4,269 research outputs found
Laplace transform of spherical Bessel functions
We provide a simple analytic formula in terms of elementary functions for the
Laplace transform j_{l}(p) of the spherical Bessel function than that appearing
in the literature, and we show that any such integral transform is a polynomial
of order l in the variable p with constant coefficients for the first l-1
powers, and with an inverse tangent function of argument 1/p as the coefficient
of the power l. We apply this formula for the Laplace transform of the memory
function related to the Langevin equation in a one-dimensional Debye model.Comment: 5 pages LATEX, no figures. Accepted 2002, Physica Script
Sine-Gordon Field Theory for the Kosterlitz-Thouless Transitions on Fluctuating Membranes
In the preceding paper, we derived Coulomb-gas and sine-Gordon Hamiltonians
to describe the Kosterlitz-Thouless transition on a fluctuating surface. These
Hamiltonians contain couplings to Gaussian curvature not found in a rigid flat
surface. In this paper, we derive renormalization-group recursion relations for
the sine-Gordon model using field-theoretic techniques developed to study flat
space problems.Comment: REVTEX, 14 pages with 6 postscript figures compressed using uufiles.
Accepted for publication in Phys. Rev.
Huygens' Principle for the Klein-Gordon equation in the de Sitter spacetime
In this article we prove that the Klein-Gordon equation in the de Sitter
spacetime obeys the Huygens' principle only if the physical mass of the
scalar field and the dimension of the spatial variable are tied by
the equation . Moreover, we define the incomplete Huygens'
principle, which is the Huygens' principle restricted to the vanishing second
initial datum, and then reveal that the massless scalar field in the de Sitter
spacetime obeys the incomplete Huygens' principle and does not obey the
Huygens' principle, for the dimensions , only. Thus, in the de Sitter
spacetime the existence of two different scalar fields (in fact, with m=0 and
), which obey incomplete Huygens' principle, is equivalent to
the condition (in fact, the spatial dimension of the physical world). For
these two values of the mass are the endpoints of the so-called in
quantum field theory the Higuchi bound. The value of the
physical mass allows us also to obtain complete asymptotic expansion of the
solution for the large time. Keywords: Huygens' Principle; Klein-Gordon
Equation; de Sitter spacetime; Higuchi Boun
Conservation laws for vacuum tetrad gravity
Ten conservation laws in useful polynomial form are derived from a Cartan
form and Exterior Differential System (EDS) for the tetrad equations of vacuum
relativity. The Noether construction of conservation laws for well posed EDS is
introduced first, and an illustration given, deriving 15 conservation laws of
the free field Maxwell Equations from symmetries of its EDS. The Maxwell EDS
and tetrad gravity EDS have parallel structures, with their numbers of
dependent variables, numbers of generating 2-forms and generating 3-forms, and
Cartan character tables all in the ratio of 1 to 4. They have 10 corresponding
symmetries with the same Lorentz algebra, and 10 corresponding conservation
laws.Comment: Final version with additional reference
Hot Electron Capture Dissociation Distinguishes Leucine from Isoleucine in a Novel Hemoglobin Variant, Hb Askew, β54(D5)Val→Ile
Population migration has led to the global dispersion of human hemoglobinopathies and has precipitated a need for their identification. An effective mass spectrometry-based procedure involves analysis of the intact α- and β-globin chains to determine their mass, followed by location of the variant amino acid residue by direct analysis of the enzymatically digested chains and low-energy collision induced dissociation of the variant peptide. Using this procedure, a variant was identified as either β54Val→Leu or β54Val→Ile, since the amino acids leucine and isoleucine cannot be distinguished using low-energy collisions. Here, we describe how hot electron capture dissociation on a Fourier transform-ion cyclotron resonance mass spectrometer was used to distinguish isoleucine from leucine and identify the mutation as β54(D5)Val→Ile. This is a novel variant, and we have named it Hb Askew
Significant changes in the skin microbiome mediated by the sport of roller derby
Diverse bacterial communities live on and in human skin. These complex communities vary by skin location on the body, over time, between individuals, and between geographic regions. Culture-based studies have shown that human to human and human to surface contact mediates the dispersal of pathogens, yet little is currently known about the drivers of bacterial community assembly patterns on human skin. We hypothesized that participation in a sport involving skin to skin contact would result in detectable shifts in skin bacterial community composition. We conducted a study during a flat track roller derby tournament, and found that teammates shared distinct skin microbial communities before and after playing against another team, but that opposing teams’ bacterial communities converged during the course of a roller derby bout. Our results are consistent with the hypothesis that the human skin microbiome shifts in composition during activities involving human to human contact, and that contact sports provide an ideal setting in which to evaluate dispersal of microorganisms between people
Mass as a Relativistic Quantum Observable
A field state containing photons propagating in different directions has a
non vanishing mass which is a quantum observable. We interpret the shift of
this mass under transformations to accelerated frames as defining space-time
observables canonically conjugated to energy-momentum observables. Shifts of
quantum observables differ from the predictions of classical relativity theory
in the presence of a non vanishing spin. In particular, quantum redshift of
energy-momentum is affected by spin. Shifts of position and energy-momentum
observables however obey simple universal rules derived from invariance of
canonical commutators.Comment: 5 pages, revised versio
Glassy Mean-Field Dynamics of the Backgammon model
In this paper we present an exact study of the relaxation dynamics of the
backgammon model. This is a model of a gas of particles in a discrete space
which presents glassy phenomena as a result of {\it entropy barriers} in
configuration space. The model is simple enough to allow for a complete
analytical treatment of the dynamics in infinite dimensions. We first derive a
closed equation describing the evolution of the occupation number
probabilities, then we generalize the analysis to the study the autocorrelation
function. We also consider possible variants of the model which allow to study
the effect of energy barriers.Comment: 21 pages, revtex, 4 uuencoded figure
Sonoluminescence as a QED vacuum effect: Probing Schwinger's proposal
Several years ago Schwinger proposed a physical mechanism for
sonoluminescence in terms of photon production due to changes in the properties
of the quantum-electrodynamic (QED) vacuum arising from a collapsing dielectric
bubble. This mechanism can be re-phrased in terms of the Casimir effect and has
recently been the subject of considerable controversy. The present paper probes
Schwinger's suggestion in detail: Using the sudden approximation we calculate
Bogolubov coefficients relating the QED vacuum in the presence of the expanded
bubble to that in the presence of the collapsed bubble. In this way we derive
an estimate for the spectrum and total energy emitted. We verify that in the
sudden approximation there is an efficient production of photons, and further
that the main contribution to this dynamic Casimir effect comes from a volume
term, as per Schwinger's original calculation. However, we also demonstrate
that the timescales required to implement Schwinger's original suggestion are
not physically relevant to sonoluminescence. Although Schwinger was correct in
his assertion that changes in the zero-point energy lead to photon production,
nevertheless his original model is not appropriate for sonoluminescence. In
other works (see quant-ph/9805023, quant-ph/9904013, quant-ph/9904018,
quant-ph/9905034) we have developed a variant of Schwinger's model that is
compatible with the physically required timescales.Comment: 18 pages, ReV_TeX 3.2, 9 figures. Major revisions: This document is
now limited to providing a probe of Schwinger's original suggestion for
sonoluminescence. For details on our own variant of Schwinger's ideas see
quant-ph/9805023, quant-ph/9904013, quant-ph/9904018, quant-ph/990503
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