Ergodic property of Markovian semigroups on standard forms of von Neumann algebras

We give sufficient conditions for ergodicity of the Markovian semigroups associated to Dirichlet forms on standard forms of von Neumann algebras constructed by the method proposed in Refs. [Par1,Par2]. We apply our result to show that the diffusion type Markovian semigroups for quantum spin systems are ergodic in the region of high temperatures where the uniqueness of the KMS-state holds.Comment: 25 page

Extensive divergence of transcription factor binding in Drosophila embryos with highly conserved gene expression

Extensive divergence of transcription factor binding in Drosophila embryos with highly conserved gene expressionComment: 7 figures, 20 supplementary figures, 6 supplementary tables Paris M, Kaplan T, Li XY, Villalta JE, Lott SE, et al. (2013) Extensive Divergence of Transcription Factor Binding in Drosophila Embryos with Highly Conserved Gene Expression. PLoS Genet 9(9): e1003748. doi:10.1371/journal.pgen.100374

Optimal routing on complex networks

We present a novel heuristic algorithm for routing optimization on complex networks. Previously proposed routing optimization algorithms aim at avoiding or reducing link overload. Our algorithm balances traffic on a network by minimizing the maximum node betweenness with as little path lengthening as possible, thus being useful in cases when networks are jamming due to queuing overload. By using the resulting routing table, a network can sustain significantly higher traffic without jamming than in the case of traditional shortest path routing.Comment: 4 pages, 5 figure

Quantum tunneling on graphs

We explore the tunneling behavior of a quantum particle on a finite graph, in the presence of an asymptotically large potential. Surprisingly the behavior is governed by the local symmetry of the graph around the wells.Comment: 18 page

A_4 flavour symmetry breaking scheme for understanding quark and neutrino mixing angles

We propose a spontaneous A_4 flavour symmetry breaking scheme to understand the observed pattern of quark and neutrino mixing. The fermion mass eigenvalues are arbitrary, but the mixing angles are constrained in such a way that the overall patterns are explained while also leaving sufficient freedom to fit the detailed features of the observed values, including CP violating phases. The scheme realises the proposal of Low and Volkas to generate zero quark mixing and tribimaximal neutrino mixing at tree-level, with deviations from both arising from small corrections after spontaneous A_4 breaking. In the neutrino sector, the breaking is A_4 --> Z_2, while in the quark and charged-lepton sectors it is A_4 --> Z_3 = C_3. The full theory has A_4 completely broken, but the two different unbroken subgroups in the two sectors force the dominant mixing patterns to be as stated above. Radiative effects within each sector are shown to deviate neutrino mixing from tribimaximal, while maintaining zero quark mixing. Interactions between the two sectors -- "cross-talk" -- induce nonzero quark mixing, and additional deviation from tribimaximal neutrino mixing. We discuss the vacuum alignment challenge the scenario faces, and suggest three generic ways to approach the problem. We follow up one of those ways by sketching how an explicit model realising the symmetry breaking structure may be constructed.Comment: 14 pages, no figures; v3: Section 5 rewritten to correct an error; new section added to the appendix; added references; v4: minor change to appendix C, version to be published by JHE

Scaling for Interfacial Tensions near Critical Endpoints

Parametric scaling representations are obtained and studied for the asymptotic behavior of interfacial tensions in the \textit{full} neighborhood of a fluid (or Ising-type) critical endpoint, i.e., as a function \textit{both} of temperature \textit{and} of density/order parameter \textit{or} chemical potential/ordering field. Accurate \textit{nonclassical critical exponents} and reliable estimates for the \textit{universal amplitude ratios} are included naturally on the basis of the ``extended de Gennes-Fisher'' local-functional theory. Serious defects in previous scaling treatments are rectified and complete wetting behavior is represented; however, quantitatively small, but unphysical residual nonanalyticities on the wetting side of the critical isotherm are smoothed out ``manually.'' Comparisons with the limited available observations are presented elsewhere but the theory invites new, searching experiments and simulations, e.g., for the vapor-liquid interfacial tension on the two sides of the critical endpoint isotherm for which an amplitude ratio $-3.25 \pm 0.05$ is predicted.Comment: 42 pages, 6 figures, to appear in Physical Review

Gravitational conundrum? Dynamical mass segregation versus disruption of binary stars in dense stellar systems

Upon their formation, dynamically cool (collapsing) star clusters will, within only a few million years, achieve stellar mass segregation for stars down to a few solar masses, simply because of gravitational two-body encounters. Since binary systems are, on average, more massive than single stars, one would expect them to also rapidly mass segregate dynamically. Contrary to these expectations and based on high-resolution Hubble Space Telescope observations, we show that the compact, 15-30 Myr-old Large Magellanic Cloud cluster NGC 1818 exhibits tantalizing hints at the >= 2 sigma level of significance (> 3 sigma if we assume a power-law secondary-to-primary mass-ratio distribution) of an increasing fraction of F-star binary systems (with combined masses of 1.3-1.6 Msun) with increasing distance from the cluster center, specifically between the inner 10 to 20" (approximately equivalent to the cluster's core and half-mass radii) and the outer 60 to 80". If confirmed, this will offer support of the theoretically predicted but thus far unobserved dynamical disruption processes of the significant population of 'soft' binary systems---with relatively low binding energies compared to the kinetic energy of their stellar members---in star clusters, which we have access to here by virtue of the cluster's unique combination of youth and high stellar density.Comment: Accepted for publication in The Astrophysical Journal; 19 pages in AASTeX format; 3 figure

Quantized spin Hall effect in Helium three-A and other p-wave paired Fermi systems

In this paper we propose the quantized spin Hall effect (SHE) in the vortex state of a rotating p-wave paired Fermi system in an inhomogeneous magnetic field and in a weak periodic potential. It is the three dimensional extension of the spin Hall effect for a 3He-A superfluid film studied in Ref. [1]. It may also be considered as a generalization of the 3D quantized charge Hall effect of Bloch electrons in Ref. [2] to the spin transport. The A-phase of 3He or, more generally, the p-wave paired phase of a cold Fermi atomic gas, under suitable conditions should be a good candidate to observe the SHE, because the system has a conserved spin current (with no spin-orbit couplings).Comment: 6 pages, revised version

A New Renormalization Scheme of Fermion Fields in Electroweak Standard Model

This paper has been withdrawn by the author,due a immature idea.Comment: 6 page

Simulation studies of permeation through two-dimensional ideal polymer networks

We study the diffusion process through an ideal polymer network, using numerical methods. Polymers are modeled by random walks on the bonds of a two-dimensional square lattice. Molecules occupy the lattice cells and may jump to the nearest-neighbor cells, with probability determined by the occupation of the bond separating the two cells. Subjected to a concentration gradient across the system, a constant average current flows in the steady state. Its behavior appears to be a non-trivial function of polymer length, mass density and temperature, for which we offer qualitative explanations.Comment: 8 pages, 4 figure