Notes on two-parameter quantum groups, (I)

A simpler definition for a class of two-parameter quantum groups associated to semisimple Lie algebras is given in terms of Euler form. Their positive parts turn out to be 2-cocycle deformations of each other under some conditions. An operator realization of the positive part is given.Comment: 11 page

On the Three-dimensional Lattice Model

Using the restricted star-triangle relation, it is shown that the $N$-state spin integrable model on a three-dimensional lattice with spins interacting round each elementary cube of the lattice proposed by Mangazeev, Sergeev and Stroganov is a particular case of the Bazhanov-Baxter model.Comment: 8 pages, latex, 4 figure

Notes on two-parameter quantum groups, (II)

This paper is the sequel to [HP1] to study the deformed structures and representations of two-parameter quantum groups $U_{r,s}(\mathfrak{g})$ associated to the finite dimensional simple Lie algebras \mg. An equivalence of the braided tensor categories \O^{r,s} and \O^{q} is explicitly established.Comment: 21 page

Qualitative picture of a new mechanism for high-Tc superconductors

Xu et al. observed enhanced Nernst effect and Iguchi et al. observed patched diamagnetism, both well above $T_c$ in underdoped high-$T_c$ superconductors (HTSCs). A new mechanism is proposed here, which seems to naturally explain, at least qualitatively, these observations, as well as the d-wave nature and continuity of pseudogap and pairing gap, the tunneling conductance above $T_c$, as well as $T^*(x)$, $T_{\nu}(x)$, $T_c(x)$, etc. This mechanism combines features of dynamic charged stripes, preformed pairs, and spin-bags: At appropriete doping levels, the doped holes (and perhaps also electrons) will promote the formation of anti-phase islands in short-range anti-ferromagnetic order. On the boundary of each such island reside two doped carriers; the unscreened Coulomb repulsion between them stabilizes its size. Superconductivity results when such ``pre-formed pairs'' Bose-condense.Comment: 8 pages, 4 figures, New3SC-4 Conference Proceedings, to be published in ijmp

On σ\sigma-quasinormal subgroups of finite groups

Let $G$ be a finite group and $\sigma =\{\sigma_{i} | i\in I\}$ some partition of the set of all primes $\Bbb{P}$, that is, $\sigma =\{\sigma_{i} | i\in I \}$, where $\Bbb{P}=\bigcup_{i\in I} \sigma_{i}$ and $\sigma_{i}\cap \sigma_{j}= \emptyset$ for all $i\ne j$. We say that $G$ is $\sigma$-primary if $G$ is a $\sigma _{i}$-group for some $i$. A subgroup $A$ of $G$ is said to be: ${\sigma}$-subnormal in $G$ if there is a subgroup chain $A=A_{0} \leq A_{1} \leq \cdots \leq A_{n}=G$ such that either $A_{i-1}\trianglelefteq A_{i}$ or $A_{i}/(A_{i-1})_{A_{i}}$ is $\sigma$-primary for all $i=1, \ldots, n$, modular in $G$ if the following conditions hold: (i) $\langle X, A \cap Z \rangle=\langle X, A \rangle \cap Z$ for all $X \leq G, Z \leq G$ such that $X \leq Z$, and (ii) $\langle A, Y \cap Z \rangle=\langle A, Y \rangle \cap Z$ for all $Y \leq G, Z \leq G$ such that $A \leq Z$. In this paper, a subgroup $A$ of $G$ is called $\sigma$-quasinormal in $G$ if $L$ is modular and ${\sigma}$-subnormal in $G$. We study $\sigma$-quasinormal subgroups of $G$. In particular, we prove that if a subgroup $H$ of $G$ is $\sigma$-quasinormal in $G$, then for every chief factor $H/K$ of $G$ between $H^{G}$ and $H_{G}$ the semidirect product $(H/K)\rtimes (G/C_{G}(H/K))$ is $\sigma$-primary.Comment: 9 page

Three-Dimensional Phase-Kink State in Thick Stack of Josephson Junctions and Terahertz Radiation

The dynamics of superconductivity phase in thick stack of Josephson junctions with strong inductive coupling, such as the one realized in layered high-$T_c$ cuprates and possibly the recently discovered FeAs-based superconductors, is investigated under a c-axis bias voltage and in the absence of an external magnetic field. The kink state found previously by the present authors is extended to three dimensions for both rectangular and cylindrical geometries. The IV characteristics are calculated and the distributions of electromagnetic field inside the samples are clarified. The solution for a cylindrical mesa exhibits a higher resonating frequency than that of a square mesa with the same linear size by a factor of $\sim 2.4$. More importantly, from the radius dependence of the resonance frequency for the cylinder geometry it is possible to confirm directly the kink state, and thus to reveal the mechanism of the strong radiation discovered in recent experiments.Comment: 6 pages, 8 figures. to be published in Phys. Rev. B. to be published in Phys. Rev.