585 research outputs found
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
Magnetic Transition in the Kondo Lattice System CeRhSn2
Our resistivity, magnetoresistance, magnetization and specific heat data
provide unambiguous evidence that CeRhSn2 is a Kondo lattice system which
undergoes magnetic transition below 4 K.Comment: 3 pages text and 5 figure
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
Maximal superintegrability on N-dimensional curved spaces
A unified algebraic construction of the classical Smorodinsky-Winternitz
systems on the ND sphere, Euclidean and hyperbolic spaces through the Lie
groups SO(N+1), ISO(N), and SO(N,1) is presented. Firstly, general expressions
for the Hamiltonian and its integrals of motion are given in a linear ambient
space , and secondly they are expressed in terms of two geodesic
coordinate systems on the ND spaces themselves, with an explicit dependence on
the curvature as a parameter. On the sphere, the potential is interpreted as a
superposition of N+1 oscillators. Furthermore each Lie algebra generator
provides an integral of motion and a set of 2N-1 functionally independent ones
are explicitly given. In this way the maximal superintegrability of the ND
Euclidean Smorodinsky-Winternitz system is shown for any value of the
curvature.Comment: 8 pages, LaTe
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
New Superconducting and Magnetic Phases Emerge on the Verge of Antiferromagnetism in CeIn
We report the discovery of new superconducting and novel magnetic phases in
CeIn on the verge of antiferromagnetism (AFM) under pressure () through
the In-nuclear quadrupole resonance (NQR) measurements. We have found a
-induced phase separation of AFM and paramagnetism (PM) without any trace
for a quantum phase transition in CeIn. A new type of superconductivity
(SC) was found in GPa to coexist with AFM that is magnetically
separated from PM where the heavy fermion SC takes place. We propose that the
magnetic excitations such as spin-density fluctuations induced by the
first-order magnetic phase transition might mediate attractive interaction to
form Cooper pairs.Comment: 4 pages, 4 EPS figures, submitted to J. Phys. Soc. Jp
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