Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators

We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed as an operator-valued function of time and so, in the appropriate norm, we may consider the vector-valued Laplace transform of this function. We obtain a spectral result on these operators and relate this to the spectrum of the generator of this semigroup. Issues of strong continuity of the semigroup are avoided. The main result is the improvement to the machinery associated with studying semiflows as one-parameter semigroups of operators and the study of the smoothness properties of semiflows defined on branched manifolds, without encoding as a suspension semiflow

Field-induced magnetic ordering in the Haldane system PbNi2V2O8

The Haldane system PbNi2V2O8 was investigated by the temperature dependent magnetization M(T) measurements at fields higher than H_c, with H_c the critical fields necessary to close the Haldane gap. It is revealed that M(T) for H > H_c exhibits a cusp-like minimum at T_{min}, below which M(T) increases with decreasing T having a convex curve. These features have been observed for both $H \parallel c$ and $H \perp c$, with c-axis being parallel to the chain. These data indicate the occurrence of field-induced magnetic ordering around T_{min}. Phase boundaries for $H \parallel c$ and $H \perp c$ do not cross each other, consistent with the theoretical calculation for negative single-ion anisotropy D.Comment: 3 figures, submitted to Phys. Rev.

Novel Quantum Criticality in CeRu2_2Si2_2 near Absolute Zero Observed by Thermal Expansion and Magnetostriction

We report linear thermal expansion and magnetostriction measurements for CeRu$_2$Si$_2$ in magnetic fields up to 52.6 mT and at temperatures down to 1 mK. At high temperatures, this compound showed Landau-Fermi-liquid behavior: The linear thermal expansion coefficient and the magnetostriction coefficient were proportional to the temperature and magnetic field, respectively. In contrast, a pronounced non-Fermi-liquid effect was found below 50 mK. The negative contribution of thermal expansion and magnetostriction suggests the existence of an additional quantum critical point

Valence and Na content dependences of superconductivity in NaxCoO2.yH2O

Various samples of sodium cobalt oxyhydrate with relatively large amounts of Na$^{+}$ ions were synthesized by a modified soft-chemical process in which a NaOH aqueous solution was added in the final step of the procedure. From these samples, a superconducting phase diagram was determined for a section of a cobalt valence of $\sim$+3.48, which was compared with a previously obtained one of $\sim$+3.40. The superconductivity was significantly affected by the isovalent exchanger of Na$^{+}$ and H$_{3}$O$^{+}$, rather than by variation of Co valence, suggesting the presence of multiple kinds of Fermi surface. Furthermore, the high-field magnetic susceptibility measurements for one sample up to 30 T indicated an upper critical field much higher than the Pauli limit supporting the validity of the spin-triplet pairing mechanism.Comment: 4 figures and 1 tabl

Tomonaga-Luttinger Liquid in a Quasi-One-Dimensional S=1 Antiferromagnet Observed by the Specific Heat

Specific heat experiments on single crystals of the S=1 quasi-one-dimensional bond-alternating antiferromagnet Ni(C_9H_24N_4)(NO_2)ClO_4, alias NTENP, have been performed in magnetic fields applied both parallel and perpendicular to the spin chains. We have found for the parallel field configuration that the magnetic specific heat (C_mag) is proportional to temperature (T) above a critical field H_c, at which the energy gap vanishes, in a temperature region above that of the long-range ordered state. The ratio C_mag/T increases as the magnetic field approaches H_c from above. The data are in good quantitative agreement with the prediction of the c=1 conformal field theory in conjunction with the velocity of the excitations calculated by a numerical diagonalization, providing a conclusive evidence for a Tomonaga-Luttinger liquid.Comment: 4 pages, 4 postscript figure