462 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
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 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
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
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
Quantum Oscillator on \DC P^n in a constant magnetic field
We construct the quantum oscillator interacting with a constant magnetic
field on complex projective spaces \DC P^N, as well as on their non-compact
counterparts, i. e. the dimensional Lobachewski spaces . We
find the spectrum of this system and the complete basis of wavefunctions.
Surprisingly, the inclusion of a magnetic field does not yield any qualitative
change in the energy spectrum. For the magnetic field does not break the
superintegrability of the system, whereas for N=1 it preserves the exact
solvability of the system.
We extend this results to the cones constructed over \DC P^N and , and perform the (Kustaanheimo-Stiefel) transformation of these systems
to the three-dimensional Coulomb-like systems.Comment: 9 pages, 1 figur
Pseudo-Casimir force in confined nematic polymers
We investigate the pseudo-Casimir force in a slab of material composed of
nematically ordered long polymers. We write the total mesoscopic energy
together with the constraint connecting the local density and director
fluctuations and evaluate the corresponding fluctuation free energy by standard
methods. It leads to a pseudo-Casimir force of a different type than in the
case of standard, short molecule nematic. We investigate its separation
dependence and its magnitude and explicitly derive the relevant limiting cases.Comment: 7 pages, 2 figure
Pressure Induced Change in the Magnetic Modulation of CeRhIn5
We report the results of a high pressure neutron diffraction study of the
heavy fermion compound CeRhIn5 down to 1.8 K. CeRhIn5 is known to order
magnetically below 3.8 K with an incommensurate structure. The application of
hydrostatic pressure up to 8.6 kbar produces no change in the magnetic wave
vector qm. At 10 kbar of pressure however, a sudden change in the magnetic
structure occurs. Although the magnetic transition temperature remains the
same, qm increases from (0.5, 0.5, 0.298) to (0.5, 0.5, 0.396). This change in
the magnetic modulation may be the outcome of a change in the electronic
character of this material at 10 kbar.Comment: 4 pages, 3 figures include
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
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