76 research outputs found
Van der Waals interactions: Evaluations by use of a statistical mechanical method
In this work the induced van der Waals interaction between a pair of neutral
atoms or molecules is considered by use of a statistical mechanical method.
Commonly this interaction is obtained by standard quantum mechanical
perturbation theory to second order. However, the latter is restricted to
electrostatic interactions between charges and dipole moments. So with
radiating dipole-dipole interaction where retardation effects are important for
large separations of the particles, other methods are needed, and the resulting
induced interaction is the Casimir-Polder interaction usually obtained by field
theory. It can also be evaluated, however, by a statistical mechanical method
that utilizes the path integral representation. We here show explicitly by use
of the statistical mechanical method the equivalence of the Casimir-Polder and
van der Waals interactions to leading order for short separations where
retardation effects can be neglected. Physically this is well known, but in our
opinion the mathematics of this transition process is not so obvious. The
evaluations needed mean a transform of the statistical mechanical free energy
expression to a form that can be identified with second order perturbation
theory. In recent works [H{\o}ye 2010] the Casimir-Polder or Casimir energy has
been added as a correction to calculations of systems like the electron clouds
of molecules.
The equivalence to van der Waals interactions to leading order indicates that
the added Casimir energy will improve the accuracy of calculated molecular
energies. We here also give numerical estimates of this energy including
analysis and estimates for the uniform electron gas
Universal behavior of dispersion forces between two dielectric plates in the low-temperature limit
The universal analytic expressions in the limit of low temperatures (short
separations) are obtained for the free energy, entropy and pressure between the
two parallel plates made of any dielectric. The analytical proof of the Nernst
heat theorem in the case of dispersion forces acting between dielectrics is
provided. This permitted us to formulate the stringent thermodynamical
requirement that must be satisfied in all models used in the Casimir physics.Comment: 6 pages, iopart.cls is used, to appear in J. Phys. A (special issue:
Proceedings of QFEXT05, Barcelona, Sept. 5-9, 2005
Derivation of the Cubic Non-linear Schr\"odinger Equation from Quantum Dynamics of Many-Body Systems
We prove rigorously that the one-particle density matrix of three dimensional
interacting Bose systems with a short-scale repulsive pair interaction
converges to the solution of the cubic non-linear Schr\"odinger equation in a
suitable scaling limit. The result is extended to -particle density matrices
for all positive integer .Comment: 72 pages, 17 figures. Final versio
Spatial correlations of vacuum fluctuations and the Casimir-Polder potential
We calculate the Casimir-Polder intermolecular potential using an effective
Hamiltonian recently introduced. We show that the potential can be expressed in
terms of the dynamical polarizabilities of the two atoms and the equal-time
spatial correlation of the electric field in the vacuum state. This gives
support to an interesting physical model recently proposed in the literature,
where the potential is obtained from the classical interaction between the
instantaneous atomic dipoles induced and correlated by the vacuum fluctuations.
Also, the results obtained suggest a more general validity of this intuitive
model, for example when external boundaries or thermal fields are present.Comment: 7 page
Using atomic interference to probe atom-surface interaction
We show that atomic interference in the reflection from two suitably
polarized evanescent waves is sensitive to retardation effects in the
atom-surface interaction for specific experimental parameters. We study the
limit of short and long atomic de Broglie wavelength. The former case is
analyzed in the semiclassical approximation (Landau-Zener model). The latter
represents a quantum regime and is analyzed by solving numerically the
associated coupled Schroedinger equations. We consider a specific experimental
scheme and show the results for rubidium (short wavelength) and the much
lighter meta-stable helium atom (long wavelength). The merits of each case are
then discussed.Comment: 11 pages, including 6 figures, submitted to Phys. Rev. A, RevTeX
sourc
The structure of the atomic helium trimers: Halos and Efimov states
The Faddeev equations for the atomic helium-trimer systems are solved
numerically with high accuracy both for the most sophisticated realistic
potentials available and for simple phenomenological potentials. An efficient
numerical procedure is described. The large-distance asymptotic behavior,
crucial for weakly bound three-body systems, is described almost analytically
for arbitrary potentials. The Efimov effect is especially considered. The
geometric structures of the bound states are quantitatively investigated. The
accuracy of the schematic models and previous computations is comparable, i.e.
within 20% for the spatially extended states and within 40% for the smaller
^4He-trimer ground state.Comment: 32 pages containing 7 figures and 6 table
A Rigorous Derivation of the Gross-Pitaevskii Energy Functional for a Two-Dimensional Bose Gas
We consider the ground state properties of an inhomogeneous two-dimensional
Bose gas with a repulsive, short range pair interaction and an external
confining potential. In the limit when the particle number is large but
is small, where is the average particle density and
the scattering length, the ground state energy and density are rigorously
shown to be given to leading order by a Gross-Pitaevskii (GP) energy functional
with a coupling constant . In contrast to the 3D
case the coupling constant depends on through the mean density. The GP
energy per particle depends only on . In 2D this parameter is typically so
large that the gradient term in the GP energy functional is negligible and the
simpler description by a Thomas-Fermi type functional is adequate.Comment: 14 pages, no figures, latex 2e. References, some clarifications and
an appendix added. To appear in Commun. Math. Phy
Semiclassical Estimates of Electromagnetic Casimir Self-Energies of Spherical and Cylindrical Metallic Shells
The leading semiclassical estimates of the electromagnetic Casimir stresses
on a spherical and a cylindrical metallic shell are within 1% of the field
theoretical values. The electromagnetic Casimir energy for both geometries is
given by two decoupled massless scalars that satisfy conformally covariant
boundary conditions. Surface contributions vanish for smooth metallic
boundaries and the finite electromagnetic Casimir energy in leading
semiclassical approximation is due to quadratic fluctuations about periodic
rays in the interior of the cavity only. Semiclassically the non-vanishing
Casimir energy of a metallic cylindrical shell is almost entirely due to
Fresnel diffraction.Comment: 12 pages, 2 figure
Matter-field theory of the Casimir force
A matter-field theory of the Casimir force is formulated in which the
electromagnetic field and collective modes of dielectric media are treated on
an equal footing. In our theory, the Casimir force is attributed to zero-point
energies of the combined matter-field modes. We analyze why some of the
existing theories favor the interpretation of the Casimir force as originating
from zero-point energies of the electromagnetic field and others from those of
the matter.Comment: 12pages, 1 Postscript figur
Retarded long-range potentials for the alkali-metal atoms and a perfectly conducting wall
The retarded long-range potentials for hydrogen and alkali-metal atoms in
their ground states and a perfectly conducting wall are calculated. The
potentials are given over a wide range of atom-wall distances and the validity
of the approximations used is established.Comment: RevTeX, epsf, 11 pages, 2 fig
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