650 research outputs found
Alternative Solution of the Path Integral for the Radial Coulomb Problem
In this Letter I present an alternative solution of the path integral for the
radial Coulomb problem which is based on a two-dimensional singular version of
the Levi-Civita transformation.Comment: 7 pages, Late
On the Path Integral in Imaginary Lobachevsky Space
The path integral on the single-sheeted hyperboloid, i.e.\ in -dimensional
imaginary Lobachevsky space, is evaluated. A potential problem which we call
``Kepler-problem'', and the case of a constant magnetic field are also
discussed.Comment: 16 pages, LATEX, DESY 93-14
Path Integral Approach for Superintegrable Potentials on Spaces of Non-constant Curvature: II. Darboux Spaces DIII and DIV
This is the second paper on the path integral approach of superintegrable
systems on Darboux spaces, spaces of non-constant curvature. We analyze in the
spaces \DIII and \DIV five respectively four superintegrable potentials,
which were first given by Kalnins et al. We are able to evaluate the path
integral in most of the separating coordinate systems, leading to expressions
for the Green functions, the discrete and continuous wave-functions, and the
discrete energy-spectra. In some cases, however, the discrete spectrum cannot
be stated explicitly, because it is determined by a higher order polynomial
equation.
We show that also the free motion in Darboux space of type III can contain
bound states, provided the boundary conditions are appropriate. We state the
energy spectrum and the wave-functions, respectively
Classification of quantum superintegrable systems with quadratic integrals on two dimensional manifolds
There are two classes of quantum integrable systems on a manifold with
quadratic integrals, the Liouville and the Lie integrable systems as it happens
in the classical case. The quantum Liouville quadratic integrable systems are
defined on a Liouville manifold and the Schr\"odinger equation can be solved by
separation of variables in one coordinate system. The Lie integrable systems
are defined on a Lie manifold and are not generally separable ones but the can
be solved. Therefore there are superintegrable systems with two quadratic
integrals of motion not necessarily separable in two coordinate systems. The
quantum analogues of the two dimensional superintegrable systems with quadratic
integrals of motion on a manifold are classified by using the quadratic
associative algebra of the integrals of motion. There are six general
fundamental classes of quantum superintegrable systems corresponding to the
classical ones. Analytic formulas for the involved integrals are calculated in
all the cases. All the known quantum superintegrable systems are classified as
special cases of these six general classes. The coefficients of the associative
algebra of the general cases are calculated. These coefficients are the same as
the coefficients of the classical case multiplied by plus quantum
corrections of order and .Comment: LaTeX file, 25 page
Multi-Channel Electron Transfer Reactions: An Analytically Solvable Model
We propose an analytical method for understanding the problem of
multi-channel electron transfer reaction in solution, modeled by a particle
undergoing diffusive motion under the influence of one donor and several
acceptor potentials. The coupling between the donor potential and acceptor
potentials are assumed to be represented by Dirac Delta functions. The
diffusive motion in this paper is represented by the Smoluchowski equation. Our
solution requires the knowledge of the Laplace transform of the Green's
function for the motion in all the uncoupled potentials.Comment: arXiv admin note: substantial text overlap with arXiv:0903.306
The Coulomb-Oscillator Relation on n-Dimensional Spheres and Hyperboloids
In this paper we establish a relation between Coulomb and oscillator systems
on -dimensional spheres and hyperboloids for . We show that, as in
Euclidean space, the quasiradial equation for the dimensional Coulomb
problem coincides with the -dimensional quasiradial oscillator equation on
spheres and hyperboloids. Using the solution of the Schr\"odinger equation for
the oscillator system, we construct the energy spectrum and wave functions for
the Coulomb problem.Comment: 15 pages, LaTe
Representation reduction and solution space contraction in quasi-exactly solvable systems
In quasi-exactly solvable problems partial analytic solution (energy spectrum
and associated wavefunctions) are obtained if some potential parameters are
assigned specific values. We introduce a new class in which exact solutions are
obtained at a given energy for a special set of values of the potential
parameters. To obtain a larger solution space one varies the energy over a
discrete set (the spectrum). A unified treatment that includes the standard as
well as the new class of quasi-exactly solvable problems is presented and few
examples (some of which are new) are given. The solution space is spanned by
discrete square integrable basis functions in which the matrix representation
of the Hamiltonian is tridiagonal. Imposing quasi-exact solvability constraints
result in a complete reduction of the representation into the direct sum of a
finite and infinite component. The finite is real and exactly solvable, whereas
the infinite is complex and associated with zero norm states. Consequently, the
whole physical space contracts to a finite dimensional subspace with
normalizable states.Comment: 25 pages, 4 figures (2 in color
Long-distance remote comparison of ultrastable optical frequencies with 1e-15 instability in fractions of a second
We demonstrate a fully optical, long-distance remote comparison of
independent ultrastable optical frequencies reaching a short term stability
that is superior to any reported remote comparison of optical frequencies. We
use two ultrastable lasers, which are separated by a geographical distance of
more than 50 km, and compare them via a 73 km long phase-stabilized fiber in a
commercial telecommunication network. The remote characterization spans more
than one optical octave and reaches a fractional frequency instability between
the independent ultrastable laser systems of 3e-15 in 0.1 s. The achieved
performance at 100 ms represents an improvement by one order of magnitude to
any previously reported remote comparison of optical frequencies and enables
future remote dissemination of the stability of 100 mHz linewidth lasers within
seconds.Comment: 7 pages, 4 figure
Doping driven magnetic instabilities and quantum criticality of NbFe
Using density functional theory we investigate the evolution of the magnetic
ground state of NbFe due to doping by Nb-excess and Fe-excess. We find
that non-rigid-band effects, due to the contribution of Fe-\textit{d} states to
the density of states at the Fermi level are crucial to the evolution of the
magnetic phase diagram. Furthermore, the influence of disorder is important to
the development of ferromagnetism upon Nb doping. These findings give a
framework in which to understand the evolution of the magnetic ground state in
the temperature-doping phase diagram. We investigate the magnetic instabilities
in NbFe. We find that explicit calculation of the Lindhard function,
, indicates that the primary instability is to finite
antiferromagnetism driven by Fermi surface nesting. Total energy
calculations indicate that antiferromagnetism is the ground
state. We discuss the influence of competing and finite
instabilities on the presence of the non-Fermi liquid behavior in
this material.Comment: 8 pages, 7 figure
- …