118,194 research outputs found
Disordered Topological Insulators via -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, is the Sobolev critical
exponent, -\la_1(\om)0 and , where
\lambda_1(\om) is the first eigenvalue of 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 }. It is interesting that we can prove the existence
of a positive least energy solution (u_\bb, v_\bb) {\it for any } (which can not hold in the special case N=4). We also study the limit
behavior of (u_\bb, v_\bb) as and phase separation is
expected. In particular, u_\bb-v_\bb will converge to {\it sign-changing
solutions} of the Brezis-Nirenberg problem, provided . 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 (~nm) 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 (), 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
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