9,951 research outputs found
Exact statistical properties of the Burgers equation
The one dimensional Burgers equation in the inviscid limit with white noise
initial condition is revisited. The one- and two-point distributions of the
Burgers field as well as the related distributions of shocks are obtained in
closed analytical forms. In particular, the large distance behavior of spatial
correlations of the field is determined. Since higher order distributions
factorize in terms of the one and two points functions, our analysis provides
an explicit and complete statistical description of this problem.Comment: 21 pages, 6 figures include
The Casimir Effect
After a review of the standard calculation of the Casimir force between two
metallic plates at zero and non-zero temperatures, we present the study of
microscopic models to determine the large-distance asymptotic force in the
high-temperature regime. Casimir's conducting plates are modelized by plasmas
of interacting charges at temperature T. The charges are either classical, or
quantum-mechanical and coupled to a (classical) radiation field. In these
models, the force obtained is twice weaker than that arising from standard
treatments neglecting the microscopic charge fluctutations inside the bodies.
The enforcement of inert boundary conditions on the field in the usual
calculations turns out to be inadequate in this regime.
Other aspects of dispersion forces are also reviewed. The status of
(non-retarded) van der Waals-London forces in a dilute medium of non-zero
temperature and density is investigated. In a proper scaling regime called the
atomic limit (high dilution and low temperature), one is able to give the exact
large-distance atomic correlations up to exponentially small terms as T->0.
Retarded van der Waals forces and forces between dielectric bodies are also
reviewed.
Finally, the Casimir effect in critical phenomena is addressed by considering
the free Bose gas. It is shown that the grand-canonical potential of the gas in
a slab at the critical value of the chemical potential has finite size
corrections of the standard Casimir type. They can be attributed to the
existence of long-range order generated by gapless excitations in the phase
with broken continuous symmetry.Comment: Lecture notes prepared for the proceedings of the 1st Warsaw School
of Statistical Physics, Kazimierz, Poland, June 2005. To appear in Acta
Physica Polonica (2006). 52 pages, 0 figures. Available at
http://th-www.if.uj.edu.pl/acta/vol37/pdf/v37p2503.pd
Quintessence Model Building
A short review of some of the aspects of quintessence model building is
presented. We emphasize the role of tracking models and their possible
supersymmetric origin.Comment: 14 pages, to appear in the proceedings of the sixth workshop of the
American University of Pari
The C-flash and the ignition conditions of type Ia supernovae
Thanks to a stellar evolution code able to compute through the
C-flash we link the binary population synthesis of single degenerate
progenitors of type Ia supernovae (SNe Ia) to their physical condition at the
time of ignition. We show that there is a large range of possible ignition
densities and we detail how their probability distribution depends on the
accretion properties. The low density peak of this distribution qualitatively
reminds of the clustering of the luminosities of Branch-normal SNe Ia. We
tighten the possible range of initial physical conditions for explosion models:
they form a one-parameter family, independent of the metallicity. We discuss
how these results may be modified if we were to relax our hypothesis of a
permanent Hachisu wind or if we were to include electron captures.Comment: 10 pages, 14 figures, MNRAS accepte
Microscopic theory of the Casimir force at thermal equilibrium: large-separation asymptotics
We present an entirely microscopic calculation of the Casimir force
between two metallic plates in the limit of large separation . The models of
metals consist of mobile quantum charges in thermal equilibrium with the photon
field at positive temperature . Fluctuations of all degrees of freedom,
matter and field, are treated according to the principles of quantum
electrodynamics and statistical physics without recourse to approximations or
intermediate assumptions. Our main result is the correctness of the asymptotic
universal formula f(d) \sim -\frac{\zeta(3) \kB T}{8\pi d^3}, .
This supports the fact that, in the framework of Lifshitz' theory of
electromagnetic fluctuations, transverse electric modes do not contribute in
this regime. Moreover the microscopic origin of universality is seen to rely on
perfect screening sum rules that hold in great generality for conducting media.Comment: 34 pages, 0 figures. New version includes restructured intro and
minor typos correcte
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