528 research outputs found
Path Integral Approach for Spaces of Non-constant Curvature in Three Dimensions
In this contribution I show that it is possible to construct
three-dimensional spaces of non-constant curvature, i.e. three-dimensional
Darboux-spaces. Two-dimensional Darboux spaces have been introduced by Kalnins
et al., with a path integral approach by the present author. In comparison to
two dimensions, in three dimensions it is necessary to add a curvature term in
the Lagrangian in order that the quantum motion can be properly defined. Once
this is done, it turns out that in the two three-dimensional Darboux spaces,
which are discussed in this paper, the quantum motion is similar to the
two-dimensional case. In \threedDI we find seven coordinate systems which
separate the Schr\"odinger equation. For the second space, \threedDII, all
coordinate systems of flat three-dimensional Euclidean space which separate the
Schr\"odinger equation also separate the Schr\"odinger equation in
\threedDII. I solve the path integral on \threedDI in the -system,
and on \threedDII in the -system and in spherical coordinates
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
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
Brillouin amplification in phase coherent transfer of optical frequencies over 480 km fiber
We describe the use of fiber Brillouin amplification (FBA) for the coherent
transmission of optical frequencies over a 480 km long optical fiber link. FBA
uses the transmission fiber itself for efficient, bi-directional coherent
amplification of weak signals with pump powers around 30 mW. In a test setup we
measured the gain and the achievable signal-to-noise ratio (SNR) of FBA and
compared it to that of the widely used uni-directional Erbium doped fiber
amplifiers (EDFA) and to our recently built bi-directional EDFA. We measured
also the phase noise introduced by the FBA and used a new and simple technique
to stabilize the frequency of the FBA pump laser. We then transferred a
stabilized laser frequency over a wide area network with a total fiber length
of 480 km using only one intermediate FBA station. After compensating the noise
induced by the fiber, the frequency is delivered to the user end with an
uncertainty below 2x10-18 and an instability sigma(tau) = 2x10-14/(tau/second)
On the Green function of linear evolution equations for a region with a boundary
We derive a closed-form expression for the Green function of linear evolution
equations with the Dirichlet boundary condition for an arbitrary region, based
on the singular perturbation approach to boundary problems.Comment: 9 page
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
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
Superconductivity on the threshold of magnetism in CePd2Si2 and CeIn3
The magnetic ordering temperature of some rare earth based heavy fermion
compounds is strongly pressure-dependent and can be completely suppressed at a
critical pressure, p, making way for novel correlated electron states close
to this quantum critical point. We have studied the clean heavy fermion
antiferromagnets CePdSi and CeIn in a series of resistivity
measurements at high pressures up to 3.2 GPa and down to temperatures in the mK
region. In both materials, superconductivity appears in a small window of a few
tenths of a GPa on either side of p. We present detailed measurements of
the superconducting and magnetic temperature-pressure phase diagram, which
indicate that superconductivity in these materials is enhanced, rather than
suppressed, by the closeness to magnetic order.Comment: 11 pages, including 9 figure
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