Statistical Mechanics Conference
97th Statistical Mechanics Conference
Sunday, May 06, 2007 at 08:00am -
CONFERENCE PROGRAM
SUNDAY, MAY 6, 2007
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8:00 - 9:00 Breakfast and Registration
9:00 - 9:20 M. Disertori, Universite de Rouen,
Rigorous Supersymmetric Approach to Random Matrix Problems
9:20 - 9:40 B. Schlein, University of California,
Derivation of the Time-Dependent Gross-Pitaevskii Equation
9:40 - 10:00 P. Fendley, University of Virginia,
Ground States of Strongly Correlated Fermions From Rhombus Tilings
10:00 - 10:20 R. Fernandez, Universite de Rouen,
New Criterion for the Convergence of the Cluster Expansion
10:20 - 10:50 Coffee
10:50 - 11:10 L. Bunimovich, Georgia Institute of Technology,
Dynamical Networks
11:10 - 11:30 H. Koch, University of Texas at Austin,
Renormalization of Flows, and Quasiperiodic Orbits
11:30 - 11:50 G. Mussardo, International School for Advanced Studies,
Breaking Integrability
11:50 - 12:10 P. Wiegmann, University of Chicago,
Hele-Shaw/DLA Problem
12:10 - 12:30 Y. Sinai, University of Princeton,
Blow Ups in Navier-Stokes System and Renormalization Group Method
12:30 - 2:00 LUNCH
(There will be a memorial service for Mrs. Yael Goldberg between 1:30 and 2:00pm)
2:00 - 2:25 G. Lawler, University of Chicago,
The Natural Parametrizaion for the Schramm-Loewner Evolution
2:25 - 2:50 S. Smirnov, University of Geneva,
Conformal Invariance in the Ising Model
2:50 - 3:15 H.T. Yau, Harvard University,
Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations
3:15 - 3:40 E. Lieb, Princeton University,
Some Thoughts About Density-Matrix-Functional Theory
3:40 - 4:10 Coffee
4:10 - 4:40 U. Landman, Georgia Institute of Technology,
Small is Different: Formation, Stability and Breakup of Nanojets - Molecular Dynamics Simulation Experiments and Stochastic Hydrodynamics
4:40 - 5:05 E. Heller, Harvard University,
From Random Waves to Statistical Mechanics: Quantum Chaos for N Particles
5:05 - 5:30 W. Bialek, Princeton University,
Ising Models for Networks of Real Neurons
5:30 - 5:55 K. Hepp, Institute for Theoretical Phsyics,
Quantum Mechanics and Higher Brain Functions: Lessons from Quantum Computation and Neurobiology
--------------Busch Campus Student Center -------------
6:00 COCKTAILS AND CONCERT IN HONOR OF JOHN CARDY, JUERG FROHLICH AND TOM SPENCER.
COCKTAILS AND CONCERT ARE SPONSORED BY SPRINGER, PUBLISHER OF THE JOURNAL OF STATISTICAL PHYSICS AND COMMUNICATIONS IN MATHEMATICAL PHYSICS.
ALL ARE INVITED
8:00 BANQUET DINNER (Reservations Required)
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MONDAY, MAY 7, 2007
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7:50 - 8:30 Breakfast and registration
8:30 - 9:50 Short Talks Session A
9:50 - 10:20 Coffee
10:20 - 10:45 B. Simon, California Institute of Technology,
Extensions of Szego's Theorem
10:45 - 11:10 A. Chakraborty, MIT,
Fluctuation Effects in T Cell Signaling
11:10 - 11:50 A. Libchaber, Rockefeller University,
Physical Aspects of the Origin of Life Problem
11:50 - 12:30 Human Rights Session
12:30 - 1:50 Lunch
1:50 - 2:20 I.M. Sigal, University of Toronto,
Renormalization Group and Scattering Theory of Electrons and Photons
2:20 - 2:40 N. Andrei, Rutgers University,
Quantum Impurities Out-of-Equilibrium: Currents and Entropy Production
2:40 - 3:00 A. Ludwig, University of California, Santa Barbara,
Boundary Critical Behavior and Multifractality at Anderson (De-)Localization Transitions"
3:00 - 3:20 A. Zamolodchikov, Rutgers University,
Fluctuating Geometry and Nucleation in 2D
3:20 - 3:50 Coffee
3:50 - 4:10 M. Douglas, Rutgers University,
Statistics of String Vacua
4:10 - 4:30 S. Goldstein, Rutgers University,
Canonical Typicality and GAP Measures for Quantum States
4:30 - 4:50 H. Pinson, University of Arizona,
Towards a Nonperturbative Renormalization Group Analysis
4:50 - 5:10 M. Zirnbauer, Cologne University,
Energy Correlations for a Random Matrix Model of Disordered Bosons
5:10 - 5:30 L. Pastur, University of Kharkov,
On the Law of Addition of Random Matrices: Covariance and the Central Limit Theorem for Traces of Resolvent
5:30 - 6:00 A. Klein, University of California, Irvine,
The Universal Occurrence of Localization in the Continuum Anderson Model
6:00 - 8:00 Cocktails and dinner
8:00 - 9:30 Round Table: Statistical Mechanical Aspects of Localization and Entanglement
Participants include: M. Aizenman, J. Cardy, J. Frohlich and T. Spencer
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TUESDAY, MAY 8, 2007
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8:00 - 8:30 Breakfast and registration
8:30 - 10:10 Short Talk Session B
10:10 - 10:35 G.B. Giacomin, Universite Paris 7,
The Localization Transition of Copolymers Near Selective Interfaces
10:35 - 11:00 Coffee
11:00 - 11:25 G. Ben Arous, NYU,
Equilibrium and Dynamic Universality Results for Mean-Field Spin Glasses
11:25 - 11:50 A. Bovier, Weierstrass Institute,
Aging in Spin Glass Models on Intermediate Time Scale: Universality of the Trap Model
11:50 - 12:15 T. Seppalainen, University of Wisconsin,
Fluctuations in the Asymmetric Simple Exclusion Process 12:15 - 12:40 U. Tauber, Virginia Tech,
Current Distribution in Driven Diffusive Systems: Field Theory Approach
12:40 - 1:50 Lunch
1:50 - 2:15 B. Vollmayr-Lee, Bucknell University,
Anomalous Dimension in the Trapping Reaction
2:15 - 2:40 J. Harnad, University of Montreal,
Tau Functions, Integrable Systems and Random Processes
2:40 - 3:05 P. Kleban, University of Maine,
On Cardy's Crossing Formula and Related Formulas in Percolation
3:05 - 3:30 F. Hansen, University of Copenhagen,
Metric Adjusted Skew Information
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.
N. Andrei, Rutgers University
Title: Quantum Impurities Out-of-Equilibrium: Currents and Entropy Production
Abstract: TBA
G. Ben-Arous, NYU
Title: Equilibrium and Dynamic Universality Results for Mean-field Spin Glasses
Abstract: TBA
W. Bialek, Princeton University
Title: Ising Models for Networks of Real Neurons
Abstract: TBA
A. Bovier,WIAS, Berlin
Coauthor(s): G. Ben-Arous and J. Cerny
Title: Ageing in spin glass models on intermediate time scale: universality of the trap model
Abstract: Link to transparencies of talk
We study a simple version of Glauber dynamics in p-spin Sherrington-Kirkpatrick models for p>2. We show that on time scales that are exponentially large in the volume, but short compared to equilibration times, the dynamics exhibits ageing described by the arcsine-law of an $alpha$-stable subordinator, as in the random energy model and the REM-like trap model. The result is due to the fact that the slow-down of the dynamics is caused by the fact that the process visits effectively independent traps whose structure, as seen from the random walk, while non-trivial, can be fully analysed. An important feature is that on the time scales considered, multiple visits of the same trap essentially never happen.
L. Bunimovich, Georgia Tech
Title: Dynamical Networks
Abstract: TBA
A. Chakraborty, MIT
Title: Fluctuation effects in T cell signaling
Abstract: TBA
M. Disertori,Universite de Rouen
Title: Rigorous Supersymmetric Approach to Random Matrix Problems
Abstract: TBA
M. Douglas, Rutgers University
Title: Statistics of String Vacua
Abstract: We give a brief introduction to the study of distributions and numbers of vacua of string/M theory, emphasizing precise questions and analogies with other fields of physics (particularly, the study of random potentials).
P. Fendley, University of Virginia
Title: Exact Results for 2+1 Dimensional Strongly-Correlated Fermions
Abstract: I discuss exact results for a model of strongly-interacting spinless fermions hopping on a two-dimensional lattice. A lower bound on the extensive ground-state entropy can be found by computing the Witten index. On the square lattice, this has been rigorously shown to be related to the number of certain kinds of rhombus tilings of the plane; I present substantial evidence that counting rhombus tilings also yields the exact number of ground states.
R. Fernandez, Universite de Rouen
Coauthor(s): A. Procacci
Title: New criterion for the convergence of the cluster expansion
Abstract: By reconsidering the traditional approach ---based on tree bounds--- we derive improved convergence conditions for the cluster expansion of general polymer models (objects with hard-core interactions). The improvement comes from a more detailed consideration of an identity due to Penrose and an alternative summation strategy. Previous convergence criteria (Cammarota-Brydges, Kotecky-Preiss, Dobrushin) are obtained through successive upper bounds of the Penrose identity. We have applied this new criterion to improve bounds on the region free of zeros of chromatic polynomials and the analyticity region of gases of hard spheres.
J.P. Garrahan, University of Nottingham
Title: Space-time thermodynamics of the glass transition
Abstract: In this talk I will describe how the dynamics of kinetically constrained models of glass formers takes place at a first-order coexistence line between active and inactive dynamical phases. This is shown by computing the large-deviation functions of suitable space-time observables, such as the number of configuration changes in a trajectory. This space-time transition occurs in the absence of any static transitions. I will present analytic and numerical results for a facilitated models and constrained lattice gases in various dimensions. I will discuss how space-time phase coexistence may underly glass transition phenomena more generally.
G. Giacomin, Universite Paris 7-Denis Diderot
Title: The Localization Transition of Copolymers Near Selective Interfaces
Abstract: The understanding of the (de)localization transition of disordered copolymers near selective interfaces appears to be very poor even in the context of the simplest models, and this in spite of a considerable effort coming from several independent groups. The problem is the one of a linear (say, directed) polymer, made up of monomers of two types (A and B), close to the interface between two solvents that interact differently with the monomers according to their types. The (quenched) disorder is in the way in which the types A and B are distributed along the chain. Energetically favored trajectories, i.e. the ones that put most of the monomers in their favorable solvent, are few and therefore entropically suppressed. The behavior of the system is then the result of a non-trivial entropy energy competition. We will present some recent results, both of theoretical and numerical nature, that do not find an explanation in the numerous approaches attempted up to now.
S. Goldstein, Rutgers University
Title: Canonical Typicality and GAP Measures for Quantum States
Abstract: Link to lecture
F. Guerra, INFN
Title: Spontaneous replica symmetry breaking in mean field spin glass theory
Abstract: TBA
F. Hansen, University of Copenhagen
Title: Metric adjusted skew information
Abstract: Link to transparencies of talk
We introduce the notion of metric adjusted skew information as a generalization of the Wigner-Yanase-Dyson skew information. It is a non-negative quantity bounded by the variance, and it vanishes for observables commuting with the state.
We show that the metric adjusted skew information is a convex function on the state manifold and also satisfy other requirements, suggested by Wigner and Yanase, to a measure of the information content in a state with respect to a conserved observable.
We show that the set of normalized Morozova-Chentsov functions is a Bauer simplex and determine the set of extreme points. We introduce the so called &lambda-skew informations, and obtain that the convex cone of these particular simple skew informations coincides with the set of all metric adjusted skew informations.
The corresponding entropies, including the Wigner-Yanase entropy, are in general not subadditive.
J. Harnad, University of Montreal
Title: Tau functions, integrable systems and random processes
Abstract: Link to tranparencies of lecture
Tau functions are essential tools in the theory of integrable systems, both classical and quantum. They can also be seen to play a role in certain classes of random processes. This is apparent, e.g., in the work of Okounkov, Reshetikhin, Olshansky and Borodin, and even Bethe ansatz techniques can be applied to "solve" certain random processes, as was shown long ago, e.g., in the work Gwa and Spohn. In this talk, I summarize some joint work with Alexander Orlov, in which new aspects of the theory of tau functions and integrable systems are used in the study of random processes.
E. Heller, Harvard University
Title: From Random Waves to Statistical Mechanics: Quantum Chaos for N Particles
Abstract: One of the approaches to quantum chaos (the quantum mechanics of classically chaotic systems) is through Berry's random wave hypothesis, which supposes that quantum eigenstates are locally random superpositions of plane waves. This idea can be extended to include constraints such as walls and collisions, and is most easily implemented in a Green function representation. In the short (real) time limit, it is simple to derive the classical limit for partition functions, etc.; however more interesting results for off-diagonal full and reduced density matrices show the transition from the microcanonical to the canonical ensemble in terms of a little known asymptotic limit of high order Bessel functions (one that is in none of the standard references). We show the canonical limit is reached rather quickly as a function of the number of particles; one use for this is the possible use of the Boltzmann rather than the real time propagator to get densities and correlation functions for few body systems.
K. Hepp, Inst. of Theoretical Physics
Title: Quantum Mechanics and Higher Brain Functions: Lessons from Quantum Computation and Neurobiology
Abstract: TBA
P. Kleban, University of Maine
Coauthor(s): R. Ziff and J. Simmons
Title: On Cardy's Crossing Formula and Related Formulas in Percolation
Abstract: TBA
A. Klein, University of California, Irvine
Title: The Universal Occurrence of Localization in the Continuum Anderson Model
Abstract: We will discuss Anderson and dynamical localization for continuum random Schrodinger operators and present a proof of localization for the continuum Anderson model with arbitrary single-site probability distribution.
H. Koch, University of Texas at Austin
Title: Renormalization of Flows, and Quasiperiodic Orbits
Abstract: In the early 1980s a renormalization group transformation was developed by MacKay and others for studying the breakup of smooth invariant circles in area-preserving maps. We describe here a more recently developed approach that renormalizes Hamiltonians and vector fields, as opposed to pairs of commuting maps. Results from this approach include KAM type theorems, the existence of a nontrivial fixed point, and critical invariant tori.
U. Landman, Georgia Tech.
Title: Small is Different: formation, stability and breakup of nanojets - molecular dynamics simulation experiments and stochastic hydrodynamics
Abstract: TBA
G. Lawler, University of Chicago
Title: The Natural Parametrization for the Schramm-Loewner Evolution
Abstract: TBA
A. Libchaber, Rockefeller University
Title: Physical Aspects of the Origin of Life Problem
Abstract: In the RNA world of the early soup we are studying how a genetic code could originate, building an RNA ribozyme that can charge an amino acid without enzymes, a primitive tRNA. We also show that the initial code could have started with four amino acids only: valine (GUC), alanine (GCC), glycine (GGC), aspartate (GAC).
- Encapsulation of cells in a membrane is another step in this puzzle. Building an artificial cell based on gene expression inside vesicles reveal the physical constraints to overcome: energy exchange, osmotic pressure, sources and sinks for protein production. This cell can sustain protein production for about one week. Self- reproduction will be the next step.
G. Mussardo, SISSA-Trieste
Title: Breaking Integrability
Abstract: Thanks to integrable quantum field theories, there has been in recent year new understanding on a large number of models of interest in statistical mechanics or in condensed matter physics, e.g. Ising model in a magnetic field or Sine-Gordon model. Integrability has permitted to determine, for instance, the exact spectrum of many systems or the explicit determination of the correlation functions of their order parameters.
In the seminar there will be discussed how to extend the analysis also to non-integrable models, in particular how to determine the spectrum of the excitations of these systems or how to compute the decay rates of the unstable particles.
L. Pastur, Institute for Low Temperatures, Kharhiv, Ukraine
Title: On the Law of Addition of Random Matrices: Covariance and the Central Limit Theorem for Traces of Resolvent
Abstract: We consider the ensemble of $ntimes n$ random matrices $ H_{n}=A_{n}+U_{n}^{dag }B_{n}U_{n}$, where $A_{n}$ and $B_{n}$ are Hermitian (real symmetric), having the limiting Normalized Counting Measure of eigenvalues (NCM), and $U_{n}$ is unitary (orthogonal), uniformly distributed over $U(n)$ ($O(n)$). We give first a more short and transparent proof of our previous result on the existence of the NCM of $H_{n}$ as the size of matrices tends to infinity. This is based on a new inequality, analogous to the Poincare-Nash inequality for Gaussian random variables. We then find the leading term of the covariance and establish the Central Limit Theorem for a class of linear eigenvalue statistics of these random matrices in the same limit.
H. Pinson, University of Arizona
Title: Towards a Nonperturbative Renormalization Group Analysis
Abstract: TBA
T. Seppalainen, University of Wisconsin
Title: Fluctuations in the Asymmetric Simple Exclusion Process
Abstract: This talk describes work done on the fluctuations of the asymmetric simple exclusion process, from results of Ferrari-Fontes 1994 through recent joint work with Marton Balazs that establishes t2/3 as the order of the variance of the net current across a characteristic curve.
B. Vollmayr-Lee, Bucknell University
Title: Anomalous Dimension in the Trapping Reaction
Abstract: TBA
Y. Sinai, Princeton University
Title: Blow Ups in Navier-Stokes System and Renormalization Group Method
Abstract: In this talk I shall describe a new approach based on the renormalization group theory which gives a possibility to constract short time singularities in complex solutions of the 3-dim Navier-Stokes system.
B. Simon, California Institute of Technology
Title: Extensions of Szego's Theorem
Abstract: TBA
S. Smirnov, Universite de Geneve
Title: Conformal invariance in the Ising model
Abstract: 2D Ising model at criticality is considered a classical example of conformal invariance in statistical mechanics, which is used in deriving many of its properties. However, it seems that no mathematical proof of this assertion has ever been given. Even most of the physics arguments concern nice domains only or do not take boundary conditions into account, and thus only give evidence of a the Mobius invariance of the scaling limit, arguably a much weaker property than. We will show that 2D Ising model at criticality is fully conformally invariant in the scaling limit, and identify the limits of interfaces with Schramm's SLE curves.
U. Tauber, Virginia Tech
Title: Current Distribution in Driven Diffusive Systems: Field Theory Approach
Link to talk
Abstract: (reports work with Vivien Lecomte and Frederic van Wijland, both at Laboratoire de Physique Theorique, Universite de Paris-Sud, Orsay and Universite Paris VII - Denis Diderot, Paris, France, published in: J. Phys. A: Math. Theor. 40, 1447-1465 (2007); e-print: cond-mat/0611265)
We investigate the asymptotic properties of the large deviation function of the integrated particle current in driven diffusive systems. It is exemplified how renormalization group techniques allow for a systematic determination of power laws in the corresponding current large deviation functions. We show that the latter are governed by known universal scaling exponents, specifically, the anomalous dimension of the noise correlators.
H.T. Yau, Harvard University
Title: Lower bound on the blow-up rate of the axisymmetric Navier-Stokes equations
Abstract: TBA
A. Zamolodchikov, Rutgers University
Title: Fluctuating geometry and Nucleation in 2D
Abstract: TBA
M. Zirnbauer, Cologne University
Title: Energy correlations for a random matrix model of disordered bosons
Abstract: Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of elliptic elements of a real symplectic Lie algebra. The presence of disorder in the physical system determines a probability measure with support on this cone. In this talk I discuss a family of such measures of exponential type, and do so in an attempt to capture, by a simple random matrix model, some generic statistical features of the characteristic frequencies of disordered bosonic quasi-particle systems. The level correlation functions of the said measures are shown to be those of a determinantal process, and the kernel of the process is expressed as a sum of bi-orthgonal polynomials. While the correlations in the bulk scaling limit are in accord with GUE (or sine kernel) universality, at the low-frequency end of the spectrum an unusual type of scaling behavior is found.
