An L^2-Index Theorem for Dirac Operators on S^1 * R^3

An expression is found for the $L^2$-index of a Dirac operator coupled to a connection on a $U_n$ vector bundle over $S^1\times{\mathbb R}^3$. Boundary conditions for the connection are given which ensure the coupled Dirac operator is Fredholm. Callias' index theorem is used to calculate the index when the connection is independent of the coordinate on $S^1$. An excision theorem due to Gromov, Lawson, and Anghel reduces the index theorem to this special case. The index formula can be expressed using the adiabatic limit of the $\eta$-invariant of a Dirac operator canonically associated to the boundary. An application of the theorem is to count the zero modes of the Dirac operator in the background of a caloron (periodic instanton).Comment: 14 pages, Latex, to appear in the Journal of Functional Analysi

(63)Cu NQR Evidence for Spatial Variation of Hole Concentration in La(2-x)Sr(x)CuO(4)

We report experimental evidence for the spatial variation of hole concentration x_(hole) in the high Tc superconductor La(2-x)Sr(x)CuO(4) (0.04 <= x <= 0.16) by using (63)Cu NQR for (63)Cu isotope enriched samples. We demonstrate that the extent of the spatial variation of the local hole concentration D(x)_(hole) is reflected on (63)1/T1 and deduce the temperature dependence. D(x)_(hole) increases below 500 - 600K, and reaches values as large as D(x)_(hole)/x ~ 0.5 below ~ 150K. We estimate the length scale of the spatial variation in x_(hole) to be R_(hole) >~ 3nm from analysis of the NQR spectrum.Comment: Accepted for publication in Physical Review Letter

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The interaction energy of well-separated Skyrme solitons

We prove that the asymptotic field of a Skyrme soliton of any degree has a non-trivial multipole expansion. It follows that every Skyrme soliton has a well-defined leading multipole moment. We derive an expression for the linear interaction energy of well-separated Skyrme solitons in terms of their leading multipole moments. This expression can always be made negative by suitable rotations of one of the Skyrme solitons in space and iso-space.We show that the linear interaction energy dominates for large separation if the orders of the Skyrme solitons' multipole moments differ by at most two. In that case there are therefore always attractive forces between the Skyrme solitons.Comment: 27 pages amslate

Cooperative behavior of qutrits with dipole-dipole interactions

We have identified a class of many body problems with analytic solution beyond the mean-field approximation. This is the case where each body can be considered as an element of an assembly of interacting particles that are translationally frozen multi-level quantum systems and that do not change significantly their initial quantum states during the evolution. In contrast, the entangled collective state of the assembly experiences an appreciable change. We apply this approach to interacting three-level systems.Comment: 5 pages, 3 figures. Minor correction

Sympathetic Cooling of Lithium by Laser-cooled Cesium

We present first indications of sympathetic cooling between two neutral, optically trapped atomic species. Lithium and cesium atoms are simultaneously stored in an optical dipole trap formed by the focus of a CO$_2$ laser, and allowed to interact for a given period of time. The temperature of the lithium gas is found to decrease when in thermal contact with cold cesium. The timescale of thermalization yields an estimate for the Li-Cs cross-section.Comment: 4 pages, proceedings of ICOLS 200

(13)C NMR investigation of the superconductor MgCNi_3 up to 800K

We report (13)C NMR characterization of the new superconductor MgCNi_3 (He et al., Nature (411), 54 (2001)). We found that both the uniform spin susceptibility and the spin fluctuations show a strong enhancement with decreasing temperature, and saturate below ~50K and ~20K respectively. The nuclear spin-lattice relaxation rate 1/(13)T_1T exhibits typical behaviour for isotropic s-wave superconductivity with a coherence peak below Tc=7.0K that grows with decreasing magnetic field.Comment: Accepted for publication in Physical Review Letter