1,794 research outputs found
Universal behavior of quantum Green's functions
We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined
in a d-dimensional domain. The object of interest is the time-independent Green
function G_z(r,r') = . Recently, in one dimension (1D),
the Green's function problem was solved explicitly in inverse form, with
diagonal elements of Green's function as prescribed variables. The first aim of
this paper is to extract from the 1D inverse solution such information about
Green's function which cannot be deduced directly from its definition. Among
others, this information involves universal, i.e. u(r)-independent, behavior of
Green's function close to the domain boundary. The second aim is to extend the
inverse formalism to higher dimensions, especially to 3D, and to derive the
universal form of Green's function for various shapes of the confining domain
boundary.Comment: 46 pages, the shortened version submitted to J. Math. Phy
A zeta function approach to the relation between the numbers of symmetry planes and axes of a polytope
A derivation of the Ces\`aro-Fedorov relation from the Selberg trace formula
on an orbifolded 2-sphere is elaborated and extended to higher dimensions using
the known heat-kernel coefficients for manifolds with piecewise-linear
boundaries. Several results are obtained that relate the coefficients, ,
in the Shephard-Todd polynomial to the geometry of the fundamental domain. For
the 3-sphere we show that is given by the ratio of the volume of the
fundamental tetrahedron to its Schl\"afli reciprocal.Comment: Plain TeX, 26 pages (eqn. (86) corrected
The Active Traveling Wave in the Cochlea
A sound stimulus entering the inner ear excites a deformation of the basilar
membrane which travels along the cochlea towards the apex. It is well
established that this wave-like disturbance is amplified by an active system.
Recently, it has been proposed that the active system consists of a set of
self-tuned critical oscillators which automatically operate at an oscillatory
instability. Here, we show how the concepts of a traveling wave and of
self-tuned critical oscillators can be combined to describe the nonlinear wave
in the cochlea.Comment: 5 pages, 2 figure
On electrostatic and Casimir force measurements between conducting surfaces in a sphere-plane configuration
We report on measurements of forces acting between two conducting surfaces in
a spherical-plane configuration in the 35 nm-1 micrometer separation range. The
measurements are obtained by performing electrostatic calibrations followed by
a residual analysis after subtracting the electrostatic-dependent component. We
find in all runs optimal fitting of the calibrations for exponents smaller than
the one predicted by electrostatics for an ideal sphere-plane geometry. We also
find that the external bias potential necessary to minimize the electrostatic
contribution depends on the sphere-plane distance. In spite of these anomalies,
by implementing a parametrixation-dependent subtraction of the electrostatic
contribution we have found evidence for short-distance attractive forces of
magnitude comparable to the expected Casimir-Lifshitz force. We finally discuss
the relevance of our findings in the more general context of Casimir-Lifshitz
force measurements, with particular regard to the critical issues of the
electrical and geometrical characterization of the involved surfaces.Comment: 22 pages, 15 figure
A three dimensional dynamic study of electrostatic charging in materials
A description is given of the physical models employed in the NASCAP (NASA Charging Analyzer Program) code, and several test cases are presented. NASCAP dynamically simulates the charging of an object made of conducting segments which may be entirely or partially covered with thin dielectric films. The object may be subject to either ground test or space user-specified environments. The simulation alternately treats (1) the tendency of materials to accumulate and emit charge when subject to plasma environment, and (2) the consequent response of the charged particle environment to an object's electrostatic field. Parameterized formulations of the emission properties of materials subject to bombardment by electrons, protons, and sunlight are presented. Values of the parameters are suggested for clean aluminum, Al2O3, clean magnesium, MgO, SiO2 kapton, and teflon. A discussion of conductivity in thin dielectrics subject to radiation and high fields is given, together with a sample calculation
Bose-Einstein condensation in arbitrarily shaped cavities
We discuss the phenomenon of Bose-Einstein condensation of an ideal
non-relativistic Bose gas in an arbitrarily shaped cavity. The influence of the
finite extension of the cavity on all thermodynamical quantities, especially on
the critical temperature of the system, is considered. We use two main methods
which are shown to be equivalent. The first deals with the partition function
as a sum over energy levels and uses a Mellin-Barnes integral representation to
extract an asymptotic formula. The second method converts the sum over the
energy levels to an integral with a suitable density of states factor obtained
from spectral analysis. The application to some simple cavities is discussed.Comment: 10 pages, LaTeX, to appear in Physical Review
Stability of the Autism Diagnostic Interview—Revised from Pre-School to Elementary School Age in Children with Autism Spectrum Disorders
This study examined the stability of scores on the ADI-R from pre-school to elementary school age in children with autism spectrum disorders (ASD). Participants were 35 children who, at T1, all had a clinical diagnosis of ASD. On initial assessment (mean age 3.5 years; SD 0.6), all met ADI-R algorithm criteria for autism. ADI-R assessments were repeated at follow up (FU; mean age 10.5 years; SD 0.8). Changes in ADI-R total, domain and ADI-R algorithm item scores were assessed. Twentyeight children continued to score above the ADI-R cut-off for autism at FU, although significant decreases in ADI-R domain and item scores were also found. In conclusion, while classification of children according to ADI-R criteria, generally remained stable between pre-school and elementary school age, many children demonstrated significant improvements in symptom severity
Integrating Teaching and Research in Undergraduate Biology Laboratory Education
A course recently designed and implemented at Stanford University applies practical suggestions for creating research-based undergraduate courses that benefit both teaching and research
Casimir effect due to a single boundary as a manifestation of the Weyl problem
The Casimir self-energy of a boundary is ultraviolet-divergent. In many cases
the divergences can be eliminated by methods such as zeta-function
regularization or through physical arguments (ultraviolet transparency of the
boundary would provide a cutoff). Using the example of a massless scalar field
theory with a single Dirichlet boundary we explore the relationship between
such approaches, with the goal of better understanding the origin of the
divergences. We are guided by the insight due to Dowker and Kennedy (1978) and
Deutsch and Candelas (1979), that the divergences represent measurable effects
that can be interpreted with the aid of the theory of the asymptotic
distribution of eigenvalues of the Laplacian discussed by Weyl. In many cases
the Casimir self-energy is the sum of cutoff-dependent (Weyl) terms having
geometrical origin, and an "intrinsic" term that is independent of the cutoff.
The Weyl terms make a measurable contribution to the physical situation even
when regularization methods succeed in isolating the intrinsic part.
Regularization methods fail when the Weyl terms and intrinsic parts of the
Casimir effect cannot be clearly separated. Specifically, we demonstrate that
the Casimir self-energy of a smooth boundary in two dimensions is a sum of two
Weyl terms (exhibiting quadratic and logarithmic cutoff dependence), a
geometrical term that is independent of cutoff, and a non-geometrical intrinsic
term. As by-products we resolve the puzzle of the divergent Casimir force on a
ring and correct the sign of the coefficient of linear tension of the Dirichlet
line predicted in earlier treatments.Comment: 13 pages, 1 figure, minor changes to the text, extra references
added, version to be published in J. Phys.
Equation of state and magnetic susceptibility of spin polarized isospin asymmetric nuclear matter
Properties of spin polarized isospin asymmetric nuclear matter are studied
within the framework of the Brueckner--Hartree--Fock formalism. The
single-particle potentials of neutrons and protons with spin up and down are
determined for several values of the neutron and proton spin polarizations and
the asymmetry parameter. It is found an almost linear and symmetric variation
of the single-particle potentials as increasing these parameters. An analytic
parametrization of the total energy per particle as a function of the asymmetry
and spin polarizations is constructed. This parametrization is employed to
compute the magnetic susceptibility of nuclear matter for several values of the
asymmetry from neutron to symmetric matter. The results show no indication of a
ferromagnetic transition at any density for any asymmetry of nuclear matter.Comment: 23 pages, 8 figures, 2 tables (submitted to Phys. Rev. C
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