5,033 research outputs found
Relativistic and Radiative Corrections to the Mollow Spectrum
The incoherent, inelastic part of the resonance fluorescence spectrum of a
laser-driven atom is known as the Mollow spectrum [B. R. Mollow, Phys. Rev.
188, 1969 (1969)]. Starting from this level of description, we discuss
theoretical foundations of high-precision spectroscopy using the resonance
fluorescence light of strongly laser-driven atoms. Specifically, we evaluate
the leading relativistic and radiative corrections to the Mollow spectrum, up
to the relative orders of (Z alpha)^2 and alpha(Z alpha)^2, respectively, and
Bloch-Siegert shifts as well as stimulated radiative corrections involving
off-resonant virtual states. Complete results are provided for the hydrogen
1S-2P_{1/2} and 1S-2P_{3/2} transitions; these include all relevant correction
terms up to the specified order of approximation and could directly be compared
to experimental data. As an application, the outcome of such experiments would
allow for a sensitive test of the validity of the dressed-state basis as the
natural description of the combined atom-laser system.Comment: 20 pages, 1 figure; RevTe
Calculation of some determinants using the s-shifted factorial
Several determinants with gamma functions as elements are evaluated. This
kind of determinants are encountered in the computation of the probability
density of the determinant of random matrices. The s-shifted factorial is
defined as a generalization for non-negative integers of the power function,
the rising factorial (or Pochammer's symbol) and the falling factorial. It is a
special case of polynomial sequence of the binomial type studied in
combinatorics theory. In terms of the gamma function, an extension is defined
for negative integers and even complex values. Properties, mainly composition
laws and binomial formulae, are given. They are used to evaluate families of
generalized Vandermonde determinants with s-shifted factorials as elements,
instead of power functions.Comment: 25 pages; added section 5 for some examples of application
Nonlinear Integral-Equation Formulation of Orthogonal Polynomials
The nonlinear integral equation P(x)=\int_alpha^beta dy w(y) P(y) P(x+y) is
investigated. It is shown that for a given function w(x) the equation admits an
infinite set of polynomial solutions P(x). For polynomial solutions, this
nonlinear integral equation reduces to a finite set of coupled linear algebraic
equations for the coefficients of the polynomials. Interestingly, the set of
polynomial solutions is orthogonal with respect to the measure x w(x). The
nonlinear integral equation can be used to specify all orthogonal polynomials
in a simple and compact way. This integral equation provides a natural vehicle
for extending the theory of orthogonal polynomials into the complex domain.
Generalizations of the integral equation are discussed.Comment: 7 pages, result generalized to include integration in the complex
domai
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
Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
We study the problem of initiation of excitation waves in the FitzHugh-Nagumo
model. Our approach follows earlier works and is based on the idea of
approximating the boundary between basins of attraction of propagating waves
and of the resting state as the stable manifold of a critical solution. Here,
we obtain analytical expressions for the essential ingredients of the theory by
singular perturbation using two small parameters, the separation of time scales
of the activator and inhibitor, and the threshold in the activator's kinetics.
This results in a closed analytical expression for the strength-duration curve.Comment: 10 pages, 5 figures, as accepted to Chaos on 2017/06/2
Minimal coupling method and the dissipative scalar field theory
Quantum field theory of a damped vibrating string as the simplest dissipative
scalar field investigated by its coupling with an infinit number of
Klein-Gordon fields as the environment by introducing a minimal coupling
method. Heisenberg equation containing a dissipative term proportional to
velocity obtained for a special choice of coupling function and quantum
dynamics for such a dissipative system investigated. Some kinematical relations
calculated by tracing out the environment degrees of freedom. The rate of
energy flowing between the system and it's environment obtained.Comment: 15 pages, no figur
Spectral singularities for Non-Hermitian one-dimensional Hamiltonians: puzzles with resolution of identity
We examine the completeness of bi-orthogonal sets of eigenfunctions for
non-Hermitian Hamiltonians possessing a spectral singularity. The correct
resolutions of identity are constructed for delta like and smooth potentials.
Their form and the contribution of a spectral singularity depend on the class
of functions employed for physical states. With this specification there is no
obstruction to completeness originating from a spectral singularity.Comment: 25 pages, more refs adde
Effects of the Lattice Discreteness on a Soliton in the Su-Schrieffer-Heeger Model
In this paper we analytically study the effects of the lattice discreteness
on the electron band in the SSH model. We propose a modified version of the TLM
model which is derived from the SSH model using a continuum approximation. When
a soliton is induced in the electron-lattice system, the electron scattering
states both at the bottom of the valence band and the top of the conduction
band are attracted to the soliton. This attractive force induces weakly
localized electronic states at the band edges. Using the modified version of
the TLM model, we have succeeded in obtaining analytical solutions of the
weakly localized states and the extended states near the bottom of the valence
band and the top of the conduction band. This band structure does not modify
the order parameters. Our result coincides well with numerical simulation
works.Comment: to be appear in J.Phys.Soc.Jpn. Figures should be requested to the
author. They will be sent by the conventional airmai
Propagation of a Solitary Fission Wave
Reaction-diffusion phenomena are encountered in an astonishing array of natural systems. Under the right conditions, self stabilizing reaction waves can arise that will propagate at constant velocity. Numerical studies have shown that fission waves of this type are also possible and that they exhibit soliton like properties. Here, we derive the conditions required for a solitary fission wave to propagate at constant velocity. The results place strict conditions on the shapes of the flux, diffusive, and reactive profiles that would be required for such a phenomenon to persist, and this condition would apply to other reaction diffusion phenomena as well. Numerical simulations are used to confirm the results and show that solitary fission waves fall into a bistable class of reaction diffusion phenomena. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4729927]United States Nuclear Regulatory Commission NRC-38-08-946Mechanical Engineerin
Microbiological influences on fracture surfaces of intact mudstone and the implications for geological disposal of radioactive waste
The significance of the potential impacts of microbial activity on the transport properties of host rocks for geological repositories is an area of active research. Most recent work has focused on granitic environments. This paper describes pilot studies investigating changes in transport properties that are produced by microbial activity in sedimentary rock environments in northern Japan. For the first time, these short experiments (39 days maximum) have shown that the denitrifying bacteria, Pseudomonas denitrificans, can survive and thrive when injected into flow-through column experiments containing fractured diatomaceous mudstone and synthetic groundwater under pressurized conditions. Although there were few significant changes in the fluid chemistry, changes in the permeability of the biotic column, which can be explained by the observed biofilm formation, were quantitatively monitored. These same methodologies could also be adapted to obtain information from cores originating from a variety of geological environments including oil reservoirs, aquifers and toxic waste disposal sites to provide an understanding of the impact of microbial activity on the transport of a range of solutes, such as groundwater contaminants and gases (e.g. injected carbon dioxide)
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