4,326 research outputs found
Thermal Casimir effect with soft boundary conditions
We consider the thermal Casimir effect in systems of parallel plates coupled
to a mass-less free field theory via quadratic interaction terms which suppress
(i) the field on the plates (ii) the gradient of the field in the plane of the
plates. These boundary interactions correspond to (i) the presence of an
electrolyte in the plates and (ii) a uniform field of dipoles, in the plates,
which are polarizable in the plane of the plates. These boundary interactions
lead to Robin type boundary conditions in the case where there is no field
outside the two plates. In the appropriate limit, in both cases Dirichlet
boundary conditions are obtained but we show that in case (i) the Dirichlet
limit breaks down at short inter-plate distances and in (ii) it breaks down at
large distances. The behavior of the two plate system is also seen to be highly
dependent on whether the system is open or closed. In addition we analyze the
Casimir force on a third plate placed between two outer plates. The force
acting on the central plate is shown to be highly sensitive to whether or not
the fluctuating scalar field is present in the region exterior to the two
confining plates.Comment: 8 pages RevTex, 2 .eps figure
Ordering of anisotropic polarizable polymer chains on the full many-body level
We study the effect of dielectric anisotropy of polymers on their equilibrium
ordering within mean-field theory but with a formalism that takes into account
the full n-body nature of van der Waals forces. Dielectric anisotropy within
polymers is to be expected as the electronic properties of the polymer will
typically be different along the polymer than across its cross section. It is
therefore physically intuitive that larger charge fluctuations can be induced
along the chain than perpendicular to it. We show that this dielectric
anisotropy leads to n-body interactions which can induce an isotropic--nematic
transition. The two body and three body components of the full van der Waals
interaction are extracted and it is shown how the two body term behaves like
the phenomenological self-aligning-pairwise nematic interaction. At the three
body interaction level we see that the nematic phase that is energetically
favorable is discotic, however on the full n-body interaction level we find
that the normal axial nematic phase is always the stable ordered phase. The
n-body nature of our approach also shows that the key parameter driving the
nematic-isotropic transition is the bare persistence length of the polymer
chain.Comment: 12 pages Revtex, 4 figure
Exact Results on Sinai's Diffusion
We study the continuum version of Sinai's problem of a random walker in a
random force field in one dimension. A method of stochastic representations is
used to represent various probability distributions in this problem (mean
probability density function and first passage time distributions). This method
reproduces already known rigorous results and also confirms directly some
recent results derived using approximation schemes. We demonstrate clearly, in
the Sinai scaling regime, that the disorder dominates the problem and that the
thermal distributions tend to zero-one laws.Comment: 14 pages Latex. To appear J. Phys.
Metastable states of a ferromagnet on random thin graphs
We calculate the mean number of metastable states of an Ising ferromagnet on
random thin graphs of fixed connectivity c. We find, as for mean field spin
glasses that this mean increases exponentially with the number of sites, and is
the same as that calculated for the +/- J spin glass on the same graphs. An
annealed calculation of the number of metastable states of energy E
is carried out. For small c, an analytic result is obtained. The result is
compared with the one obtained for spin glasses in order to discuss the role
played by loops on thin graphs and hence the effect of real frustration on the
distribution of metastable states.Comment: 15 pages, 3 figure
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