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 CeCu2(Si1−xGex)2CeCu_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 NbFe2_{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