8 research outputs found
The Casimir force at high temperature
The standard expression of the high-temperature Casimir force between perfect
conductors is obtained by imposing macroscopic boundary conditions on the
electromagnetic field at metallic interfaces. This force is twice larger than
that computed in microscopic classical models allowing for charge fluctuations
inside the conductors. We present a direct computation of the force between two
quantum plasma slabs in the framework of non relativistic quantum
electrodynamics including quantum and thermal fluctuations of both matter and
field. In the semi-classical regime, the asymptotic force at large slab
separation is identical to that found in the above purely classical models,
which is therefore the right result. We conclude that when calculating the
Casimir force at non-zero temperature, fluctuations inside the conductors can
not be ignored.Comment: 7 pages, 0 figure
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
Thermal quantum electrodynamics of nonrelativistic charged fluids
The theory relevant to the study of matter in equilibrium with the radiation
field is thermal quantum electrodynamics (TQED). We present a formulation of
the theory, suitable for non relativistic fluids, based on a joint functional
integral representation of matter and field variables. In this formalism
cluster expansion techniques of classical statistical mechanics become
operative. They provide an alternative to the usual Feynman diagrammatics in
many-body problems which is not perturbative with respect to the coupling
constant. As an application we show that the effective Coulomb interaction
between quantum charges is partially screened by thermalized photons at large
distances. More precisely one observes an exact cancellation of the dipolar
electric part of the interaction, so that the asymptotic particle density
correlation is now determined by relativistic effects. It has still the
decay typical for quantum charges, but with an amplitude strongly
reduced by a relativistic factor.Comment: 32 pages, 0 figures. 2nd versio
Atom-wall dispersive forces: a microscopic approach
We present a study of atom-wall interactions in non-relativistic quantum
electrodynamics by functional integral methods. The Feynman-Kac path integral
representation is generalized to the case when the particle interacts with a
radiation field, providing an additional effective potential that contains all
the interactions induced by the field. We show how one can retrieve the
standard van der Waals, Casimir-Polder and classical Lifshiftz forces in this
formalism for an atom in its ground state. Moreover, when electrostatic
interactions are screened in the medium, we find low temperature corrections
that are not included in the Lifshitz theory of fluctuating forces and are
opposite to them.Comment: 4 figure
Screening of classical Casimir forces by electrolytes in semi-infinite geometries
We study the electrostatic Casimir effect and related phenomena in
equilibrium statistical mechanics of classical (non-quantum) charged fluids.
The prototype model consists of two identical dielectric slabs in empty space
(the pure Casimir effect) or in the presence of an electrolyte between the
slabs. In the latter case, it is generally believed that the long-ranged
Casimir force due to thermal fluctuations in the slabs is screened by the
electrolyte into some residual short-ranged force. The screening mechanism is
based on a "separation hypothesis": thermal fluctuations of the electrostatic
field in the slabs can be treated separately from the pure image effects of the
"inert" slabs on the electrolyte particles. In this paper, by using a
phenomenological approach under certain conditions, the separation hypothesis
is shown to be valid. The phenomenology is tested on a microscopic model in
which the conducting slabs and the electrolyte are modelled by the symmetric
Coulomb gases of point-like charges with different particle fugacities. The
model is solved in the high-temperature Debye-H\"uckel limit (in two and three
dimensions) and at the free fermion point of the Thirring representation of the
two-dimensional Coulomb gas. The Debye-H\"uckel theory of a Coulomb gas between
dielectric walls is also solved.Comment: 25 pages, 2 figure
Analytical and Numerical Demonstration of How the Drude Dispersive Model Satisfies Nernst's Theorem for the Casimir Entropy
In view of the current discussion on the subject, an effort is made to show
very accurately both analytically and numerically how the Drude dispersive
model, assuming the relaxation is nonzero at zero temperature (which is the
case when impurities are present), gives consistent results for the Casimir
free energy at low temperatures. Specifically, we find that the free energy
consists essentially of two terms, one leading term proportional to T^2, and a
next term proportional to T^{5/2}. Both these terms give rise to zero Casimir
entropy as T -> 0, thus in accordance with Nernst's theorem.Comment: 11 pages, 4 figures; minor changes in the discussion. Contribution to
the QFEXT07 proceedings; matches version to be published in J. Phys.