Minimal model fusion rules from 2-groups

The fusion rules for the $(p,q)$-minimal model representations of the Virasoro algebra are shown to come from the group G = \boZ_2^{p+q-5} in the following manner. There is a partition $G = P_1 \cup ...\cup P_N$ into disjoint subsets and a bijection between $\{P_1,...,P_N\}$ and the sectors $\{S_1,...,S_N\}$ of the $(p,q)$-minimal model such that the fusion rules $S_i * S_j = \sum_k D(S_i,S_j,S_k) S_k$ correspond to $P_i * P_j = \sum_{k\in T(i,j)} P_k$ where $T(i,j) = \{k|\exists a\in P_i,\exists b\in P_j, a+b\in P_k\}$.Comment: 8 pages, amstex, v2.1, uses fonts msam, msbm, no figures, tables constructed using macros: cellular and related files are included. This paper will be submitted to Communications in Math. Physics. A compressed dvi file is available at ftp://math.binghamton.edu/pub/alex/fusionrules.dvi.Z , and compressed postscript at ftp://math.binghamton.edu/pub/alex/fusionrules.ps.

Deformations and dilations of chaotic billiards, dissipation rate, and quasi-orthogonality of the boundary wavefunctions

We consider chaotic billiards in d dimensions, and study the matrix elements M_{nm} corresponding to general deformations of the boundary. We analyze the dependence of |M_{nm}|^2 on \omega = (E_n-E_m)/\hbar using semiclassical considerations. This relates to an estimate of the energy dissipation rate when the deformation is periodic at frequency \omega. We show that for dilations and translations of the boundary, |M_{nm}|^2 vanishes like \omega^4 as \omega -> 0, for rotations like \omega^2, whereas for generic deformations it goes to a constant. Such special cases lead to quasi-orthogonality of the eigenstates on the boundary.Comment: 4 pages, 3 figure

Parametric Evolution for a Deformed Cavity

We consider a classically chaotic system that is described by a Hamiltonian H(Q,P;x), where (Q,P) describes a particle moving inside a cavity, and x controls a deformation of the boundary. The quantum-eigenstates of the system are |n(x)>. We describe how the parametric kernel P(n|m) = , also known as the local density of states, evolves as a function of x-x0. We illuminate the non-unitary nature of this parametric evolution, the emergence of non-perturbative features, the final non-universal saturation, and the limitations of random-wave considerations. The parametric evolution is demonstrated numerically for two distinct representative deformation processes.Comment: 13 pages, 8 figures, improved introduction, to be published in Phys. Rev.

secCl is a cys-loop ion channel necessary for the chloride conductance that mediates hormone-induced fluid secretion in Drosophila

Organisms use circulating diuretic hormones to control water balance (osmolarity), thereby avoiding dehydration and managing excretion of waste products. The hormones act through G-protein-coupled receptors to activate second messenger systems that in turn control the permeability of secretory epithelia to ions like chloride. In insects, the chloride channel mediating the effects of diuretic hormones was unknown. Surprisingly, we find a pentameric, cys-loop chloride channel, a type of channel normally associated with neurotransmission, mediating hormone-induced transepithelial chloride conductance. This discovery is important because: 1) it describes an unexpected role for pentameric receptors in the membrane permeability of secretory epithelial cells, and 2) it suggests that neurotransmitter-gated ion channels may have evolved from channels involved in secretion

An assessment of aerosol‐cloud interactions in marine stratus clouds based on surface remote sensing

An assessment of aerosol-cloud interactions (ACI) from ground-based remote sensing under coastal stratiform clouds is presented. The assessment utilizes a long-term, high temporal resolution data set from the Atmospheric Radiation Measurement (ARM) Program deployment at Pt. Reyes, California, United States, in 2005 to provide statistically robust measures of ACI and to characterize the variability of the measures based on variability in environmental conditions and observational approaches. The average ACIN (= dlnNd/dlna, the change in cloud drop number concentration with aerosol concentration) is 0.48, within a physically plausible range of 0–1.0. Values vary between 0.18 and 0.69 with dependence on (1) the assumption of constant cloud liquid water path (LWP), (2) the relative value of cloud LWP, (3) methods for retrieving Nd, (4) aerosol size distribution, (5) updraft velocity, and (6) the scale and resolution of observations. The sensitivity of the local, diurnally averaged radiative forcing to this variability in ACIN values, assuming an aerosol perturbation of 500 c-3 relative to a background concentration of 100 cm-3, ranges betwee-4 and -9 W -2. Further characterization of ACI and its variability is required to reduce uncertainties in global radiative forcing estimates

Statistical Properties of Random Banded Matrices with Strongly Fluctuating Diagonal Elements

The random banded matrices (RBM) whose diagonal elements fluctuate much stronger than the off-diagonal ones were introduced recently by Shepelyansky as a convenient model for coherent propagation of two interacting particles in a random potential. We treat the problem analytically by using the mapping onto the same supersymmetric nonlinear $\sigma-$model that appeared earlier in consideration of the standard RBM ensemble, but with renormalized parameters. A Lorentzian form of the local density of states and a two-scale spatial structure of the eigenfunctions revealed recently by Jacquod and Shepelyansky are confirmed by direct calculation of the distribution of eigenfunction components.Comment: 7 pages,RevTex, no figures Submitted to Phys.Rev.

Localization in Strongly Chaotic Systems

We show that, in the semiclassical limit and whenever the elements of the Hamiltonian matrix are random enough, the eigenvectors of strongly chaotic time-independent systems in ordered bases can on average be exponentially localized across the energy shell and decay faster than exponentially outside the energy shell. Typically however, matrix elements are strongly correlated leading to deviations from such behavior.Comment: RevTeX, 5 pages + 3 postscript figures, submitted to Phys. Rev. Let

Quantum-Mechanical Non-Perturbative Response of Driven Chaotic Mesoscopic Systems

Consider a time-dependent Hamiltonian $H(Q,P;x(t))$ with periodic driving $x(t)=A\sin(\Omega t)$. It is assumed that the classical dynamics is chaotic, and that its power-spectrum extends over some frequency range $|\omega|<\omega_{cl}$. Both classical and quantum-mechanical (QM) linear response theory (LRT) predict a relatively large response for $\Omega<\omega_{cl}$, and a relatively small response otherwise, independently of the driving amplitude $A$. We define a non-perturbative regime in the $(\Omega,A)$ space, where LRT fails, and demonstrate this failure numerically. For $A>A_{prt}$, where $A_{prt}\propto\hbar$, the system may have a relatively strong response for $\Omega>\omega_{cl}$, and the shape of the response function becomes $A$ dependent.Comment: 4 pages, 2 figures, revised version with much better introductio