
comes from the other zone, and so the procedure alternates between the zones.
It can be viewed as a dialogue of multipoles where the black hole changes its
shape (mass multipoles) in response to the field (multipoles) created by its
periodic "mirrors", and that in turn changes its field and so on. We present
the leading correction to the full metric including the first correction to the
area-temperature relation, the leading term for black hole eccentricity and the
"Archimedes effect". The next order corrections will appear in a sequel. On the
way we determine independently the static perturbations of the Schwarzschild
black hole in dimension d>=5, where the system of equations can be reduced to
"a master equation" - a single ordinary differential equation. The solutions
are hypergeometric functions which in some cases reduce to polynomials.Comment: 47 pages, 12 figures, minor corrections described at the end of the
introductio
Magneto-acoustic Waves in a Magnetic Slab Embedded in an Asymmetric Magnetic Environment: The Effects of Asymmetry
Modeling the behavior of magnetohydrodynamic waves in a range of magnetic geometries mimicking solar
atmospheric waveguides, from photospheric flux tubes to coronal loops, can offer a valuable contribution to the
field of solar magneto-seismology. The present study uses an analytical approach to derive the dispersion relation
for magneto-acoustic waves in a magnetic slab of homogeneous plasma enclosed on its two sides by semi-infinite
plasma of different densities, temperatures, and magnetic field strengths, providing an asymmetric plasma
environment. This is a step further in the generalization of the classic magnetic slab model, which is symmetric
about the slab, was developed by Roberts, and is an extension of the work by Allcock & Erdélyi where a magnetic
slab is sandwiched in an asymmetric nonmagnetic plasma environment. In contrast to the symmetric case, the
dispersion relation governing the asymmetric slab cannot be factorized into separate sausage and kink eigenmodes.
The solutions obtained resemble these well-known modes; however, their properties are now mixed. Therefore we
call these modes quasi-sausage and quasi-kink modes. If conditions on the two sides of the slab do not differ
strongly, then a factorization of the dispersion relation can be achieved for the further analytic study of various
limiting cases representing a solar environment. In the current paper, we examine the incompressible limit in detail
and demonstrate its possible application to photospheric magnetic bright points. After the introduction of a
mechanical analogy, we reveal a relationship between the external plasma and magnetic parameters, which allows
for the existence of quasi-symmetric modes
The General Correlation Function in the Schwinger Model on a Torus
In the framework of the Euclidean path integral approach we derive the exact
formula for the general N-point chiral densities correlator in the Schwinger
model on a torusComment: 17 pages, misprints corrected, references adde
Quantum Mechanics on the cylinder
A new approach to deformation quantization on the cylinder considered as
phase space is presented. The method is based on the standard Moyal formalism
for R^2 adapted to (S^1 x R) by the Weil--Brezin--Zak transformation. The
results are compared with other solutions of this problem presented by
Kasperkovitz and Peev (Ann. Phys. vol. 230, 21 (1994)0 and by Plebanski and
collaborators (Acta Phys. Pol. vol. B 31}, 561 (2000)). The equivalence of
these three methods is proved.Comment: 21 pages, LaTe
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