2,546 research outputs found
Finite size corrections to the blackbody radiation laws
We investigate the radiation of a blackbody in a cavity of finite size. For a
given geometry, we use semiclassical techniques to obtain explicit expressions
of the modified Planck's and Stefan-Boltzmann's blackbody radiation laws as a
function of the size and shape of the cavity. We determine the range of
parameters (temperature, size and shape of the cavity) for which these effects
are accessible to experimental verification. Finally we discuss potential
applications of our findings in the physics of the cosmic microwave background
and sonoluminescence.Comment: 5 pages, 1 figure, journal versio
Chaotic dephasing in a double-slit scattering experiment
We design a computational experiment in which a quantum particle tunnels into
a billiard of variable shape and scatters out of it through a double-slit
opening on the billiard's base. The interference patterns produced by the
scattered probability currents for a range of energies are investigated in
relation to the billiard's geometry which is connected to its classical
integrability. Four billiards with hierarchical integrability levels are
considered: integrable, pseudo-integrable, weak-mixing and strongly chaotic. In
agreement with the earlier result by Casati and Prosen [1], we find the
billiard's integrability to have a crucial influence on the properties of the
interference patterns. In the integrable case most experiment outcomes are
found to be consistent with the constructive interference occurring in the
usual double-slit experiment. In contrast to this, non-integrable billiards
typically display asymmetric interference patterns of smaller visibility
characterized by weakly correlated wave function values at the two slits. Our
findings indicate an intrinsic connection between the classical integrability
and the quantum dephasing, responsible for the destruction of interference
Casimir Energy and Entropy between perfect metal Spheres
We calculate the Casimir energy and entropy for two perfect metal spheres in
the large and short separation limit. We obtain nonmonotonic behavior of the
Helmholtz free energy with separation and temperature, leading to parameter
ranges with negative entropy, and also nonmonotonic behavior of the entropy
with temperature and with the separation between the spheres. The appearance of
this anomalous behavior of the entropy is discussed as well as its
thermodynamic consequences.Comment: 10 pages and 8 figures. Accepted for publication in the Proceedings
of the tenth conference on Quantum Field Theory under the influence of
external conditions - QFEXT'1
Closed-orbit theory for spatial density oscillations
We briefly review a recently developed semiclassical theory for quantum
oscillations in the spatial (particle and kinetic energy) densities of finite
fermion systems and present some examples of its results. We then discuss the
inclusion of correlations (finite temperatures, pairing correlations) in the
semiclassical theory.Comment: LaTeX, 10pp., 2 figure
Some Calculable Contributions to Entanglement Entropy
Entanglement entropy appears as a central property of quantum systems in
broad areas of physics. However, its precise value is often sensitive to
unknown microphysics, rendering it incalculable. By considering parametric
dependence on correlation length, we extract finite, calculable contributions
to the entanglement entropy for a scalar field between the interior and
exterior of a spatial domain of arbitrary shape. The leading term is
proportional to the area of the dividing boundary; we also extract finite
subleading contributions for a field defined in the bulk interior of a
waveguide in 3+1 dimensions, including terms proportional to the waveguide's
cross-sectional geometry; its area, perimeter length, and integrated curvature.
We also consider related quantities at criticality and suggest a class of
systems for which these contributions might be measurable.Comment: 4+ pages, 1 figure. v2: Some clarifications and more references;
updated to resemble version published in PR
Application of the Trace Formula in Pseudointegrable Systems
We apply periodic-orbit theory to calculate the integrated density of states
from the periodic orbits of pseudointegrable polygon and barrier
billiards. We show that the results agree so well with the results obtained
from direct diagonalization of the Schr\"odinger equation, that about the first
100 eigenvalues can be obtained directly from the periodic-orbit calculations
in good accuracy.Comment: 5 Pages, 4 Figures, submitted to Phys. Rev.
Stochastic Quantization and Casimir Forces: Pistons of Arbitrary Cross Section
Recently, a method based on stochastic quantization has been proposed to
compute the Casimir force and its fluctuations in arbitrary geometries. It
relies on the spectral decomposition of the Laplacian operator in the given
geometry. Both quantum and thermal fluctuations are considered. Here we use
such method to compute the Casimir force on the plates of a finite piston of
arbitrary cross section. Asymptotic expressions valid at low and high
temperatures and short and long distances are obtained. The case of a piston
with triangular cross section is analysed in detail. The regularization of the
divergent stress tensor is described.Comment: 10 pages and 4 figures. Accepted for publication in the Proceedings
of the tenth conference on Quantum Field Theory under the influence of
external conditions - QFEXT'1
Spectroscopy of annular drums and quantum rings: perturbative and nonperturbative results
We obtain systematic approximations to the states (energies and wave
functions) of quantum rings (annular drums) of arbitrary shape by conformally
mapping the annular domain to a simply connected domain. Extending the general
results of Ref.\cite{Amore09} we obtain an analytical formula for the spectrum
of quantum ring of arbirtrary shape: for the cases of a circular annulus and of
a Robnik ring considered here this formula is remarkably simple and precise. We
also obtain precise variational bounds for the ground state of different
quantum rings. Finally we extend the Conformal Collocation Method of
\cite{Amore08,Amore09} to the class of problems considered here and calculate
precise numerical solutions for a large number of states ().Comment: 12 pages, 12 figures, 2 table
Resonance Patterns in a Stadium-shaped Microcavity
We investigate resonance patterns in a stadium-shaped microcavity around
, where is the refractive index, the vacuum
wavenumber, and the radius of the circular part of the cavity. We find that
the patterns of high resonances can be classified, even though the
classical dynamics of the stadium system is chaotic. The patterns of the high
resonances are consistent with the ray dynamical consideration, and appears
as the stationary lasing modes with low pumping rate in the nonlinear dynamical
model. All resonance patterns are presented in a finite range of .Comment: 8 pages, 9 figure
Quantal Consequences of Perturbations Which Destroy Structurally Unstable Orbits in Chaotic Billiards
Non-generic contributions to the quantal level-density from parallel segments
in billiards are investigated. These contributions are due to the existence of
marginally stable families of periodic orbits, which are structurally unstable,
in the sense that small perturbations, such as a slight tilt of one of the
segments, destroy them completely. We investigate the effects of such
perturbation on the corresponding quantum spectra, and demonstrate them for the
stadium billiard
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