Brillouin amplification supports 1×10−201\times10^{-20} accuracy in optical frequency transfer over 1400~km of underground fibre

We investigate optical frequency transfer over a 1400~km loop of underground fibre connecting Braunschweig and Strasbourg. Largely autonomous fibre Brillouin amplifiers (FBA) are the only means of intermediate amplification, allowing phase-continuous measurements over periods up to several days. Over a measurement period of about three weeks we find a weighted mean of the transferred frequency's fractional offset of $(1.1\pm0.4)\times10^{-20}$. In the best case we find an instability of $6.9\times10^{-21}$ and a fractional frequency offset of $4.4\times10^{-21}$ at an averaging time of around 30~000~s. These results represent an upper limit for the achievable uncertainty over 1400 km when using a chain of remote Brillouin amplifiers, and allow us to investigate systematic effects at the $10^{-20}$-level

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

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.

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$_c$, 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

A non-linear Oscillator with quasi-Harmonic behaviour: two- and nn-dimensional Oscillators

A nonlinear two-dimensional system is studied by making use of both the Lagrangian and the Hamiltonian formalisms. The present model is obtained as a two-dimensional version of a one-dimensional oscillator previously studied at the classical and also at the quantum level. First, it is proved that it is a super-integrable system, and then the nonlinear equations are solved and the solutions are explicitly obtained. All the bounded motions are quasiperiodic oscillations and the unbounded (scattering) motions are represented by hyperbolic functions. In the second part the system is generalized to the case of $n$ degrees of freedom. Finally, the relation of this nonlinear system with the harmonic oscillator on spaces of constant curvature, two-dimensional sphere $S^2$ and hyperbolic plane $H^2$, is discussed.Comment: 30 pages, 4 figures, submitted to Nonlinearit

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