4,531 research outputs found
Evaluation of Casimir energies through spectral functions
This is an introductory set of lectures on elliptic differential operators
and boundary problems, and their associated spectral functions. The role of
zeta functions and traces of heat kernels in the regularization of Casimir
energies is emphasized, and the renormalization issue is discussed through
simple examples.Comment: Lectures given at the IFSAP, St. Petersburg, Russia, December 2000.
LateX, 31 page
Finite temperature properties of the Dirac operator under local boundary conditions
We study the finite temperature free energy and fermion number for Dirac
fields in a one-dimensional spatial segment, under two different members of the
family of local boundary conditions defining a self-adjoint Euclidean Dirac
operator in two dimensions. For one of such boundary conditions, compatible
with the presence of a spectral asymmetry, we discuss in detail the
contribution of this part of the spectrum to the zeta-regularized determinant
of the Dirac operator and, thus, to the finite temperature properties of the
theory.Comment: Final version, to appear in Journal of Physics
Boundary conditions in the Dirac approach to graphene devices
We study a family of local boundary conditions for the Dirac problem
corresponding to the continuum limit of graphene, both for nanoribbons and
nanodots. We show that, among the members of such family, MIT bag boundary
conditions are the ones which are in closest agreement with available
experiments. For nanotubes of arbitrary chirality satisfying these last
boundary conditions, we evaluate the Casimir energy via zeta function
regularization, in such a way that the limit of nanoribbons is clearly
determined.Comment: 10 pages, no figure. Section on Casimir energy adde
Undulated cylinders of charged diblock copolymers
We study the cylinder to sphere morphological transition of diblock
copolymers in aqueous solution with a hydrophobic block and a charged block. We
find a metastable undulated cylinder configuration for a range of charge and
salt concentrations which, nevertheless, occurs above the threshold where
spheres are thermodynamically favorable. By modeling the shape of the cylinder
ends, we find that the free energy barrier for the transition from cylinders to
spheres is quite large and that this barrier falls significantly in the limit
of high polymer charge and low solution salinity. This suggests that observed
undulated cylinder phases are kinetically trapped structures
Thermodynamics of conformal fields in topologically non-trivial space-time backgrounds
We analyze the finite temperature behaviour of massless conformally coupled
scalar fields in homogeneous lens spaces . High and low
temperature expansions are explicitly computed and the behavior of
thermodynamic quantities under thermal duality is scrutinized. The analysis of
the entropy of the different lens spaces in the high-temperature limit points
out the appearance of a topological nonextensive entropy, besides the standard
Stefan-Boltzmann extensive term. The remaining terms are exponentially
suppressed by the temperature. The topological entropy appears as a subleading
correction to the free energy that can be obtained from the determinant of the
lens space conformal Laplacian operator. In the low-temperature limit the
leading term in the free energy is the Casimir energy and there is no trace of
any power correction in any lens space. In fact, the remaining corrections are
always exponentially suppressed by the inverse of the temperature. The duality
between the results of both expansions is further analyzed in the paper.Comment: 21 pages, 2 figure
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