15 research outputs found
Induced fermionic current in toroidally compactified spacetimes with applications to cylindrical and toroidal nanotubes
The vacuum expectation value of the fermionic current is evaluated for a
massive spinor field in spacetimes with an arbitrary number of toroidally
compactified spatial dimensions in presence of a constant gauge field. By using
the Abel-Plana type summation formula and the zeta function technique we
present the fermionic current in two different forms. Non-trivial topology of
the background spacetime leads to the Aharonov-Bohm effect on the fermionic
current induced by the gauge field. The current is a periodic function of the
magnetic flux with the period equal to the flux quantum. In the absence of the
gauge field it vanishes for special cases of untwisted and twisted fields.
Applications of the general formulae to Kaluz-Klein type models and to
cylindrical and toroidal carbon nanotubes are given. In the absence of magnetic
flux the total fermionic current in carbon nanotubes vanishes, due to the
cancellation of contributions from two different sublattices of the graphene
hexagonal lattice.Comment: 18 pages, 5 figures, explicit regularization procedure adde
Thermal Casimir effect for neutrino and electromagnetic fields in closed Friedmann cosmological model
We calculate the total internal energy, total energy density and pressure,
and the free energy for the neutrino and electromagnetic fields in Einstein and
closed Friedmann cosmological models. The Casimir contributions to all these
quantities are separated. The asymptotic expressions for both the total
internal energy and free energy, and for the Casimir contributions to them are
found in the limiting cases of low and high temperatures. It is shown that the
neutrino field does not possess a classical limit at high temperature. As for
the electromagnetic field, we demonstrate that the total internal energy has
the classical contribution and the Casimir internal energy goes to the
classical limit at high temperature. The respective Casimir free energy
contains both linear and logarithmic terms with respect to the temperature. The
total and Casimir entropies for the neutrino and electromagnetic fields at low
temperature are also calculated and shown to be in agreement with the Nernst
heat theorem.Comment: 23 pages, to appear in Phys. Rev.
Casimir energy and a cosmological bounce
We review different computation methods for the renormalised energy momentum
tensor of a quantised scalar field in an Einstein Static Universe. For the
extensively studied conformally coupled case we check their equivalence; for
different couplings we discuss violation of different energy conditions. In
particular, there is a family of masses and couplings which violate the weak
and strong energy conditions but do not lead to spacelike propagation. Amongst
these cases is that of a minimally coupled massless scalar field with no
potential. We also point out a particular coupling for which a massless scalar
field has vanishing renormalised energy momentum tensor. We discuss the
backreaction problem and in particular the possibility that this Casimir energy
could both source a short inflationary epoch and avoid the big bang singularity
through a bounce.Comment: 13 pages, LaTeX, 8 figure
Space-Time Description of Scalar Particle Creation by a Homogeneous Isotropic Gravitational Field
We give the generalization of the method of the space-time description of
particle creation by a gravitational field for a scalar field with nonconformal
coupling to the curvature. The space-time correlation function is obtained for
a created pair of the quasi-particles, corresponding to a diagonal form of the
instantaneous Hamiltonian. The case of an adiabatic change of the metric of
homogeneous isotropic space is analyzed. We show that the created pairs of
quasi-particles in de Sitter space should be interpreted as pairs of virtual
particles.Comment: 7 pages, 3 figure
Multidimensional cut-off technique, odd-dimensional Epstein zeta functions and Casimir energy of massless scalar fields
Quantum fluctuations of massless scalar fields represented by quantum
fluctuations of the quasiparticle vacuum in a zero-temperature dilute
Bose-Einstein condensate may well provide the first experimental arena for
measuring the Casimir force of a field other than the electromagnetic field.
This would constitute a real Casimir force measurement - due to quantum
fluctuations - in contrast to thermal fluctuation effects. We develop a
multidimensional cut-off technique for calculating the Casimir energy of
massless scalar fields in -dimensional rectangular spaces with large
dimensions and dimensions of length and generalize the technique to
arbitrary lengths. We explicitly evaluate the multidimensional remainder and
express it in a form that converges exponentially fast. Together with the
compact analytical formulas we derive, the numerical results are exact and easy
to obtain. Most importantly, we show that the division between analytical and
remainder is not arbitrary but has a natural physical interpretation. The
analytical part can be viewed as the sum of individual parallel plate energies
and the remainder as an interaction energy. In a separate procedure, via
results from number theory, we express some odd-dimensional homogeneous Epstein
zeta functions as products of one-dimensional sums plus a tiny remainder and
calculate from them the Casimir energy via zeta function regularization.Comment: 42 pages, 3 figures. v.2: typos corrected to match published versio
Thermal Casimir effect in ideal metal rectangular boxes
The thermal Casimir effect in ideal metal rectangular boxes is considered
using the method of zeta functional regularization. The renormalization
procedure is suggested which provides the finite expression for the Casimir
free energy in any restricted quantization volume. This expression satisfies
the classical limit at high temperature and leads to zero thermal Casimir force
for systems with infinite characteristic dimensions. In the case of two
parallel ideal metal planes the results, as derived previously using thermal
quantum field theory in Matsubara formulation and other methods, are reproduced
starting from the obtained expression. It is shown that for rectangular boxes
the temperature-dependent contribution to the electromagnetic Casimir force can
be both positive and negative depending on side lengths. The numerical
computations of the scalar and electromagnetic Casimir free energy and force
are performed for cubesComment: 10 pages, 4 figures, to appear in Europ. Phys. J.