Statistical Mechanics Conference Main Page

101st Statistical Mechanics Conference

RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY
HILL CENTER, ROOM 114
SUNDAY - TUESDAY
MAY 10-12, 2009

SCHEDULE OF SHORT TALKS

Session A

A1- Stefan Grosskinsky*, Paul Chleboun, Gunter M. Schuetz, University of Warwick
Title: Instability if condensation in the zero-range process with random interaction
Abstract: The zero-range process is a driven diffusive system that is known to exhibit a condensation transition. We study this transition in the presence of quenched disorder in the particle interactions using rigorous arguments. Even small disorder leads to an abrupt change of the critical exponent in the interaction strength below which a condensation transition may occur, and the local critical densities may exhibit large fluctuations.

A2- Jianzhong Wu, University of California in Riverside
Title: Solvation of a spherical cavity in simple liquids: stretching the limits
Abstract: Dissolution of a solute into any solvent necessitates creation of a cavity devoid of the solvent molecules. The cavity solvation free energy is exactly known at both very small and large length scales but in between it can only be estimated by various approximations. Guided by simulation results for the solvation of small cavities and the density functional theory, we analyze the size dependence of the solvation free energy, contact density of solvent molecules, and the interfacial tension for a spherical cavity in Lennard-Jones fluids and in a system of hard spheres. Unlike cavity formation in the hard-sphere system, a quadratic curvature expansion is insufficient to connect smoothly the exact results in the microscopic and macroscopic limits for the cavity surface tension or equivalently the contact solvent density in Lennard-Jones fluids. In consideration of the sensitivity of solvation to molecular details at small length scales, we conjecture that a heuristic approach will be promising for practical purposes to bridge the thermodynamic limit at large length scales and exact results for cavity formation at very small length scales.

A3- Stefan Kehrein, University of Munich, Germany
Title: Weak interaction quenches in quantum many-body systems
Abstract: Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the nonequilibrium properties of a Fermi liquid [1,2]. We apply an interaction quench within the Fermi liquid phase of the Hubbard model by switching on a weak interaction suddenly, that is we investigate the opposite limit of the adiabatic Landau Fermi liquid paradigm. We analytically follow the real-time dynamics of the momentum distribution and observe an extended prethermalized quasi-stationary nonequilibrium Fermi liquid state, which then thermalizes on a longer time scale. These different regimes are independent of the specific kind of interaction and have recently been confirmed by a QMC simulation of a Hubbard model within dynamical mean field theory [3]. [1] M. Moeckel and S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008) [2] M. Moeckel and S. Kehrein, arXiv:0903.1561, to appear in Ann. Phys. (2009) [3] M. Eckstein, M. Kollar and P. Werner, Preprint arXiv:0904.0976

A4- Ronald Fisch, Princeton University
Title: Finite-scaling critical behavior of randomly pinned spin-density waves
Abstract: We have performed Monte Carlo studies of the 3D $XY$ model with random uniaxial anisotropy, which is a model for randomly pinned spin-density waves. We study $L \times L \times L$ simple cubic lattices, using $L$ values in the range 16 to 64, and with random anisotropy strengths of $D / 2 J$ = 1, 2, 3, 6 and $\infty$. There is a well-defined finite temperature critical point, $T_c$, for each these values of $D / 2 J$. We present results for the angle-averaged magnetic structure factor, $S ( k )$ at $T_c$ for $L = 64$. We also use finite-size scaling analysis to study scaling functions for the critical behavior of the specific heat, the magnetization and the longitudinal magnetic susceptibility. Good data collapse of the scaling functions over a wide range of $T$ is seen for $D / 2 J$ = 6 and $\infty$. For our finite values of $D / 2 J$ the scaled magnetization function increases with $L$ below $T_c$, and appears to approach an $L$-independent limit for large $L$. This suggests that the system is ferromagnetic below $T_c$. See arXiv:09024049

A5- Mustafa Keskin, Erciyes University
Title: Existence of a dynamic compensation temperature of a mixed spin-2 and spin-5/2 Ising ferrimagnetic system in an oscillating field
Abstract: The magnetic properties of a nonequilibrium mixed spin-2 and spin-5/2 Ising ferrimagnetic system with a crystal-field interaction in the presence of a time-varying magnetic field on a hexagonal lattice are studied by using the Glauber-type stochastic dynamics. The lattice is formed by alternate layers of spins S=q 2 and S=5/2. For this spin arrangement, any spin at one lattice site has two nearest-neighbor spins on the same sublattice, and four on the other sublattice. The intersublattice interaction is antiferromagnetic. We employ the Glauber transitions rates to construct the mean-field dynamical equations for the average sublattice magnetizations. We study time variations of the average magnetizations in order to find the phases in the system, and the temperature dependence of the dynamic sublattice magnetizations and total magnetization to obtain the dynamic phase transition points and dynamic compensation points, respectively, as well as to characterize the nature of transitions. We also investigate the effect of a crystal-field interaction and the exchange couplings between the nearest-neighbor pairs of spins on the compensation phenomenon and present the dynamic phase diagrams. According to values of interaction parameters, the system exhibits the paramagnetic, three different ferrimagnetic, the non-magnetic, six different mixed phases, and the compensation temperature or the N-type behavior in the Neel classification nomenclature. A comparison is made with the results of the other mixed spin Ising systems. *Supported by the Scientific and Technological Research Council of Turkey, Grant No: 107T533 and Erciyes University Research Funds, Grant No: FBA-06-01.

A6- Eduardo Neves*, R. Fernandez and L. R. Fontes, University of Sao Paulo, Brazil
Title: Density-profile processes describing biological signaling networks: Almost sure convergence to deterministic trajectories
Abstract: We introduce jump processes in $\Rk$, called density-profile processes}, to model biological signaling networks. Our modeling setup describes the macroscopic evolution of a finite-size spin-flip model with $k$ types of spins with arbitrary number of internal states interacting through a non-reversible stochastic dynamics. We are mostly interested on the multi-dimensional empirical-magnetization vector in the thermodynamic limit, and prove that, within arbitrary finite time-intervals, its path converges almost surely to a deterministic trajectory determined by a first-order (non-linear) differential equation with explicit bounds on the distance between the stochastic and deterministic trajectories. As parameters of the spin-flip dynamics change, the associated dynamical system may go through bifurcations, associated to phase transitions in the statistical mechanical setting. We present two simple biological examples, the repressilator and the p53 module, with interesting bifurcation diagrams.

A7- Hussain Zaidi*, Luke Langsjoen, Joe Straley, Eugene Kolomeisky, University of Virginia
Title: Geometrical Interpretation of the Non-universal Casimir Energy of An Infinite Cylindrical Wedge
Abstract: The majority of calculations in the literature on the Casimir energy of curved bodies focus on the universal part of the energy, implicitly assuming that the non-universal terms subtracted from the energy have no physical consequence. We explicitly calculate the non-universal terms for the particular case of an infinite cylindrical wedge and show that these terms are important quantities that arise out of the dependence of the surface tension and the bending/rigidity coefficients of a body on the energy cut-off in our calculations. This lends support to a recent phenomenological argument in favor of a geometrical interpretation of the non-universal terms of the Casimir energy.

A8- Rafael Greenblatt*, Michael Aizenman, and Joel L. Lebowitz, Rutgers University
Title: Rigorous derivation of the Imry-Ma phenomenon for quantum lattice systems
Abstract: In 1975 Y. Imry and S.-k. Ma argued that quenched disorder of a certain type disrupts first order phase transitions (e.g. ferromagnetism) in a variety of systems at low dimension ($d \leq 2$ or, in some cases, $d \leq 4$). A rigorous proof for a wide variety of classical lattice spin systems has been known for some time; I will outline a generalization to a comparable class of quantum systems.

A9- Alessandro Giuliani* and V. Mastropietro
Title: Rigorous construction of the ground state correlations of graphene
Abstract: We consider the 2D Hubbard model on the honeycomb lattice, as a model for graphene in the presence of screened Coulomb interactions. At half filling and weak coupling, we compute the free and ground state energy and we construct the correlation functions up to zero temperature in terms of convergent series; analiticity is proved by constructive fermionic renormalization group methods. The interaction produces a modification of the Fermi velocity and of the wave function renormalization without changing the asymptotic infrared properties of the model; the interacting charge and spin velocities develop an a-symmetry in the two coordinate directions. A construction at all orders of the case of unscreened Coulomb interactions will also be reported.

A10- Stefan Mashkevich* and Stephane Ouvry, Schrodinger Inc.
Title: Title: Statistics of discrete planar random walks
Abstract: An exact formula for the generating function of the probability distribution of the area covered by a closed random walk of a given length on a square lattice is derived.

A11- N. Diamantis, U. Nottingham and Peter Kleban*, University of Maine
Title: A Hamburger Theorem for Percolation
Abstract: We consider the three new crossing probabilities for percolation recently found via conformal field theory by Simmons, Kleban and Ziff [1]. We prove that all three of them (i) may be simply expressed in terms of Cardy and Watts' crossing probabilities, (ii) are (weakly holomorphic) second-order modular forms of weight 0 (and a single particular type) on the congruence group \Gamma(2), (iii) under some technical assumptions (similar to those used in [2]), are completely determined by their transformation laws. It is interesting that the only physical input in (iii) is Cardy's crossing formula, which suggests an unknown connection between all crossing-type formulas.

Session B

B1- Sungchul Ji*, Julie Bianchini, William Kim, Andrew Davidson, Rutgers University
Title: Experimental Evidence for a Quasi-Deterministic Relation between Structural and Timing Genes in the Budding Yeast Saccharomyces cerevisiae
Abstract: The genome of the budding yeast cell consists of about 6300 structural genes (coding for proteins) which accounts for approximately 70% of the total DNA mass. The changes in the genome-wide RNA levels were measured with DNA arrays by Garcia-Martinez et al (Mol Cell 15, 303-313, 2004) at 6 time points (0, 5, 120, 360, 450 and 850 minutes) after replacing glucose with galactose. When these data were plotted against time, a set of over 6000 trajectories was obtained. Each one of these trajectories carries two types of information which can be represented in i) the N-dimensional sequence (genotype) space, where a point represents an N nucleotide-long RNA molecule, and ii) the 6-dimenisional 'concentration (phenotype) space', wherein a point represents the kinetic trajectory of an RNA molecule measured over the 6 time points. Thus, for any pair of RNA molecules, it is possible to calculate i) the genotypic similarity as the degree of the overlap between the pair of nucleotide sequences (using the on-line CrustalW2 program), and ii) the phenotypic distance as the Euclidean distance between the corresponding two points in the concentration space. When the phenotypic distances of a set of 200 to 300 RNA pairs were plotted against the associated genotypic similarities, more than 95% of the points was found to fall into two groups - a) the 'structural gene-dependent' (i.e., rule-governed) group consisting of the points lying along the diagonal line with slopes varying from - 10 and - 60 (depending on the metabolic functions of the proteins encoded by the RNAs), and b) the 'structural gene-independent' (i.e., 'non-deterministic' or 'creative') group comprising those points lying along either horizontal or vertical lines below the diagonal. These observations suggest that the yeast genome contains two types of genes- i) the well-known 'structural genes' coding for the 3-D structures of RNA molecules (accounting for observation a) above), and ii) the 'timing genes' postulated here to encode the timing of the expression of the enzymes involved in transcribing or degrading RNA molecules, thereby controlling intracellular levels of RNA molecules (accounting for observation b)). Furthermore, the Garcia-Martinez et al data demonstrate that the relation between structural genes and timing genes is quasi-deterministic (i.e., neither deterministic nor random), reminiscent of the rule-governed creativity in linguistics and consistent with the cell language theory formulated over a decade ago (S. Ji, BioSystems 44, 17-39, 1997).

B2- Sungchul Ji, Rutgers University
Title: Three Kinds of Informations (Iconic, Indexical, and Symbolic) Carried by Molecular Signs
Abstract: The information theory of molecular biology can be viewed as a branch of semiotics, the scientific study of signs, because signs carry information. According to the American chemist-logician- philosopher Charles Sanders Peirce (1839-11914), (i) a sign stands for something (called object) to someone (interpreter or receiver) in some context (environmental contingencies) and ii) there are three kinds of signs - iconic signs (e.g., a statute) related to their objects by similarity, indexical signs (e.g., smoke) related to their objects by causality, and symbolic signs (e.g., words) related to their objects by convention, rules, and/or codes which are arbitrary from the standpoint of physics and chemistry. Applying these concepts and definitions to the molecular information processing systems in the living cell, it may be conjectured (1) that DNA serves as the sign for RNA to cells during the transcription step catalyzed by transcriptosomes, RNA in turn serving as the sign for proteins during the translation step catalyzed by ribosomes, (2) that the relation between DNA and RNA during transcription is primarily iconic (due to Watson-Crick base paring) and indexical (requiring the mechanical energy stored in DNA as conformational strains or conformons [S. Ji, BioSystems 54:107-130 (2000)]), and (3) the relation between RNA and proteins during translation is iconic (owing to the complementary shapes of codons and anti-codons), indexical (requiring conformons in ribosome to drive the orderly movement of aminoacyl tRNA molecules along the mRNA track), and symbolic (due to the arbitrariness of the relation between the codons of mRNA and the corresponding amino acids carried by tRNA) [M. Barbieri, The Organic Codes: An Introduction to Semantic Biology, Cambridge University Press, Cambridge, 2003]. If these conjectures prove to be correct in principle, it would be logical to conclude that biological information processing in the cell cannot be completely characterized in terms of the laws of physics and chemistry alone but requires in addition the rules (e.g., genetic codes) engendered by biological evolution, thus supporting the von Neumann-Pattee principle of matter-sign complementarity as applied to self-reproducing systems in biology [H. Pattee, BioSystems 60:5-12 (2001); S. Ji, N. Y. Acad. Sci., 870:411-417 (1999)]. In other words, biology is not an autonomous science separate from physics and chemistry as some evolutionary biologists assert but a triadic science rooted in physics, chemistry, and semiotics.

B3- Andrea Apolloni, Virginia Tech.
Title: Diffusion of innovation and cultural fragmentation in dynamic scenario
Abstract: Axelrod's model describes the dissemination of a set of cultural traits in a society. In a social context individual choices toward a determined attitude are at the basis of the formation of groups, communities, parties.We show that the introduction of group dynamics in a dissmination process could, under certain conditions, avoid the flattening of culture to a single though and preserve cultural attitudes. We also considered an innovation process on this dynamical background

B4- Nerses Ananikyan*, V. Abgaryan , L. Ananikyan, A. Kocharian Yerevan Physics Institute
Title: Negativity and Thermal Entanglement for a Spin 1 Heisenberg Model with Longitudunal
Abstract: By using the concept of negativity, we study thermal entanglement for a spin-1 Heisenberg model with longitudinal crystal field (uniaxial single-ion anisotropy). The axial term splits the degeneracy of the spin-states on the basis of the magnitude of the spin's z projection. The introduction of uniaxial single-ion anisotropy gives rise to some interesting aspects. We have exactly examined the value of negativity depends on uniaxial single-ion anisotropy with several values of the exchange anisotropy.

B5- Benjamin Sauerwine* and M. Widom, Carnegie Mellon University
Title: Competition between structural elements in riboswitches
Abstract: Riboswitches, a primitive method of gene control at the time of transcription, may have mutually exclusive structural elements known as the terminator hairpin and the antiterminator hairpin. The fate of the genetic transcript depends on which structure is dominant as the RNAp reaches a polyuracil pause site downstream. We study the timescale and frequency with which the antiterminator survives based on the presence of a portion of a bound aptamer region.

B6- Andrej Kosmrlj, MIT, Grad student
Title: Thymic selection of T-cell receptors as an extreme value problem
Abstract: T lymphocytes (T cells) orchestrate adaptive immune responses upon activation. T cell activation requires sufficiently strong binding of T cell receptors (TCRs) on their surface to short peptides (p) derived from foreign proteins, which are bound to major histocompatibility (MHC) gene products (displayed on antigen presenting cells). A diverse and self-tolerant T cell repertoire is selected in the thymus. We map thymic selection processes to an extreme value problem and provide an analytic expression for the amino acid compositions of selected TCRs (which enable its recognition functions).

B7- Juan Mallarino, Universidad de Los Andes, Columbia
Title: Statistical mechanics of a three-dimensional multi-component coulomb gas and an infinite cylindrical colloid through HNC approximation
Abstract: Under the infinite diluted approximation of the colloid within the multi-component gas, we present the results and implications over the long range effective potential of the colloid. The results show a shielding behavior of charges around the colloid. The latter study will be the basis for the study of a diluted colloid suspension in an ionic compound and it's thermodynamic properties.

B8- Hui Dai*, Zachary Geary, and Leo P. Kadanoff, University of Chicago
Title: Asymptotics of eigenvalues and eigenvectors of Toeplitz matrices
Abstract: A Toeplitz matrix is one in which the matrix elements are constant along diagonals. The Fisher-Hartwig matrices are much-studied singular matrices in the Toeplitz family. The matrices are defined for all orders, $N$. They are parametrized by two constants, $\alpha$ and $\beta$. Their spectrum of eigenvalues has a simple asymptotic form in the limit as $N$ goes to infinity. Here we study the structure of their eigenvalues and eigenvectors in this limiting case. We specialize to the case $0<\alpha<|\beta|<1$, where the behavior is particularly simple.

B9- Tobias Kuna, University of Reading
Title: Hydrodynamic scaling for jump type processes in the continuum
Abstract: On the lattice hydrodynamic scaling limits have been obtained for gradient and non-gradient systems. In the continuum, one can define jump type dynamics which are formally analogous to the lattice dynamics. I will report on first results and explain difference between the continuum and the lattice versions. This is an investigation in collaboration with P. Butta, T. Funaki, O. Kutoviy.

B10- Vadim Oganesyan*, A. Pal, and D. Huse, College of Staten Island, CUNY
Title: Energy transport in disordered classical spin chains at high temperature
Abstract: We present a numerical study of the diffusion of energy at high temperature in strongly disordered chains of interacting classical spins evolving deterministically. We find that quenched randomness strongly suppresses transport, with the diffusion constant becoming reduced by several orders of magnitude upon the introduction of only moderate disorder. We have also looked for but not found signs of a classical many-body localization transition at any nonzero strength of the spin-spin interactions.

B11- Michael Kiessling, Rutgers University
Title: Some monotonicity properties of ground state energies
Abstract: I announce some theorems about certain monotonicity properties of the ground state energies of classical and quantum N body systems as functions of N and explain some applications.