97th Statistical Mechanics Conference Short Talks and Abstracts SESSION A * For author presenting the talk

A1 - M. Pinsky, University of Nevada, Reno Averaging Reduction for Nonlinear Systems with Dense and Multiple Resonances Normal forms and averaging reduction techniques are widely used for analysis of local dynamics of nonlinear systems. However, for systems with multiple and dense resonances the application of standard techniques offers little simplification mostly due to the intrinsic problem of the small divisor. A novel technique for separation of fast and slow components of local dynamics of nonlinear systems is introduced. This technique reaches no limitation for systems with practically arbitrary resonance structure and permits to adjust the degree of averaging and the accuracy of corresponding approximations. Numerical implementation of this technique is considered as well.

A2 - *A. Ayyer, M. Stenlund, Rutgers University Exponential Decay of Correlations for Randomly Chosen Hyperbolic Toral Automorphisms We consider pairs of toral automorphisms (A,B) satisfying an invariant cone property. At each iteration, A acts with probability p and B with probability 1-p. We prove exponential decay of correlations for a class of Holder continuous observables.

A3 - L. Andrey, Academy of Sciences No Quantum Limits to the Second Law of Thermodynamics There have been many attempts to prove the existence of quantum limits to the 2nd Law of Thermodynamics, last years. On the basis of quantum information theory it will be reasoned that such attempts are false. In fact the role of quantum entanglement in this game will be stressed. So, if your theory is found to be against the 2nd Law of Thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation, as Eddington has said.

A4 - S. Adams, Max Planck Institute for Math. and Sciences Large Deviations for Empirical Path Measures in Cycles of Integer Partitions Consider a large system of $N$ Brownian motions in $\mathbb{R}^d$ on some fixed time interval $[0,\beta]$ with symmetrised initial-terminal condition. That is, the terminal location of a motion is affixed to the initial point of a motion, which is given by a random permutation on all motions of the system. We integrate over all initial points confined in boxes with respect to the Lebesgue measure, and we divide by a normalisation (partition function). Such systems play an important role in quantum physics in the description of Boson systems at positive temperature $1/\beta$. We describe the large-$N$ behaviour of the empirical path measure (the mean of the Dirac measures in the $N$ paths) in the thermodynamic limit. The rate function is given as a variational formula involving a certain entropy functional and a Fenchel-Legendre transform. The entropy term governs the large-$N$ behaviour of discrete shape measures of integer partitions. Any integer partition determines a conjugacy class of permutations of certain cycle structure. Depending on the dimension and the density $ \rho $, there is phase transition behaviour for the empirical path measure.

A5 - *A. Giuliani, J.L. Lebowitz and E. Lieb, Princeton University Spin Models with Long Range Competing Interactions: Striped Nature of the Ground States In this talk I will present some recent rigorous results on the stripe-patterned nature of the ground states in 2D models of discrete dipoles interacting via a long range dipole-dipole interaction and a nearest neighbor ferromagnetic exchange interaction. The proofs are based on a combination of reflection positivity methods and apriori estimates on the energy of Peierl's contours.

A6 - *P.K. Mohanty, B.D Todd and D.J. Saeles, SINP Generic Features of the Wealth Distribution in Ideal-Gas-Like Markets We provide an exact solution to the ideal-gas-like models studied in econophysics to understand the microscopic origin of Pareto-law. In these class of models the key ingredient necessary for having a self-organized scale-free steady-state distribution is the trading or collision rule where agents or particles save a definite fraction of their wealth or energy and invests the rest for trading. Using a Gibbs ensemble approach we could obtain the exact distribution of wealth in this model. Moreover we show that in this model (a) good savers are always rich and (b) every agent poor or rich invests the same amount for trading. Nonlinear trading rules could alter the generic scenario observed here.

A7 - *S. Das and M. Fisher, University of Maryland Is the Stillinger-Lovett Sum Rule for an Electrolyte Correct at Criticality? ven for a 1:1 electrolyte the answer is "no" if the system is not fully charge symmetric. Then, as argued by Stell [1] and demonstrated recently in an exactly soluble ionic spherical model [2], the diverging density fluctuations mix into the charge correlations and induce a breakdown of the SL sum rule xi_Z,1=xi_D [3] just at criticality. Here xi_Z,1 is the second moment of the charge-charge correlation function while xi_D2 = c(T/rho) is the square of the Debye length. However, xi_Z,1^c = xi_D^c is expected [1,2,4] for a fully charge-symmetric model, such as the RPM. Nevertheless, our extensive grandcanonical MC simulations [5], using (T,mu) histogram reweighting and finite-size scaling, satisfy the SL rules away from criticality but indicate a violation at criticality with xi_Z,1^c about 10% greater than xi_D^c. References 1. G. Stell, J. Stat. Phys, 78, 197 (1995); see also M.E. Fisher, J. Stat. Phys. 75, 1 (1994). 2. J.-N. Aqua and M.E. Fisher, Phys. Rev. Lett. 92, 135702 (2004). 3. F.H. Stillinger and R. Lovett, J. Chem. Phys. 48, 3858 (1968). 4. B.P. Lee and M.E. Fisher, Europhys. Lett. 39, 611 (1997). 5. S.K. Das, Y.C. Kim and M.E. Fisher [to be published].

A8 - *Stefan Mashkevich, S. Matveenko, and S. Ouvry, Schrodinger, Inc Exact Results for the Spectra of Bosons and Fermions with Contact Interaction An N-body bosonic model with delta-contact interactions projected on the lowest Landau level is considered. For a given number of particles in a given angular momentum sector, any energy level can be obtained exactly by means of diagonalizing a finite matrix: they are roots of algebraic equations. A complete solution of the three-body problem is presented, some general properties of the N-body spectrum are pointed out, and a number of novel exact analytic eigenstates are obtained.

A9 - *S.J. Rahi, P. Virnau, L. Mirny, and M. Kardar, MIT Prediction of Transcription Factor Specificity Using All-Atom Models We study the binding of transcription factor PurR to DNA. We compare ab initio specificity predictions based on all-atom models with bioinformatics predictions based on sequence similarity. We show that the specificity is predominantly due to protein-DNA interactions allowing us to predict the consensus sequence easily. Using binding energies we go on to score the binding of close mutants of PurR to DNA sequences, which is out of reach for bioinformatics tools. The results are compared to experimental data.

A10 - *A. Rosso, A. Zoia, and M. Kardar, MIT Fractional Laplacian in Bounded Domains The fractional Laplacian $-(-\triangle)^{\frac{\alpha}{2}}$ operator emerges in the formulation of a wide class of physical systems, including L\'evy Flights and stochastic interfaces. In this paper, we provide a discretized version of this operator which is well suited to deal with boundary conditions on a finite interval. Then, we numerically investigate the eigenfunctions and eigenvalues of the operator and discuss their meaning in the light of two physical models, namely hopping particles and elastic springs. Some analytical results concerning the structure of the eigenvalues spectrum are also derived.

A11 - *A. Zoia, Y. Kantor, and M. Kardar, MIT Distributions of Passage Times and Distances Along Critical Curves We numerically compute the probability $p_{d_f}(\ell | R)$ that two points on a fractal curve in two dimensions are separated by a distance $\ell$ along the curve: one point is on the edge of the semi-infinite plane and the second at a distance $R$. The stochastic Loewner equation is used to efficiently generate self-similar curves with different fractal dimensions $d_f$. The scaled distribution functions $p_{d_f}(\ell / R^{d_f})$ become broader as $d_f$ is increased and are characterized by tails that decay faster than a simple exponential. These results are utilized in a new model for anomalous transport in inhomogeneous matter, whose behavior is contrasted with those from fractional dynamics.

A12 - *M. Kardar and Y. Kantor First Passage Time Distribution for a Tagged Monomer Fluctuations of a tagged monomer in a long polymer is sub-diffusive at short times. We numerically study the distribution of the first time the tagged monomer reaches a fixed (absorbing) boundary. This distribution is found to decay exponentially at large times, in contrast to the power law decay predicted from fractional Fokker-Planck descriptions of a sub-diffusive particle.

SESSION B * For author presenting the talk

B1 - S. Ji, Rutgers University Is Life an 'Informed' Critical Phenomenon? If we can associate 'critical phenomena' with those states of physical systems wherein long-range interactions occur between mciro- and meso- or macro-scale structures or events, then life on the simplest level, namely, the cell, can be logically viewed as an example of critical phenomena, since a molecule (e.g., a homrone) binding to a cell surface receptor can trigger a chain of events in the nucleus (which is typically 104 nm away from the cell surface) leading to mesoscopic and macroscopic morphological changes of cells and their higher-order structures such as the shapes of the nose or eyes. One interesting difference between the critical phenomena studied in condensed matter physics and in cell biology is that 'cellular critical phenomena' are reltively robust against enviornmetnal conditions as evidenced by the fact that cells can survive and flourish under widely different environmental condtions, from the antartic to the eqatorial regions. One possibility to account for this difference is to invoke the existence of two classes of critical phenomena in nature -- i) the passive (or down-hill) critical phenomena as traditionally studied in physics, and ii) the active (or free-energy-driven up-hill) critical phenomena reported here. We may refer to the former as the 'abiotic' criticality' and the latter as the 'biotic' criticality'. We recently obtained evidence that the dissipative structures comprising the time-dependent mRNA levels in budding yeast undergoing glucose-galactose shift (measured with DNA arrays) exhbit "active criticality" as evidenced by the power law relation found to hold between the cluster number (k) and the novel order parameter called "transcript density (d_T)" defined as the fraction of total transcripts with a given funciton that is found in a set of contiguous clusters divided by the fraction of these clusters over the total cluster number k. That is, it was found that d_T = a k^w, where a is a constant and w is the 'critical exponent', whose numerical values (from 1/4 to 3/4) seem to reflect the biological functions of mRNA clusters. If these resutls (obtained using the ViDaExpert software of A. Zinovyev, Curie Institue, Paris) can be confirmed by using several other clustering methods, the idea of active or biotic criticality may be established as a useful new concept in cell biology and additionally bring condensed matter physics and cell biology closer together.

B2 - R. Fisch, Princeton University "Aspect-ratio scaling of domain wall entropy for the 2-dimensional +- J Ising spin glass The ground state entropy of the 2D Ising spin glass with +1 and -1 bonds is studied for $L \times M$ square lattices with $L \le M$ and $p$ = 0.5, where $p$ is the fraction of negative bonds, using periodic and/or antiperiodic boundary conditions. From this we obtain the domain wall entropy as a function of $L$ and $M$. It is found that for domain walls which run in the short, $L$ direction, there are finite-size scaling functions which depend on the ratio $M / L^{1.25}$. When $M$ is larger than $L$, very different scaling forms are found for odd $L$ and even $L$. For the zero-energy domain walls, which occur when $L$ is even, the probability distribution of domain wall entropy becomes highly singular, and apparently multifractal, as $M / L^{1.25}$ becomes large. See cond-mat/0703137

B3 - *T. Klongcheongsan & U. Tauber, Virginia Tech Monte Carlo Simulation of Half-Loop and Double-Kink Excitations in the Strongly Pinned Bose Glass Phase We study the dynamics of driven magnetic vortices in disordered high-temperature superconductors using Metropolis algorithm based Monte Carlo simulations for 3D elastic flux lines. In particular, we have studied flux creep through thermally activated half loops and double kinks in the strongly pinned Bose-glass phase. Our preliminary results indicate that these excitations occur at low driving force just below and near the depinning current, and govern the system's relaxation to its nonequilibrium steady state.

B4 - *A. Toom & A. V. Rocha, UFPE Substitution Operators We take any finite set A and call it alphabet. Its elements are called letters. Any finite sequence of letters is called a word. A^Z is our configuration space. M is the set of normalized translation-invariant measure on A^Z. We define a class of maps from M to M called substitution operators or s.o. for short. To define a s.a. we need two words U and V (with a special condition on U) and a number r in [0,1]. The s.o. turns any U entering a configuration into V with a rate r. We study properties of s.o. including their continuity and convexity.

B5 - F. Frascoli, Swinburne University of Technology Chaotic Properties of Liquids Undere Planar Elongational Flow The simulation of planar elongational flow (PEF) in a nonequilibrium steady state for arbitrarily long times has been recently made possible, combining the SLLOD algorithm from non-equilibrium molecular dynamics (NEMD) methods with periodic boundary conditions for the simulation box [1]. Some of the chaotic aspects of atomic liquid systems under PEF [2] are discussed in this talk, and a comparison with the properties of the SLLOD algorithm for planar shear flow [3] is given. The spectra of Lyapunov exponents for different types of constrained dynamics are illustrated. These include the NVT, NVE and the NpT [4] regimes, with the use of Gaussian and NoséHoover constraining techniques. The conjugate pairing rule is tested and its validity is confirmed for PEF. This allows the evaluation of nonequilibrium transport coefficients with the calculation of two Lyapunov exponents and represents a viable alternative to standard NEMD calculations.

B6 - J. Jalkanen, Helsinki University of Technology Numerical Study on Heteroepitaxial Naniislands in Two Dimensions We study numerically the equilibrium shapes, shape transitions and optimal shapes of small coherent heteroepitaxial nanoislands. We estimate the equilibrium shapes for different material parameters by atomistic energy minimization. For Stranski-Krastanow systems we vary the coverage to explore the experimentally observed optimal island sizes. We develope an analytical expression for the island energetics. The formula is able to explain the simulation results and can be used estimate system properties as long as the system is free of dislocations.

B7 - Y. Nagahata, Osaka University Regularity of the Diffusion Coefficient Matrix for Lattice Gas Reversible Under Gibbs Measurs with Mixing Condition By using (generalized) dual process, we show that the diffusion coefficient matrix is continuously differentiable with respect to order parameter.

B8 - *C. Scullard and R. Ziff, University of Chicago General Method for Predicting Approximate Bond Percolation Thresholds We present a general method for predicting the bond percolation thresholds of two-dimensional periodic lattices. The method makes correct predictions for all exactly solved lattices, and appears to be very close, but not quite exact, for other unsolved Archimedean lattices. For these we find the following: kagome: p_c=0.524430..., (3,122): p_c=0.740423..., (33,42): p_c=0.419308..., (3,4,6,4):p_c=0.524821..., (4,82):p_c=0.676835... . The best published numerical values for these lattices are: kagome: p_c=0.5244053 +/0.0000003 (Ziff 1997), (3,122): p_c=0.74042195 ± 0.0000008, (33,42): 0.41964191± .00000043, (3,4,6,4):p_c =0.52483258 +/ .00000053, (4,82): p_c=0.67680232 ± .00000063 (Parviainen 2003). The value for the kagome lattice is identical with that conjectured by Wu in 1979. This method should therefore be seen as an extension to other Archimedean lattices of Wu's original approximation.

B9 - *J.J.H. Simmons and P. Kleban, University of Maine Exact Factorization of Correlation Functions in 2D Critical Percolation Using conformal field theory we derive several exact results for higher-order correlation functions in 2D critical percolation. These functions factorize exactly into products involving lower-order correlations and operator product expansion coefficients.

B10 - *Y. Shokef, G. Shulkind and D. Levine, University of Pennsylvania Isolated Non-Equilibrium Systems in Contact We investigate a solvable model for energy conserving non-equilibrium steady states. The time-reversal asymmetry of the dynamics leads to the violation of detailed balance and to ergodicity breaking, as manifested by the presence of dynamically inaccessible states. Two such systems in contact do not reach the same effective temperature if standard definitions are used. However, we identify the effective temperature that controls energy flow. Although this operational temperature does reach a common value upon contact, the total entropy of the joint system can decrease. See http://arXiv.org/cond-mat/0703040

B11 - *D. Gioev, P. Deift, T. Kriecherbauer & M. Vanlessen, University of Rochester Universality for Orthogonal and Symplectic Hermite-Type and Laguerre-Type Random Matrix Ensembles Universality in the bulk and at the soft edge of the spectrum for orthogonal and symplectic ensembles (OE's and SE's) of random matrices with weights of the form $w(x)=\exp(-V(x))$, $V$ is a polynomial of even degree with positive leading coefficient on the line, was earlier proved by the speaker and Percy Deift using asymptotic analysis of Widom's formulae for the $\beta=1$ and $4$ correlation kernels. In this talk we will describe the recent result on the universality in the bulk and also at the soft and hard spectral edges for OE's and SE's with weights of the form $w(x)=x^\alpha \exp(-V(x))$, $\alpha>0$, $V$ is a polynomial with positive leading coefficient on the half-line. There are new difficulties that have to be resolved over and above the case of Hermite-type weights.