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

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.

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

New Superconducting and Magnetic Phases Emerge on the Verge of Antiferromagnetism in CeIn3_3

We report the discovery of new superconducting and novel magnetic phases in CeIn$_3$ on the verge of antiferromagnetism (AFM) under pressure ($P$) through the In-nuclear quadrupole resonance (NQR) measurements. We have found a $P$-induced phase separation of AFM and paramagnetism (PM) without any trace for a quantum phase transition in CeIn$_3$. A new type of superconductivity (SC) was found in $P=2.28-2.5$ 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

The Coulomb-Oscillator Relation on n-Dimensional Spheres and Hyperboloids

In this paper we establish a relation between Coulomb and oscillator systems on $n$-dimensional spheres and hyperboloids for $n\geq 2$. We show that, as in Euclidean space, the quasiradial equation for the $n+1$ dimensional Coulomb problem coincides with the $2n$-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