Spin relaxation and decoherence of two-level systems

We revisit the concepts of spin relaxation and spin decoherence of two level (spin-1/2) systems. From two toy-models, we clarify two issues related to the spin relaxation and decoherence: 1) For an ensemble of two-level particles each subjected to a different environmental field, there exists an ensemble relaxation time $T_1^*$ which is fundamentally different from $T_1$. When the off-diagonal coupling of each particle is in a single mode with the same frequency but a random coupling strength, we show that $T_1^*$ is finite while the spin relaxation time of a single spin $T_1$ and the usual ensemble decoherence time $T_2^*$ are infinite. 2) For a two-level particle under only a random diagonal coupling, its relaxation time $T_1$ shall be infinite but its decoherence time $T_2$ is finite.Comment: 5 pages, 2 figure

^{115}In-NQR evidence for unconventional superconductivity in CeIn_3 under pressure

We report evidence for unconventional superconductivity in CeIn_3 at a pressure P = 2.65 GPa above critical pressure (P_c ~ 2.5 GPa) revealed by the measurements of nuclear-spin-lattice-relaxation time (T_1) and ac-susceptibility (ac-chi). Both the measurements of T_1 and ac-chi have pointed to a superconducting transition at T_c = 95 mK, which is much lower than an onset temperature T_{onset} = 0.15 K at zero resistance. The temperature dependence of 1/T_1 shows no coherence peak just below T_c, indicative of an unconventional nature for the superconductivity induced in CeIn_3.Comment: 4 pages, 4 figures, to be published in Phys.Rev.

Reduction of manifolds with semi-negative holomorphic sectional curvature

In this note, we continue the investigation of a projective K\"ahler manifold $M$ of semi-negative holomorphic sectional curvature $H$. We introduce a new differential geometric numerical rank invariant which measures the number of linearly independent {\it truly flat} directions of $H$ in the tangent spaces. We prove that this invariant is bounded above by the nef dimension and bounded below by the numerical Kodaira dimension of $M$. We also prove a splitting theorem for $M$ in terms of the nef dimension and, under some additional hypotheses, in terms of the new rank invariant

Field-Induced Ferromagnetic Order and Colossal Magnetoresistance in La_{1.2}Sr_{1.8}Mn_2O_7: a ^{139}La NMR study

In order to gain insights into the origin of colossal magneto-resistance (CMR) in manganese oxides, we performed a ^{139}La NMR study in the double-layered compound La_{1.2}Sr_{1.8}Mn_2O_7. We find that above the Curie temperature T_C=126 K, applying a magnetic field induces a long-range ferromagnetic order that persists up to T=330 K. The critical field at which the induced magnetic moment is saturated coincides with the field at which the CMR effect reaches to a maximum. Our results therefore indicate that the CMR observed above T_C in this compound is due to the field-induced ferromagnetism that produces a metallic state via the double exchange interaction