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100th Statistical Mechanics Conference


RUTGERS, THE STATE UNIVERSITY OF NEW JERSEY
HILL CENTER, ROOM 114
SUNDAY, MONDAY AND TUESDAY
DECEMBER 13-18, 2008


Organized by: Joel L. Lebowitz, lebowitz@math.rutgers.edu
Co-organized by: Peter Winkler, peter.winkler@Dartmouth.EDU

Here is a list of invited speakers for both the Statistical Mechanics Conference and the DIMACS workshop. Talk titles and abstracts will be posted as the information becomes available. Please continue to check back and if you are a speaker and your talk information does not appear please register or email it in.



  • Michael Aizenman, Princeton University
    Title: A Dynamical Perspective on the Success of Parisi's Hierarchical Ansatz Coauthor: L.P. Arguin
    Abstract: TBA

  • Phil Anderson, Princeton University
    Title: The Unreasonable Effectiveness of Experimental Physics in Mathematics
    Abstract: A panel discussion organized by Joel on Wigner's famous remark stimulated me to propose its converse. It has been my observation that interesting mathematics is as (or more) often stimulated by the observation of experimental anomalies than vice versa. Some very famous examples are the equivalence of gravitational and inertial mass , which Einstein wrote about in 1907 but took 8 years to find the math for general relativity; the Lamb shift, which played an enormous role in QED; and of course, the whole history of the discovery of the quantum theory, from Black Bodies on. I will give immodest examples from my own career: localization, a theorem in pure math stimulated by a specific experiment; spin glass theory, all a result of the observation of a phase transition by Budnick, Canella and Mydosh and leading inter alia to two popular algorithms for complex optimization; the Higgs phenomenon, first noticed as the anomalous absence of Goldstone modes in superconductors; and several more if time.

  • Laszlo Barabasi, University of Notre Dame
    Title: From Networks to Human Mobility Patterns
    Abstract: Despite their importance for the formation of social networks, urban planning, traffic forecasting and the spread of biological and mobile viruses, our understanding of the basic laws governing human mobility is limited owing to the lack of tools to monitor the time-resolved location of individuals. I will discuss a study that explores the trajectory of anonymized mobile phone users, finding that in contrast with the random trajectories predicted by the prevailing Levy flight and random walk models, human trajectories show a high degree of temporal and spatial regularity, each individual being characterized by a time independent characteristic travel distance and a significant probability to return to a few highly frequented locations. After correcting for differences in travel distances and the inherent anisotropy of each trajectory, the individual travel patterns collapse into a single spatial probability distribution, indicating that, despite the diversity of their travel history, humans follow simple reproducible patterns.

  • Murray Batchelor,Australian National University
    Title: Scaling function of the 2D ising model in a magnetic field
    Abstract:TBA

  • Jozsef Beck,Rutgers University
    Title: Randomness of the irrational rotation by square root of two
    Abstract:TBA

  • Gerard Ben Arous, New York University, Courant Institute
    Title: Random walks on random trees: trapping, scaling limits, and fluctuation-dissipation
    Abstract:TBA

  • Kurt Binder, Universitat Mainz
    Title: Surface-directed spinodal decomposition: Lattice model versus Ginzburg-Landau Theory
    Abstract: When a binary mixture is quenched into the unstable region of the phase diagram, phase separation starts by spontaneous growth of long wavelength concentration fluctuations ("spinodal decomposition"). In the presence of surfaces, the latter provide nontrivial boundary conditions for this growth. In this talk it is shown how lattice models can be used to derive these boundary conditions, but the lattice models can also be simulated directly, and can thus be used to clarify the conditions under which the Ginzburg-Landau type theory is valid. In this way, it is shown that the latter is accurate only in the immediate vicinity of the bulk critical point, if thermal fluctuations also can be neglected (i.e., for the late stages of phase separation). In contrast, a local kinetic mean field theory can take full account of nonlinearities and rapid concentration variations, and thus has much wider validity. However, the extension to spinodal decomposition in fluid binary mixtures (which can be simulated only by brute force large scale molecular dynamics methods) remains an unsolved challenge.
    * Fruitful collaborations with H. L. Frisch, S. Puri, S. K. Das, and J. Horbach are gratefully acknowledged. This talk is dedicated to the memory of Harry L. Frisch who died in 2007.

  • B. Bollobás, University of Cambridge and University of Memphis
    Title: Models of real-world networks: Inhomogeneous Random Graphs and Convergent Graph Sequences
    Abstract: In the past decade or so, much work has been done constructing and analyzing models of real-world graphs. The random graphs in these models are inhomogeneous and sparse, and their degree sequences frequently have power-law distributions. Recently, Janson, Riordan and I defined a very general model of sparse inhomogeneous random graphs which include exactly most of the models that have been studied.

    In order to decide how well our random graph G(n, κ) approximates a given real-world graph Gn, it would be desirable to establish a distance between a random graph model and a graph, so that the approximation is judged to be better and better as the distance tends to 0. For dense graphs (graphs with n vertices and at least cn2 edges), such a program has been carried out very successfully in a series of papers by Borgs, Chayes, Lovász, Sós, Szegedy and Vesztergombi. In particular, they introduced several metrics on the space of dense finite (weighted) graphs and showed them to be equivalent.

    In this talk I shall report on some very recent work that Oliver Riordan and I have done on a possible general theory of metrics on sparse graphs. We have investigated to what extent the ideas of Borgs, Chayes, Lovász, Sós, Szegedy and Vesztergombi can be carried over to the sparse setting, and what can be said about the connection between the metrics and the ideas of Bollobás, Janson and Riordan. Not surprisingly, the difficulties that arise are considerably greater than in the dense case; in fact, the difficulties increase as the graphs get sparser.

  • Pavel Bleher, Indiana University-Purdue University Indianapolis
    Title: Exact solution of the six vertex model with domain wall boundary conditions
    Abstract: We obtain the large N asymptotics of the partition function of the six vertex model with domain wall boundary conditions in the disordered and ferroelectric phases, and also on the critical line between these two phases. The solution is based on the Riemann-Hilbert approach. We will also discuss our new results about the arctic circle type theorem for the six vertex model.

  • Christian Borgs, Microsoft
    Title: Polya Urns and Convergence of Preferential Attachment Graphs
    Abstract:TBA

  • Edouard Brezin,ENS
    Title: Non-linear sigma models : a retrospective look
    Abstract : various applications of these models will be reviewed

  • John Cardy, University of Oxford
    Title: Universality, Integrability and Analyticity
    Abstract:TBA

  • David Ceperley, University of Illinois at Urbana-Champaign
    Title:The 2D quantum one component plasma as seen by Path Integral Monte Carlo
    Coauthors: B. Clark and M. Casula
    Abstract:We report results of Path Integral calculations of particles interacting with a 1/r potential in 2d focusing on quantum effects at low temperature. We see the melting line and hexatic transition persist into the quantum regime. Jamei, Kivelson, and Spivak argue that microemulsion phases must be present between the Wigner crystal and the fluid phase at low temperature but we have not yet identified such an intervening phase.

  • Philippe Choquard, EPFL
    Coauthors: J. Stubbe, M. Vuffray
    Title: Bound States of Mean Field Equations for a Gravitational Bose Equation Condensate Gas
    Abstract:The mean field approximation for a system of non relativistic selfgravitating bosons yields a nonlinear nonlocal equation equivalent to the Schrodinger-Newton equations. Old and new results on the existence of bound states of Schrodinger-Newton equations in any dimension are presented. Taking into account repulsive pair interactions astrophysicists have recently proposed models where cold Bose stars form a Bose-Einstein condensate. We show the existence and uniqueness of ground states of the Gross-Pitaevskii equation for a gravitationally trapped Bose-Einstein condensate and its Thomas-Fermi limit. As a preamble we outline the mean field concept in statistical mechanics, fluid mechanics and cosmology.

  • E.G.D. Cohen, Rockefeller University
    Nonequilibrium Statistical Mechanics in its Bronze Age
    Abstract: During the middle of the 20th century, a world wide effort was made for a systematic generalization of the Boltzmann Equation for a dilute gas,containing only binary collisions between particles, to higher densities. Although numerous such formal generalizations were indeed made by many of the leaders in Statistical Mechanics at the time, it turned out that these were all wrong , since they contained divergences, the more so the larger the groups of colliding particles that were included. As a by-product it was proved that, also contrary to general opinion, in any dimension, three hard balls have a maximum of 4 rather than 3 collisions, which is the case for a one-dimensional gas of hard rods. After a brief sketch of these developments, some general conclusions are drawn.

  • Pierluigi Contucci,Universita di Bologna
    Title: Short-Range Spin Glasses: Looking Back, Looking Forward
    Abstract:The seminar will review some rigorous results for finite dimensional spin glasses mostly about factorization properties of the quenched measure. Some new numerical results will be presented and discussed.

  • Bernard Derrida, ENS, France
    Title: Current Fluctuations in non-equilibrium steady states
    Abstract: The fluctuations of the current through a system maintained in a non-equilibrium steady state by contact with two reservoirs at unequal densities have in general a non-Gaussian distribution which can be computed exactly for diffusive systems [1,2,3]. For a system at equilibrium on a ring geometry, the cumulants of these fluctuations take a universal scaling form which can be understood by Bethe ansatz calculation as well as by a macroscopic fluctuation theory [4].
      [1] T. Bodineau, B. Derrida, Phys. Rev. Lett. 92, 180601 (2004) Current fluctuations in non-equilibrium diffusive systems: an additivity principle
      [2] T. Bodineau, B. Derrida, Phys. Rev. E 72, 066110 (2005) Distribution of current in non-equilibrium diffusive systems and phase transitions
      [3] T. Bodineau, B. Derrida, C. R. Physique 8, 540-555 (2007) Cumulants and large deviations of the current through non-equilibrium steady states
      [4] C. Appert, B. Derrida, V. Lecomte, F. Van Wijland, Phys. Rev. E 78, 021122 (2008) Universal cumulants of the current in diffusive systems on a ring.


  • Freeman Dyson,IAS
    Title: Birds and Frogs
    Abstract: Some mathematicians are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. Frogs live in the mud below and see only the flowers that grow nearby. I happen to be a frog, but Joel Lebowitz is a bird. Mathematics needs both frogs and birds. Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details. My talk will describe some of the outstanding birds and frogs that I have known during the last seventy years.

  • Daniel Fisher, University of Stanford
    Title: Sex and evolutionary dynamics of microbes
    Abstract:TBA

  • Michael E. Fisher, University of Maryland
    Title: Landau & Zeldovich, 1943; Stillinger & Lovett, 1968: Are Electrolytes Metallic at Criticality?

  • Juerg Froehlich, ETH Zurich
    Title: Out of Equilibrium
    Abstract: I review recent progress in the area of open quantum systems and non-equilibrium statistical mechanics. Among the topics described will be transport phenomena between different thermal reservoirs, quantum friction and quantum Brownian motion.

  • Giovanni Gallavotti, INFN
    Title: On the physical significance of finite thermostats
    Abstract:TBA

  • David Galvin, University of Notre Dame
    Title:A threshold phenomenon for independent sets in the hypercube
    Abstract: We show that an independent set drawn from the hypercube {0,1}^d according to the hard-core distribution exhibits a sharp transition around \lambda=1: for \lambda>1, almost surely the independent set is completely contained in one of the two partition classes of the cube, while for \lambda<1 almost surely it has exponentially many vertices from each of the partition classes.

  • Geoffrey Grimmett, University of Cambridge
    Title: Using sharp-threshold theorems in statistical mechanics
    Abstract: Sharp-threshold theorems of Kahn et al, and Talagrand, may be extended to probability measures satisfying the FKG lattice condition. They may be applied to random-cluster and Ising models, and maybe elsewhere...

  • Olle Haggstrom, Chalmers University of Technology
    Title: Random walk on a one-dimensional percolation cluster
    Abstract: Standard bond percolation on a one-dimensional periodic lattice fails, for any p<1, to have an infinite open cluster. Here we show how to make sense of conditioning on the existence of an open path from minus infinity to plus infinity. The resulting measure is translation invariant and exhibits a certain Markovian structure. The latter allows us to understand biased random walk on the infinite open cluster in some detail. This is joint work with Marina Axelson-Fisk.

  • Shlomo Havlin, Bar-Ilan University
    Title: Novel Percolation in Networks
    Abstract:TBA

  • Chris Jarzynski,University of Maryland
    Title: Fluctuation theorems, work relations, and the Arrow of Time
    Abstract:TBA

  • Rick Kenyon, Brown University
    Title: Dimers and Harnack Curves
    Abstract:TBA

  • Vladimir Korepin, Stony Brook University
    Title: Application of Fisher-Hartwig Formula to Quantum Spin Chains
    Abstract:Fisher-Hartwig formula describes asymptotic of determinant of large Toeplitz matrix. It was discovered in 1968 and published in Adv. Chem. Phys. It has multiple applications to physics and mathematics. I will describe how to use the formula for evaluation of entanglement entropy in the ground state of XY spin chain. It also can be used for calculation of time and temperature dependent correlation function. I argue that in the future the entanglement entropy and correlations can be calculated in XXZ spin chain, which is currently an open problem.

  • Arnie Levine, IAS
    Title: Evolutionary selection and counter selection in human genes involved in reproduction over the past 30,000 years
    Abstract:TBA

  • Elliott Lieb, Princeton University
    Title: A retrospective on rigorous results on the Bose gas
    Abstract:TBA

  • Andrea Liu, University of Pennsylvania
    Title: Jamming: How far have we come, and what still lies ahead?
    Abstract: TBA

  • Juan Maldacena, IAS
    Title: Black holes as source of information
    Abstract: The gauge/gravity duality implies a relation between the thermodynamic properties of certain strongly coupled theories and black hole solutions of suitable gravitational equations. We quickly review the nature of this relationship and mention some of the theories for which it applies. We describe how the black holes can be used for computing thermodynamic and transport properties in these systems.

  • Marc Mezard, CNRS and Universite Paris-Sud
    Title: Message passing strategies in physics and computer science
    Abstract:Message passing is a very useful framework for studying disordered systems with many interacting variables. The simplest message passing strategies have been discovered independently several times over the last 50 years, in communication theory, in statistical physics, in artificial intelligence,... They can be used both for practical algorithmic design, and for analytical work on phase diagrams and phase transitions. This talk will survey some of the recent progress in this field, with special emphasis on topics which are of common interest to physics and computer science

  • Thomas Natterman, University of Cologne, Institute for Theoretical Physics
    Coauthors: G.M. Falco and V.L. Pokrovsky
    Title:Localized states and interaction induced delocalization in Bose gases with quenched disorder
    Abstract:Very diluted Bose gas placed into a disordered environment falls into a fragmented localized state. At some critical density the repulsion between particles overcomes the disorder. The gas transits into a coherent superfluid state. In this talk the geometrical and energetic characteristics of the localized state at zero temperature and the critical density at which the quantum phase transition from the localized to the superfluid state proceeds are found. For atoms in traps four different regimes are found, only one of it is superfluid. The theory applies to lower 1 and 2 dimensions as well and allows semi-quantitative predictions that can be checked in experiments with ultracold atomic gases.

  • Mark Newman, University of Michigan
    Title:Random graphs as models of networks
    Abstract: The random graph, which is essentially a percolation model, is one of the oldest and best studied models of networks, and is attractive because it is exactly solvable for many of its properties, both local and global. Recently work on real-world networks such as the Internet, the web, and social networks, however, has revealed a variety of unexpected features that are quite unlike the features of random graphs. This talk will discuss recent work on extending exactly solvable random models of networks to include realistic representations of some of these features, including degree distributions, degree correlations, and directed and bipartite structure. I will also give some comparisons between the predictions of network models and empirical network measurements and show that in some cases the two are in surprisingly good agreement.

  • Jerome Percus, NYU Courant Institute
    Title: Classical fluid transport under molecular scale confinement
    Abstract: When particles cannot pass each other in a narrow tube, the iterated spatial restriction felt by a specified particle slows down its long time average motion: inertial dynamics becomes diffusive, diffusion becomes subdiffusive,... In the idealized point particle one-dimensional prototype, the unhindered spatial and temporal behavior of a classical particle is easily translated to its behavior in the full system, resulting in a long-time description which is stretched Markov both in space and time. Bulk properties are analogously described.

  • Yuval Peres, University of California, Berkeley
    Title: Internal DLA and the abelian sandpile
    Abstract:TBA

  • Dana Randall, Georgia Tech.
    Title: Mixing times of local Markov chains on biased lattice configurations
    Abstract:TBA

  • Sid Redner, Boston University
    Title: Consensus Formation on Simple and Complex Social Networks
    Abstract:TBA

  • Robert Seiringer, Princeton University
    Title: The Lieb-Liniger Model as a Limit of Dilute Bosons in Three Dimensions
    Abstract: We show that the Lieb-Liniger model for one-dimensional bosons with repulsive $\delta$-function interaction can be rigorously derived via a scaling limit from a dilute three-dimensional Bose gas with arbitrary repulsive interaction potential of finite scattering length. For this purpose, we give bounds on both the eigenvalues and corresponding eigenfunctions of three-dimensional bosons in strongly elongated traps and relate them to the corresponding quantities in the Lieb-Liniger model.

  • Jan Sengers, University of Maryland
    Title: Critical Phenomena in Macromolecular Solutions
    Abstract: During the past decade enormous progress has been made concerning our understanding of the behavior of fluids near critical points. The thermodynamic critical behavior of fluids satisfies scaling laws with critical exponents characteristic for the universality class of Ising-like systems, while the critical behavior of transport phenomena is described by the mode-coupling theory of critical dynamics. The present lecture will discuss in which ways the critical behavior of macromolecular solutions differs from that of molecular fluids. The differences are caused by a competition between the spatial range of the critical fluctuations and an additional mesoscopic length scale associated with the size of the macromolecules and by a competition between the decay time of the critical fluctuations and a viscoelastic relaxation time of the macromolecules. The effects of these competitions will be demonstrated on the basis of accurate static and dynamic light-scattering experiments pursued at the University of Maryland in collaboration with M.A. Anisimov and A.F. Kostko.

  • S. Shlosman, Centre de Physique Theorique
    Title: Gibbs ensemble of noninteresecting paths and determinantal processes
    Abstract: TBA

  • Boris Shraiman, University of California, Santa Barbara
    Title: Alleles versus genotypes: collective behavior of interacting genes in the presence of recombination
    Abstract:TBA

  • Vladas Sidoravicius, CWI-Amsterdam and IMPA-Rio de Janeiro
    Title: Recurrence of Markov chains and DLA type growth Abstract:I will discuss the DLA type growth with infinitely many particles simultaneously performing independent random walks and sticking to the growing aggregate at the moment of collision. The density of particles is the parameter of the model, and I will discuss how it influences the growth rate, geometric shape of the aggregate, and how it is related to ergodic properties of the system.

  • Yakov Sinai, Princeton University
    Title: Chaos: Yesterday, Today and Tomorrow
    Abstract:TBA

  • Alistair Sinclair,University of California, Berkeley
    Title:Mixing time for the solid-on-solid model
    Abstract: This talk concerns the mixing time of a natural local Markov chain (the Glauber dynamics) on configurations of the solid-on-solid model of statistical physics. This model has been proposed, among other things, as an idealization of the behavior of contours in the Ising model at low temperatures. Our main result is an upper bound on the mixing time of O~(n^{3.5}), which is tight within a factor of O~(\sqrt{n}). The proof also gives some insight into the actual evolution of the contours.
    Joint work with Fabio Martinelli.

  • Stanislav Smirnov, University of Geneva
    Title: 10 years of Schramm Loewner Evolution
    Abstract:TBA

  • Sara Solla, Northwestern University
    Title: Statistical physics, Bayesian inference, and neural information processing
    Abstract: The Gibbs ensemble allows us to compute a partition function by summing over all possible configurations of a set of degrees of freedom coupled through known interactions. A complementary approached, based on a partition function obtained by summing over all possible interactions compatible with observed or desired macroscopic properties, has provided a powerful tool for studying learning in adaptive systems. I will review the theoretical foundation of this approach and the thermodynamic theory of learning that it provides. I will then discuss the equivalence between this formulation and the Bayesian approach to statistical inference. Finally, I will present a recent application of these ideas to the problem of information processing in the brain.

  • Gregory Sorkin, IBM, Watson Research Center
    Title: The Power of Choice in a Generalized Plya Urn Model
    Abstract: We introduce a "Plya choice" urn model combining elements of the well known "power of two choices" model and the "rich get richer" model. From a set of $k$ urns, randomly choose $c$ distinct urns with probability proportional to the product of a power $\gamma>0$ of their occupancies, and increment one with the smallest occupancy. The model has an interesting phase transition. If $\gamma \leq 1$, the urn occupancies are asymptotically equal with probability 1. For $\gamma>1$, this still occurs with positive probability, but there is also positive probability that some urns get only finitely many balls while others get infinitely many.

  • Herbert Spohn, Universitat Munchen
    Title: Kinetics of the Bose-Einstein condensation
    Abstract: In the kinetic regime a weakly interacting Bose fluid is governed by the Boltzmann-Nordheim equation, which we discuss in case of a homogeneous fluid with an isotropic momentum distribution. In particular, the post-nucleation self-similar solution will be explained.

  • K.R. Sreenivasan,The Abdus Salam Inter. Centre for Theo. Physics
    Title: Hydrodynamic Turbulence
    Abstract:TBA

  • Gene Stanley, Boston University
    Title: Liquid Water: New Results in Bulk, Nanoconfined, and Biological Environments
    Abstract: This talk will introduce some of the 63 anomalies of the most complex of liquids, water. We will demonstrate some recent progress in understanding these anomalies by combining information provided by recent experiments and simulations on water in bulk, nanoconfined, and biological environments. We will interpret evidence from recent experiments designed to test the hypothesis that liquid water may display "polymorphism" in that it can exist in two different phases -- and discuss recent work on water's transport anomalies [1] as well as the unusual behavior of water in biological environments [2]. Finally, we will discuss how the general concept of liquid polymorphism [3] is proving useful in understanding anomalies in other liquids, such as silicon, silica, and carbon, as well as metallic glasses, which have in common that they are characterized by two characteristic length scales in their interactions.
      [1] P. Kumar, S. V. Buldyrev, S. L. Becker, P. H. Poole, F. W. Starr, and H. E. Stanley, "Relation between the Widom line and the Breakdown of the Stokes-Einstein Relation in Supercooled Water," Proc. Natl. Acad. Sci. USA 104, 9575-9579 (2007).
      [2] P. Kumar, Z. Yan, L. Xu, M. G. Mazza, S. V. Buldyrev, S.-H. Chen. S. Sastry, and H. E. Stanley, "Glass Transition in Biomolecules and the Liquid-Liquid Critical Point of Water," Phys. Rev. Lett. 97, 177802 (2006).
      [3] H. E. Stanley, ed., LIQUID POLYMORPHISM [Advances in Chemical Physics], series edited by S. A. Rice (Wiley, New York, 2008).


  • Jeff Steif, Chalmers University of Technology
    Title: Stochstic domination and the Ising model
    Abstract: (1). We show that the plus and minus states for the Ising model on Zd dominate the same set of product measures. We show that this latter fact however completely fails on the homogenous 3-ary tree. (2). While it is known that the plus states for different temperatures on Zd are never stochastically ordered, on the homogenous 3-ary tree, almost the complete opposite is the case. (3). On Zd, the set of product measures which the plus state for the Ising model dominates is strictly decreasing in the interaction parameter. (4). An FKG exchangeable finite process dominates a product measure if and only the relevant inequality holds for the event of all 0's. (5). Extending these results to an amenable/nonamenable dichotomy would be interesting. This is based on joint work with Tom Liggett.

  • Edriss Titi, Weizmann Institite of Science & University of California, Irvine
    Title:Recent Advances in the Three-dimensional Navier-Stokes Equations, Geophysical and Turbulence Models
    Abstract:In this talk I will survey some of recent development on the question of global regularity of the three-dimensional Navier-Stokes equations, and some relevant geophysical and turbulence models.

  • R.J. van den Berg, Centrum Wiskunde & Informatica
    Title: Connections between 2D invasion and critical percolation
    Abstract:TBA

  • Srinivasan Varadhan, New York University, Courant Institute
    Title: Scaling Limits of Large Systems: Past, Present and Future
    Abstract:TBA

  • Ben Widom, Cornell University
    Title: Critical points on the surfaces and lines at which phases meet
    Abstract:TBA

  • Harold Widom,University of California, Santa Cruz
    Title: Formulas and Asymptotics for the Asymmetric Simple Exclusion Process
    Abstract: In joint work with Craig A. Tracy we consider the asymmetric simple exclusion process on the integers. For a finite system we use the Bethe Ansatz to obtain a formula for the probability of a given configuration at time t. From this we derive a formula, which extends to some infinite systems, for the probability distribution for the position of a given particle at time t. In the case of step initial condition (particles initially at the positive integers) the probability can be expressed in terms of Fredholm determinants. Asymptotic results are obtained using this representation.

  • Julia Yeomans, The Rudolf Peierls Centre for Theoretical Physics
    Coauthors:G. Alexander and C. Pooley
    Title: Hydrodynamic Interactions Between Microswimmers
    Abstract:Because of their size bacteria and fabricated microswimmers swim at low Reynolds number, a regime where the effect of hydrodynamic interactions can be appreciable and counterintuitive.

    We present our recent results on the hydrodynamic interactions experienced by two simple linked-sphere model microswimmers, focusing on side-by-side swimming and scattering events. We describe how the interactions depend on not only on the relative position and orientation, but also on the relative phase of the two swimmers. We show that the symmetry under time reversal of the Stokes equations leads to exact statements about the scattering of certain swimmers. Finally, we describe the collective properties of a suspension of hydrodynamically interacting dumb-bells, which provides a simple model of active apolar fluids.

  • Emil Yuzbashyan, Rutgers University
    Title: The Link between Integrability, Level Crossings, and Exact Solution in Quantum Models
    Coauthors: H. K. Owusu and K. Wagh
    Abstract:TBA

  • Royce Zia, Virginia Tech
    Title: Twenty five years after KLS: A celebration of non-equilibrium statistical mechanics
    Abstract:When Lenz proposed a simple model for phase transitions in magnetism, he couldn't have imagined that the "Ising model" was to become a crown jewel in field of equilibrium statistical mechanics. Its role spans the spectrum, from a good pedagogical example to a universality class in critical phenomena. A quarter century ago, Katz, Lebowitz and Spohn found a similar treasure. By introducing a seemingly trivial modification to the Ising lattice gas, they took it into the vast realms of non-equilibrium statistical mechanics. An abundant variety of unexpected behavior emerged and caught many of us by surprise. I will attempt to review what lessons we have learned, to enumerate some of the outstanding puzzles, and to speculate on what other surprises might be lying in waiting.