Disordered Topological Insulators via C∗C^*-Algebras

The theory of almost commuting matrices can be used to quantify topological obstructions to the existence of localized Wannier functions with time-reversal symmetry in systems with time-reversal symmetry and strong spin-orbit coupling. We present a numerical procedure that calculates a Z_2 invariant using these techniques, and apply it to a model of HgTe. This numerical procedure allows us to access sizes significantly larger than procedures based on studying twisted boundary conditions. Our numerical results indicate the existence of a metallic phase in the presence of scattering between up and down spin components, while there is a sharp transition when the system decouples into two copies of the quantum Hall effect. In addition to the Z_2 invariant calculation in the case when up and down components are coupled, we also present a simple method of evaluating the integer invariant in the quantum Hall case where they are decoupled.Comment: Added detail regarding the mapping of almost commuting unitary matrices to almost commuting Hermitian matrices that form an approximate representation of the sphere. 6 pages, 6 figure

Premature recruitment of oocyte pool and increased mTOR activity in Fmr1 knockout mice and reversal of phenotype with rapamycin.

While mutations in the fragile X mental retardation-1 (FMR1) gene are associated with varying reproductive outcomes in females, the effects of a complete lack of FMR1 expression are not known. Here, we studied the ovarian and reproductive phenotypes in an Fmr1 knockout (KO) mouse model and the role of mammalian target of rapamycin (mTOR) signaling. Breeding, histologic and mTOR signaling data were obtained at multiple time points in KO and wild type (WT) mice fed a control or rapamycin (mTOR inhibitor) diet. KO mice showed an earlier decline in ovarian reserve than WT mice with an increased proportion of activated follicles. mTOR and phosphorylated S6 kinase (p-S6K) levels, a measure of downstream mTOR signaling, were elevated in the KO ovaries. Rapamycin blocked these effects in KO mice, and increased the primordial follicle pool and age of last litter in WT mice. Our data demonstrates an early decline in reproductive capacity in Fmr1 KO mice and proposes that premature recruitment of the primordial pool via altered mTOR signaling may be the mechanism. Reversal of phenotypes and protein levels in rapamycin-treated KO mice, as well as increased reproductive lifespan of rapamycin-fed WT mice, suggest the mTOR pathway as a potential therapeutic target

Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid

We study inelastic decay of bosonic excitations in a Luttinger liquid. In a model with linear excitation spectrum the decay rate diverges. We show that this difficulty is resolved when the interaction between constituent particles is strong, and the excitation spectrum is nonlinear. Although at low energies the nonlinearity is weak, it regularizes the divergence in the decay rate. We develop a theoretical description of the approach of the system to thermal equilibrium. The typical relaxation rate scales as the fifth power of temperature

Positive Least Energy Solutions and Phase Separation for Coupled Schrodinger Equations with Critical Exponent: Higher Dimensional Case

We study the following nonlinear Schr\"{o}dinger system which is related to Bose-Einstein condensate: {displaymath} {cases}-\Delta u +\la_1 u = \mu_1 u^{2^\ast-1}+\beta u^{\frac{2^\ast}{2}-1}v^{\frac{2^\ast}{2}}, \quad x\in \Omega, -\Delta v +\la_2 v =\mu_2 v^{2^\ast-1}+\beta v^{\frac{2^\ast}{2}-1} u^{\frac{2^\ast}{2}}, \quad x\in \om, u\ge 0, v\ge 0 \,\,\hbox{in \om},\quad u=v=0 \,\,\hbox{on \partial\om}.{cases}{displaymath} Here \om\subset \R^N is a smooth bounded domain, $2^\ast:=\frac{2N}{N-2}$ is the Sobolev critical exponent, -\la_1(\om)0 and $\beta\neq 0$, where \lambda_1(\om) is the first eigenvalue of $-\Delta$ with the Dirichlet boundary condition. When \bb=0, this is just the well-known Brezis-Nirenberg problem. The special case N=4 was studied by the authors in (Arch. Ration. Mech. Anal. 205: 515-551, 2012). In this paper we consider {\it the higher dimensional case $N\ge 5$}. It is interesting that we can prove the existence of a positive least energy solution (u_\bb, v_\bb) {\it for any $\beta\neq 0$} (which can not hold in the special case N=4). We also study the limit behavior of (u_\bb, v_\bb) as $\beta\to -\infty$ and phase separation is expected. In particular, u_\bb-v_\bb will converge to {\it sign-changing solutions} of the Brezis-Nirenberg problem, provided $N\ge 6$. In case \la_1=\la_2, the classification of the least energy solutions is also studied. It turns out that some quite different phenomena appear comparing to the special case N=4.Comment: 48 pages. This is a revised version of arXiv:1209.2522v1 [math.AP

A single intrinsic Josephson junction with double-sided fabrication technique

We make stacks of intrinsic Josephson junctions (IJJs) imbedded in the bulk of very thin ($d\leq 100$~nm) $\mathrm{Bi_2Sr_2CaCu_2O_{8+x}}$ single crystals. By precisely controlling the etching depth during the double-sided fabrication process, the stacks can be reproducibly tailor-made to be of any microscopic height ($0-9 \mathrm{nm} <d$), i.e. enclosing a specified number of IJJ (0-6), including the important case of a single junction. We discuss reproducible gap-like features in the current-voltage characteristics of the samples at high bias.Comment: 3 pages, 4 figures, to be published in APL May. 2