4 research outputs found
The bulk correlation length and the range of thermodynamic Casimir forces at Bose-Einstein condensation
The relation between the bulk correlation length and the decay length of
thermodynamic Casimir forces is investigated microscopically in two
three-dimensional systems undergoing Bose-Einstein condensation: the perfect
Bose gas and the imperfect mean-field Bose gas. For each of these systems, both
lengths diverge upon approaching the corresponding condensation point from the
one-phase side, and are proportional to each other. We determine the
proportionality factors and discuss their dependence on the boundary
conditions. The values of the corresponding critical exponents for the decay
length and the correlation length are the same, equal to 1/2 for the perfect
gas, and 1 for the imperfect gas
Excess free energy and Casimir forces in systems with long-range interactions of van-der-Waals type: General considerations and exact spherical-model results
We consider systems confined to a -dimensional slab of macroscopic lateral
extension and finite thickness that undergo a continuous bulk phase
transition in the limit and are describable by an O(n) symmetrical
Hamiltonian. Periodic boundary conditions are applied across the slab. We study
the effects of long-range pair interactions whose potential decays as as , with and , on
the Casimir effect at and near the bulk critical temperature ,
for . For the scaled reduced Casimir force per unit cross-sectional
area, we obtain the form L^{d} {\mathcal F}_C/k_BT \approx \Xi_0(L/\xi_\infty)
+ g_\omega L^{-\omega}\Xi\omega(L/\xi_\infty) + g_\sigma L^{-\omega_\sigm a}
\Xi_\sigma(L \xi_\infty). The contribution decays for
algebraically in rather than exponentially, and hence
becomes dominant in an appropriate regime of temperatures and . We derive
exact results for spherical and Gaussian models which confirm these findings.
In the case , which includes that of nonretarded van-der-Waals
interactions in dimensions, the power laws of the corrections to scaling
of the spherical model are found to get modified by logarithms.
Using general RG ideas, we show that these logarithmic singularities originate
from the degeneracy that occurs for the spherical
model when , in conjunction with the dependence of .Comment: 28 RevTeX pages, 12 eps figures, submitted to PR