434 research outputs found
On the density-potential mapping in time-dependent density functional theory
The key questions of uniqueness and existence in time-dependent density
functional theory are usually formulated only for potentials and densities that
are analytic in time. Simple examples, standard in quantum mechanics, lead
however to non-analyticities. We reformulate these questions in terms of a
non-linear Schr\"odinger equation with a potential that depends non-locally on
the wavefunction.Comment: 8 pages, 2 figure
Ordered structures in rotating ultracold Bose gases
The characterization of small samples of cold bosonic atoms in rotating
microtraps has recently attracted increasing interest due to the possibility to
deal with a few number of particles per site in optical lattices. We analyze
the evolution of ground state structures as the rotational frequency
increases. Various kinds of ordered structures are observed. For atoms,
the standard scenario, valid for large sytems, is absent, and only gradually
recovered as increases. The vortex contribution to the total angular
momentum as a function of ceases to be an increasing function of
, as observed in experiments of Chevy {\it et al.} (Phys. Rev. Lett.
85, 2223 (2000)). Instead, for small , it exhibits a sequence of peaks
showing wide minima at the values of , where no vortices appear.Comment: 35 pages, 17 figure
Topology of the gauge-invariant gauge field in two-color QCD
We investigate solutions to a nonlinear integral equation which has a central
role in implementing the non-Abelian Gauss's Law and in constructing
gauge-invariant quark and gluon fields. Here we concern ourselves with
solutions to this same equation that are not operator-valued, but are functions
of spatial variables and carry spatial and SU(2) indices. We obtain an
expression for the gauge-invariant gauge field in two-color QCD, define an
index that we will refer to as the ``winding number'' that characterizes it,
and show that this winding number is invariant to a small gauge transformation
of the gauge field on which our construction of the gauge-invariant gauge field
is based. We discuss the role of this gauge field in determining the winding
number of the gauge-invariant gauge field. We also show that when the winding
number of the gauge field is an integer , the gauge-invariant
gauge field manifests winding numbers that are not integers, and are
half-integers only when .Comment: 26 pages including 6 encapsulated postscript figures. Numerical
errors have been correcte
Green's function for a Schroedinger operator and some related summation formulas
Summation formulas are obtained for products of associated Lagurre
polynomials by means of the Green's function K for the Hamiltonian H =
-{d^2\over dx^2} + x^2 + Ax^{-2}, A > 0. K is constructed by an application of
a Mercer type theorem that arises in connection with integral equations. The
new approach introduced in this paper may be useful for the construction of
wider classes of generating function.Comment: 14 page
Quantum Effects for the Dirac Field in Reissner-Nordstrom-AdS Black Hole Background
The behavior of a charged massive Dirac field on a Reissner-Nordstrom-AdS
black hole background is investigated. The essential self-adjointness of the
Dirac Hamiltonian is studied. Then, an analysis of the discharge problem is
carried out in analogy with the standard Reissner-Nordstrom black hole case.Comment: 18 pages, 5 figures, Iop styl
Slow light in photonic crystals
The problem of slowing down light by orders of magnitude has been extensively
discussed in the literature. Such a possibility can be useful in a variety of
optical and microwave applications. Many qualitatively different approaches
have been explored. Here we discuss how this goal can be achieved in linear
dispersive media, such as photonic crystals. The existence of slowly
propagating electromagnetic waves in photonic crystals is quite obvious and
well known. The main problem, though, has been how to convert the input
radiation into the slow mode without loosing a significant portion of the
incident light energy to absorption, reflection, etc. We show that the
so-called frozen mode regime offers a unique solution to the above problem.
Under the frozen mode regime, the incident light enters the photonic crystal
with little reflection and, subsequently, is completely converted into the
frozen mode with huge amplitude and almost zero group velocity. The linearity
of the above effect allows to slow light regardless of its intensity. An
additional advantage of photonic crystals over other methods of slowing down
light is that photonic crystals can preserve both time and space coherence of
the input electromagnetic wave.Comment: 96 pages, 12 figure
A new test for random number generators: Schwinger-Dyson equations for the Ising model
We use a set of Schwinger-Dyson equations for the Ising Model to check
several random number generators. For the model in two and three dimensions, it
is shown that the equations are sensitive tests of bias originated by the
random numbers. The method is almost costless in computer time when added to
any simulation.Comment: 6 pages, 3 figure
On the class SI of J-contractive functions intertwining solutions of linear differential equations
In the PhD thesis of the second author under the supervision of the third
author was defined the class SI of J-contractive functions, depending on a
parameter and arising as transfer functions of overdetermined conservative 2D
systems invariant in one direction. In this paper we extend and solve in the
class SI, a number of problems originally set for the class SC of functions
contractive in the open right-half plane, and unitary on the imaginary line
with respect to some preassigned signature matrix J. The problems we consider
include the Schur algorithm, the partial realization problem and the
Nevanlinna-Pick interpolation problem. The arguments rely on a correspondence
between elements in a given subclass of SI and elements in SC. Another
important tool in the arguments is a new result pertaining to the classical
tangential Schur algorithm.Comment: 46 page
Explicit solutions to the Korteweg-de Vries equation on the half line
Certain explicit solutions to the Korteweg-de Vries equation in the first
quadrant of the -plane are presented. Such solutions involve algebraic
combinations of truly elementary functions, and their initial values correspond
to rational reflection coefficients in the associated Schr\"odinger equation.
In the reflectionless case such solutions reduce to pure -soliton solutions.
An illustrative example is provided.Comment: 17 pages, no figure
Photon propagator, monopoles and the thermal phase transition in 3D compact QED
We investigate the gauge boson propagator in three dimensional compact
Abelian gauge model in the Landau gauge at finite temperature. The presence of
the monopole plasma in the confinement phase leads to appearance of an
anomalous dimension in the momentum dependence of the propagator. The anomalous
dimension as well as an appropriate ratio of photon wave function
renormalization constants with and without monopoles are observed to be order
parameters for the deconfinement phase transition. We discuss the relation
between our results and the confining properties of the gluon propagator in
non--Abelian gauge theories.Comment: 4 pages, 5 EPS figures, RevTeX 4, uses epsfig.sty; repaced to match
version accepted for publication in Phys. Rev. Lett. (discussion on fits is
extended
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