439 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

### 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$_c$, making way for novel correlated electron states close
to this quantum critical point. We have studied the clean heavy fermion
antiferromagnets CePd$_2$Si$_2$ and CeIn$_3$ 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$_c$. 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

### 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

### Non-Fermi liquid states in the pressurized $CeCu_2(Si_{1-x}Ge_x)_2$ system: two critical points

In the archetypal strongly correlated electron superconductor CeCu$_2$Si$_2$
and its Ge-substituted alloys CeCu$_2$(Si$_{1-x}$Ge$_{x}$)$_2$ two quantum
phase transitions -- one magnetic and one of so far unknown origin -- can be
crossed as a function of pressure \cite{Yuan 2003a}. We examine the associated
anomalous normal state by detailed measurements of the low temperature
resistivity ($\rho$) power law exponent $\alpha$. At the lower critical point
(at $p_{c1}$, $1\leq\alpha\leq 1.5$) $\alpha$ depends strongly on Ge
concentration $x$ and thereby on disorder level, consistent with a
Hlubina-Rice-Rosch scenario of critical scattering off antiferromagnetic
fluctuations. By contrast, $\alpha$ is independent of $x$ at the upper quantum
phase transition (at $p_{c2}$, $\alpha\simeq 1$), suggesting critical
scattering from local or Q=0 modes, in agreement with a density/valence
fluctuation approach.Comment: 4 pages, including 4 figures. New results added. Significant changes
on the text and Fig.

### Superintegrability on the two-dimensional hyperboloid

In this work we examine the basis functions for classical and quantum mechanical systems on the two-dimensional hyperboloid that admit separation of variables in at least two coordinate systems. We present all of these cases from a unified point of view. In particular, all of the special functions that arise via variable separation have their essential features expressed in terms of their zeros. The principal new results are the details of the polynomial bases for each of the nonsubgroup bases, not just the subgroup spherical coordinate cases, and the details of the structure of the quadratic symmetry algebras

### Doping driven magnetic instabilities and quantum criticality of NbFe$_{2}$

Using density functional theory we investigate the evolution of the magnetic
ground state of NbFe$_{2}$ 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$_{2}$. We find that explicit calculation of the Lindhard function,
$\chi_{0}(\mathbf{q})$, indicates that the primary instability is to finite
$\mathbf{q}$ antiferromagnetism driven by Fermi surface nesting. Total energy
calculations indicate that $\mathbf{q}=0$ antiferromagnetism is the ground
state. We discuss the influence of competing $\mathbf{q}=0$ and finite
$\mathbf{q}$ instabilities on the presence of the non-Fermi liquid behavior in
this material.Comment: 8 pages, 7 figure

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