616 research outputs found
Casimir Energy for concentric - spheres
We study the vacuum interaction of a scalar field and two concentric spheres
defined by a singular potential on their surfaces. The potential is a linear
combination of the Dirac- and its derivative. The presence of the delta
prime term in the potential causes that it behaves differently when it is seen
from the inside or from the outside of the sphere. We study different cases for
positive and negative values of the delta prime coupling, keeping positive the
coupling of the delta. As a consequence, we find regions in the space of
couplings, where the energy is positive, negative or zero. Moreover, the sign
of the couplings cause different behavior on the value of the Casimir
energy for different values of the radii. This potential gives rise to general
boundary conditions with limiting cases defining Dirichlet and Robin boundary
conditions what allows us to simulate purely electric o purely magnetic
spheres.Comment: 9 pages, 8 figures We are submitting this manuscript for publication
in Physical Review
Surface Divergences and Boundary Energies in the Casimir Effect
Although Casimir, or quantum vacuum, forces between distinct bodies, or
self-stresses of individual bodies, have been calculated by a variety of
different methods since 1948, they have always been plagued by divergences.
Some of these divergences are associated with the volume, and so may be more or
less unambiguously removed, while other divergences are associated with the
surface. The interpretation of these has been quite controversial. Particularly
mysterious is the contradiction between finite total self-energies and surface
divergences in the local energy density. In this paper we clarify the role of
surface divergences.Comment: 8 pages, 1 figure, submitted to proceedings of QFEXT0
Casimir self-energy of a \delta-\delta' sphere
We extend previous work on the vacuum energy of a massless scalar field in
the presence of singular potentials. We consider a single sphere denoted by the
so-called "delta-delta prime" interaction. Contrary to the Dirac delta
potential, we find a nontrivial one-parameter family of potentials such that
the regularization procedure gives an unambiguous result for the Casimir
self-energy. The procedure employed is based on the zeta function
regularization and the cancellation of the heat kernel coefficient a_2. The
results obtained are in agreement with particular cases, such as the Dirac
delta or Robin and Dirichlet boundary conditions
Double-delta potentials: one dimensional scattering. The Casimir effect and kink fluctuations
The path is explored between one-dimensional scattering through
Dirac- walls and one-dimensional quantum field theories defined on a
finite length interval with Dirichlet boundary conditions. It is found that two
's are related to the Casimir effect whereas two 's plus the
first transparent Psch-Teller well arise in the context of the
sine-Gordon kink fluctuations, both phenomena subjected to Dirichlet boundary
conditions. One or two delta wells will be also explored in order to describe
absorbent plates, even though the wells lead to non unitary Quantum Field
Theories.Comment: 15 pages. To be published in the International Journal of Theoretical
Physic
Casimir interaction between plane and spherical metallic surfaces
We give an exact series expansion of the Casimir force between plane and
spherical metallic surfaces in the non trivial situation where the sphere
radius , the plane-sphere distance and the plasma wavelength
have arbitrary relative values. We then present numerical
evaluation of this expansion for not too small values of . For metallic
nanospheres where and have comparable values, we interpret
our results in terms of a correlation between the effects of geometry beyond
the proximity force approximation (PFA) and of finite reflectivity due to
material properties. We also discuss the interest of our results for the
current Casimir experiments performed with spheres of large radius .Comment: 4 pages, new presentation (highlighting the novelty of the results)
and added references. To appear in Physical Review Letter
Toward an Integrated Model of Pathological Personality Traits: Common Hierarchical Structure of the PID-5 and the DAPP-BQ
A dimensional classification seems to be the next move in the personality disorders field. However, it is not clear whether we have one dimensional model or many, or whether the currently available dimensional instruments measure the same traits. To help clarify these issues, we administered the Personality Inventory for DSM-5 (PID-5) and the Dimensional Assessment of Personality Pathology (DAPP-BQ) to 414 psychiatric outpatients. Factor analyses showed that a common hierarchical structure underlies both instruments, and that both cover every aspect of this structure equally well. Furthermore, disattenuated correlations indicated that two thirds of the PID and DAPP facets measure essentially the same traits, although the pairings were not exactly as predicted. Among higher-order domains, only PID Negative Affectivity and Detachment converged unambiguously with DAPP Emotional Dysregulation and Inhibition. Overall, the PID-5 and the DAPP-BQ reflect one and the same structure of personality pathology and can be used interchangeably
Topological entropy and renormalization group flow in 3-dimensional spherical spaces
We analyze the renormalization group (RG) flow of the temperature independent term of the entropy in the high temperature limit ß/a « 1 of a massive field theory in 3-dimensional spherical spaces, M 3, with constant curvature 6/a 2. For masses lower than 2p/ß , this term can be identified with the free energy of the same theory on M 3 considered as a 3-dimensional Euclidean space-time. The non-extensive part of this free energy, S hol, is generated by the holonomy of the spatial metric connection. We show that for homogeneous spherical spaces the holonomy entropy S hol decreases monotonically when the RG scale flows to the infrared. At the conformal fixed points the values of the holonomy entropy do coincide with the genuine topological entropies recently introduced. The monotonic behavior of the RG flow leads to an inequality between the topological entropies of the conformal field theories connected by such flow, i.e. S top UV¿>¿S top IR . From a 3-dimensional viewpoint the same term arises in the 3-dimensional Euclidean effective action and has the same monotonic behavior under the RG group flow. We conjecture that such monotonic behavior is generic, which would give rise to a 3-dimensional generalization of the c-theorem, along the lines of the 2-dimensional c-theorem and the 4-dimensional a-theorem. The conjecture is related to recent formulations of the F-theorem. In particular, the holonomy entropy on lens spaces is directly related to the topological Rényi entanglement entropy on disks of 2-dimensional flat spaces
Local and Global Casimir Energies for a Semitransparent Cylindrical Shell
The local Casimir energy density and the global Casimir energy for a massless
scalar field associated with a -function potential in a 3+1
dimensional circular cylindrical geometry are considered. The global energy is
examined for both weak and strong coupling, the latter being the well-studied
Dirichlet cylinder case. For weak-coupling,through ,
the total energy is shown to vanish by both analytic and numerical arguments,
based both on Green's-function and zeta-function techniques. Divergences
occurring in the calculation are shown to be absorbable by renormalization of
physical parameters of the model. The global energy may be obtained by
integrating the local energy density only when the latter is supplemented by an
energy term residing precisely on the surface of the cylinder. The latter is
identified as the integrated local energy density of the cylindrical shell when
the latter is physically expanded to have finite thickness. Inside and outside
the delta-function shell, the local energy density diverges as the surface of
the shell is approached; the divergence is weakest when the conformal stress
tensor is used to define the energy density. A real global divergence first
occurs in , as anticipated, but the proof is supplied
here for the first time; this divergence is entirely associated with the
surface energy, and does {\em not} reflect divergences in the local energy
density as the surface is approached.Comment: 28 pages, REVTeX, no figures. Appendix added on perturbative
divergence
- …