Statistical Mechanics Conference
91st Statistical Mechanics Conference
Sunday, May 16, 2004 at 08:00am -
Conference Program
SUNDAY, MAY 16, 2004
8:00 - 9:00 - Breakfast and Registration
9:00 - 9:20
C.K. Hu, Academia Sinica,
Exact Finite-Size Corrections for Critical Ising and Dimer Models
9:20 - 9:40
F. Stillinger, Princeton University,
Pair Correlation Function Realizability Problems
9:40 - 10:00
S. Torquato, Princeton University,
Local Density Fluctuations, Hyperuniformity, and Order Metrics
10:00 - 10:20
P. Debenedetti, Princeton University,
Energy Landscape Statistics
10:20 - 10:50 - Coffee
10:50 - 11:10
G. Slade, University of British Columbia,
Phase Transition in High-Dimensional Networks
11:10 - 11:30
S. Havlin, Bar Ilan University,
Structure and Stability of Complex Networks
11:30 - 11:50
M. Newman, University of Michigan,
The Statistical Mechanics of Networks
11:50 - 12:10
S. Solla, Northwestern University,
Self-Sustained Activity and Failure in a Small-World Network of Excitable Neurons
12:10 - 12:30
R. da Silveira, Harvard University,
Minimal Paths in a Model Cortex
12:30 - 2:00 Lunch
2:00 - 2:20
Y. Sinai, Princeton University,
New Results from Mathematical Hydrodynamics
2:20 - 2:40
C. Newman, NYU/Courant Institute,
The Full Scaling Limit of 2D Critical Percolation
2:40 - 3:00
L. Blum, University of Puerto Rico,
Analytical Theory of Liquid Water: A Phase Transition with Potential Interest in Biology
3:00 - 3:20
J.D. Weeks, University of Maryland,
Screeing, Structure, and Simulations of Ionic Fluids
3:20 - 4:00
D. Chandler, University of California, Berkeley,
Geometry and Dynamic Scaling of Structural Glass Formers
4:00 - 4:30 - Coffee
4:30 - 4:50
M. Magnasco, Rockefeller University,
Virtual Gating in the Nuclear Pore Complex
4:50 - 5:10
A. Sengupta, Rutgers University,
Specificity of Protein-DNA Interaction in Transcription Control: Physics, Evolution and Bioinformatics
5:10 - 5:50
D. Fisher, Harvard University,
Evolution: Is ANYTHING Understood Quantitatively?
6:00
COCKTAIL PARTY
7:00
PIANO RECITAL BY RENANA GUTTMAN
Bach, Janacek, Chopin
THE COCKTAIL PARTY AND CONCERT ARE SPONSORED BY KLUWER ACADEMIC/PLENUM, PUBLISHERS OF THE JOURNAL OF STATISTICAL PHYSICS
ALL ARE INVITED
8:00
BANQUET DINNER (Reservations Required)
Please join us at the banquet to toast the following birthdays:
Douglas Abraham, David Chandler and John Weeks - sixty
Lesser Blum and Frank Stillinger - seventy
MONDAY, MAY 17, 2004
8:00 - 8:30 - Breakfast and Registration
8:30 - 9:30
SHORT TALKS, SESSION A
9:30 - 9:50
D. Vanderbilt, Rutgers University,
Electronic Structure of an Insulator in a Finite Electric Field: What to Do When There Is No Ground State
9:50 - 10:10
S. Sachdev, Yale University,
Breakdown of the Landau-Ginzburg-Wilson Paradigm at Quantum Phase Transitions
10:10 - 10:30
T. Senthil, MIT,
Deconfined Quantum Criticality
10:30 - 11:00 - Coffee
11:00 - 11:40
A. Libchaber, Rockefeller University,
Techniques from Physics, Problems from Biology
11:40 - 12:30
Human Rights and Social Responsibilities of Scientists
E. Chudnovsky, J. L. Lebowitz and others
12:30 - 1:50 - Lunch
1:50 - 2:30
R. W. Kenyon, Princeton University,
Limit Shapes and Fluctuations of Crystalline Surfaces
2:30 - 2:50
V.B. Priezzhev, Joint Institute for Nuclear Research, Russia,
Exact Nonstationary Probabilities in the Asymmetric Exclusion Process on a Ring
2:50 - 3:10
P. Chandra, Rutgers University,
Relaxation in a Simple Spin System
3:10 - 3:30
A. Neimark, TRI/Princeton,
Phase Transitions and Nucleation in Finite Volumes
3:30 - 4:00 - Coffee
4:00 - 4:20
C. Marchetti, Syracuse University,
Hydrodynamic Instabilities in Motor-Microtubules Mixtures
4:20 - 4:40
M. Shelley, NYU/Courant,
Locomotion by Destabilizing Symmetries
4:40 - 5:20
E. Siggia, Rockefeller University,
Evolution and Development: What can Physics Contribute
5:20 - 6:00
W. Bialek, Princeton University,
Which Bits Does the Brain Use?
6:00 - 7:55 - Cocktails and Dinner
7:55 - 8:35
S. Leibler, Rockefeller University,
On Cellular Switches, Gates and Clocks
8:35 -
What Can Statistical Mechanics Do for Biology? A Discussion.
M. E. Fisher, Chair. Participants include: B. Bialek, D. Fisher, J. L. Lebowitz, E. Siggia and others.
TUESDAY, MAY 18, 2004
8:00 - 8:30 - Breakfast and Registration
8:30 - 10:00
SHORT TALKS, SESSION B
10:00 - 10:40
G. Lawler, Cornell University,
Brownian Loops and Central Charge
10:40 - 11:00 - Coffee
11:00 - 11:20
S. Redner, Boston University,
Dynamics of Consensus and Contention in Interacting Spin Systems
11:20 - 11:40
G. Forgacs, University of Missouri,
Directing the Sell-Assembly of Cells and Tissues Into Organ Modules by Exploiting Their Physical Properties
11:40 - 12:00
E. Sontag, Rutgers University,
Interconnections of Monotone Systems with Steady-State Characteristics, and Multi-stability of Biochemical Systems
12:00 - 1:20 - Lunch
1:20 - 1:40
L. Berlyand , Penn State,
Ginzburg-Landau Minimizers with Prescribed Degrees in Perforated Domains. Capacity of the Domain and Emergence of Vortices
1:40 - 2:00
I. V. Lebed, Central Aero Hydrodynamic Institute, Russia
The Pair Functions Theory in Hydrodynamics
2:00 - 2:20
J. Wang, SUNY at Stony Brook/Citigroup,
Energy Landscape and Specificity of Biomolecular Bindings
2:20 - 2:40
D. Saakian, Institute of Physics, Academica Sinica, Taiwan and Yerevan Physics Institute, Armenia.
Exact Solution of Eigen Model of Evolution
2:40 - 2:55 - Coffee
2:55 - SHORT TALKS, SESSION C
Statistical Mechanics Conference, May 16-18, 2004
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L. Berlyand, Penn State University Title: "Ginzburg-Landau Minimizers with Prescribed Degrees in Perforated Domains. Capacity of the Domain and Emergence of Vortices" Abstract: Please click here. |
G.L. Celardo, University of Milan and Catholic University of Brescia Title: "Broken Ergodicity and Phase Transitions in Classical and Quantum Systems with Long-Range Interaction" Abstract: A one dimensional classically chaotic spin chain with asymmetric coupling and two different inter-spin interactions, nearest neighbors and all-to-all, has been considered. Depending on the interaction range, dynamical properties, as ergodicity and chaoticity are strongly different. Indeed, even in presence of chaoticity, the model displays a lack of ergodicity only in presence of all to all interaction and below an energy threshold, that persists in the thermodynamical limit. Energy threshold can be found analytically and results can be generalized for a generic XY model with asymmetric coupling. We analyze the conseguences of this broken ergodicity with respect to phase transitions, in both the classical and quantum case. |
G. Forgacs, University of Missouri Title: "Directing the Self-Assembly of Cells and Tissues Into Organ Modules by Exploiting Their Physical Properties" Abstract: I will illustrate how functional organ modules of prescribed shape can be constructed by rapid prototyping (i.e. printing) using special delivery devices and spherical cellular aggregates of appropriate composition as bio-ink particles. I will also discuss the biophysical basis of this technology by modeling the process and show the strong similarity between the experimental and model realization of tubular tissue structures. |
A. Kazarnovskii-Krol, Yale University Title: "Conjectural Hypegeometric Series for Three-Body Calogero-Sutherland Model/Hypergeometric Functions Associated to Root System of Type A2 and Products Over Positive Roots" Abstract: In this talk I'll present very nice conjectural hypergeometric series for three-body Calogero-Sutherland model/ hypergeometric functions associated to root system of type A2 and discuss their applications. |
R. Kenyon, Princeton University Title: "Limit Shapes and Fluctuations of Crystalline Surfaces" Abstract: For simple models of random crystalline surfaces such as those arising in the 3D Ising model at very low temperature, we show that the scaling limit shapes are defined by integrable nonlinear PDEs resembling the complex Burger's equation. We also discuss the (zero temperature) fluctuations of the limit shapes which are proved to be Gaussian. |
S. Kiselev, Colorado School of Mines Title: A Simplified Crossover Droplet Model for Adsorption of Pure Fluids in Slit Pores" Abstract: Please click here. |
I. Lebed, Central Aero Hydrodynamic Institute, Russia Title: "The Pair Functions Theory in Hydrodynamics" Abstract: Direct numerical integration of the Navier-Stokes equations for unstable flows have become possible as late as in recent years owing to a rapid development of the computer technology. A detailed comparison of the numerical and experimental results for a sphere in a free-stream flow reveals that the calculated turbulence development pattern fails to agree with visualized pattern without shadow of doubt [1]. This suggest the necessity of consideration with due attention the pair functions theory. Contrary to the derivation of the classical kinetics and the classical hydrodynamics equations both the hypothesis of molecular chaos "Stossszahlansatz" and any auxilary assumptions are not used when deriving the equations for pair functions. Within the frameworks of the pair functions theory clasiical Boltzmann algorithm for drawing up a balance of individual particles is abandoned in favor of algorithm for drawing up a balance of specially composed pairs of particles. Derived equations for pair functions were used in problem on flow around a solid sphere [2]. The success of the pair functions equations in this problem allows to conclude that the Navier-Stokes equations are not applicable to interpreting the turbulence. 1). I.V.Lebed Physica A 2002,v.315,p.228 2). I.V.Lebed Chem.Phys.Reports 1997,V.16,p.1263; 1998,V.17,p.411 |
N. Lehman, University of Duisburg-Essen Title: "Exact Eigenvalue Density of Complex Wishart Matrices" Abstract Using the supersymmetry method I calculate the exact expression for Green s function in the ensemble of complex Hermitian Wishart matrices. The eigenvalue density in this and derived ensembles can be inferred. |
A. Libchaber, Rockefeller University Title: "Techniques from Physics, Problems from Biology'" Abstract: I will present shortly three themes: Optical resonances for DNA hybridization Thermal convection for a hypothesis on the origin of life Quantum dots for developmental biology. |
V. Los, Ukranian/American Center for Excellence in Information Technology Title: "Homogeneous Generalized Master Equations" Abstract: Using the method, based on the projection operator technique, the conventional exact inhomogeneous time-convolution and time-convolutionless (time local) generalized master equations (TC-GME and TCL-GME) for a distribution function (statistical operator) have been turned into the exact homogeneous generalized master equations (TC-HGME and TCL-HGME). The irrelevant initial condition (inhomogeneous) terms in the GMEs caused by the correlations at an initial state of the whole system, have been transferred to the (mass) operator governing the evolution of the relevant part of a distribution function (statistical operator). The obtained TC-HGME and TCL-HGME are exact and, therefore, no information has been lost at such a transformation. No approximation like the Bogolubov principle of weakening of initial correlations or random phase approximation (RPA) has been used in order to obtain the HGMEs. The influence of initial correlations on the time-evolution of the (sub)system of interest (e.g. an open quantum system interacting with a reservoir) is treated by these equations consistently with the collisions by means of the modified (mass) operator acting on the relevant part of a distribution function (statistical operator) and including additional terms related to the initial correlations. The obtained HGMEs are valid on any timescale, for any initial moment of time and any initial correlations. In particular, they describe the short-time behaviour including the initial stage of the evolution, when the initial correlations may matter and which may be necessary to properly describe, e.g., the effects of interaction of the condensed matter systems with the ultra-short (femtosecond) laser pulses. The TC-HGME was applied in [1] to the case of a dilute gas of classical particles and the homogeneous equation for a one-particle distribution function retaining initial correlations was obtained in the linear approximation on the small density parameter and for the space homogeneous case. This equation allows for considering the dilute classical gas evolution at all times and converts into the conventional Boltzmann equation on the appropriate timescale if all initial correlations vanish on this timescale. The time-convolution quantum HGME has also been applied to the case of space homogeneous gas of quantum particles, and the homogeneous quantum equation retaining initial correlations for the one-particle density matrix (momentum distribution function) has been derived. This equation describes the evolution process at all times and includes both the quantum initial correlations and initial correlations caused by interaction between particles. The conditions for converting this equation into the conventional quantum kinetic equation are considered. References [1]. V. F. Los, J. Phys. A: Math. Gen., 34 (2001) 6389. |
D. Lubensky, Rutgers University Title: "How to Make a Neurocrystal: The Developmental Patterning of the Fly's Retina" Abstract: A number of steps in the development of higher organisms require the generation of a periodic pattern of cell fates. One of the best studied and most remarkable examples of such a process occurs in the development of the compound eye of the fruit fly, where a hexagonal lattice of photoreceptors is specified from an initially undifferentiated sheet of cells. After reviewing the known genetic interactions in this system, I will argue that they can be modelled by a system of reaction-diffusion equations. These equations capture many of the observed features of the patterning process and make predictions about when the patterning should fail as parameters are varied in recombinant flies. |
P. Maas, Technische Universitaet Ilmenau, Institute of Physics, Germany Title: "Markovian Approach to Density Functionals" Abstract: I discuss a general method for deriving exact density functionals with finite-range pairwise interactions in one dimension. This method is based on a generalized Markov property, which allows one to set up a rather transparent scheme that covers all previously known exact functionals for lattice gas or fluid systems. Corresponding continuum functionals are derived by applying a proper limiting procedure. A generalization to higher dimensions yields approximate functionals that by construction reduce to the exact ones upon dimensional reduction. |
Hildegard Meyer-Ortmanns, University of Bremen Title: "Proposal of a Complexity Measure for Networks" Abstract: We propose a complexity measure which addresses the functional flexibility of networks. It is conjectured that the functional flexibility is reflected in a specific topological "diversity" of the assigned graphs, resulting from a resolution of their vertices and a rewiring of their edges under certain constraints. The application will be a classification of networks in artificial or biological systems, where functionality plays a central role. |
M. Mounsef, University of Bourgogne Title: "Estimation of the Spectral Density" Abstract: In this work, we are interested in the theoretical aspet of the estimate of the spectral density of a dynamic process under the assumption of the topological mixture. Initially we give an estimator to core by using the periodogram, but this estimator is inconsistent, from where the smooting of the periodogram with a spectral window. In second time, using the exponential inequality, we show the convergence almost sure of this estimator. |
M. Porter, Georgia Institute of Technology Title: "Bose-Einstein Condensates in Optical Lattices and Superlattices" Abstract: Bose-Einstein condensates (BECs), whose existence was predicted in 1924 by Einstein and Bose, were discovered experimentally in 1995 using dilute vapors of sodium and rubidium. Their dynamics at zero temperature is modeled by the Gross-Pitaevksii equation. When loaded into an optical lattice or superlattice, BECs exhibit a band structure (spatial resonance structure). In this talk, I will overview recent results describing the wave functions of BECs in lattice and superlattice potentials. I will consider both localized and spatially extended solutions. |
M. Planat, Laboratoire de Physique et MÈtrologie des Oscillateurs du CNRS Title: "Time Perception, the Quantum Phase and the Cyclotomic Field" Abstract: I develop the idea that time perception is the quantum counterpart to time measurement. Phase-locking and prime number theory were proposed as the unifying concepts for understanding the optimal synchronization of clocks and their 1/f frequency noise. Time perception is shown to depend on the thermodynamics of a quantum algebra of number and phase operators already proposed for quantum computational tasks, and to evolve according to a Hamiltonian mimicking Fechner's law. The mathematics is Bost and Connes quantum model for prime numbers. The picture that emerges is a unique perception state above a critical temperature and plenty of them allowed below, which are parametrized by the symmetry group for the primitive roots of unity. Squeezing of phase fluctuations close to the phase transition temperature may play a role in memory encoding and conscious activity. Text: quant-ph/0403020 |
V.B.Priezzhev, Joint Institute for Nuclear Research, Russia Title: "Exact Nonstationary Probabilities in the Asymmetric Exclusion Process on a Ring" Abstract: The complete solution of the master equation for a system of interacting particles of finite density is presented. By using a new form of the Bethe ansatz, the totally asymmetric exclusion process on a ring is solved for arbitrary initial conditions and time intervals. |
D.B. Saakian & C.K. Hu, Institute of Physics, Academica Sinica,Taiwan, and Yerevan Physics Institute, Armenia. Title: Exact Solution of Evolution Models Abstract: We map Eigen model of biological evolution [Naturwissenschaften 58, 465 (1971)] into a quantum spin model with non-Hermitean Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We solve exactly the dynamics of the parallel mutation- selection model of evolution by Kimura for the case of single peak fitness landscape (using the mapping of the model to quantum spin statistical mechanics by Baake and co-authors). In contrary to widely accepted opinion among biologists, two schemes of mutation- selection (Eigen model like and Kimura one like) have different relaxation periods even at low mutation rates, for the larger mutation schemes the difference is drastical (Kimura scheme relaxes exponentially faster). An exact solution of the problem by means of statistical mechanics reveals an important effect, missed during the approximate (numerical investigation. |
S. Sachdev, Yale University Title: "Breakdown of the Landau-Ginzburg-Wilson Paradigm at Quantum Phase Transitons" Abstract: I will introduce the theory of quantum phase transitions of Mott insulators between antiferromagnetically ordered and paramagnetic states in spatial dimensions greater than one. For Mott insulators with an even number of S=1/2 spins per unit cell, the Landau-Ginzburg-Wilson (LGW) theory for the destruction of magnetic order agrees well with numerical and experimental studies. However, for Mott insulators with an odd number of S=1/2 spins per unit cell the situation is much more subtle. We argue that the spin Berry phases lead to spontaneous bond order in the paramagnet. Although the bond-ordered state has only conventional lattice-symmetry-breaking order and integer spin excitations, it cannot be understood within the LGW theory of the magnetic order. The phases with magnetic and bond order are separated by a second order quantum critical point, which also contradicts LGW theory. A theory for this novel critical point is presented in the talk by T. Senthil. |
S. Sen, SUNY at Buffalo Title: "Long Time Dynamics of Nonlinear Chains: The New "Quasi-Equilibrium" Phase" Abstract: The work I would like to talk about involves the fate of solitary and antisolitary waves in the long time limit of 1D chains (not in the thermodynamic limit)with purely nonlinear interactions. We argue that these systems show a novel equilibrium like phase where no memory of initial condtions is retained, Maxwellian velocity distribution is achieved, and yet there is no eenergy equipartition. Research supported by NSF |
T. Senthil, MIT Title: "Deconfined Quantum Criticality" Abstract: Following up on the previous talk by S. Sachdev, we consider the zero temperature transition between Neel and valence bond solid phases of spin-1/2 quantum antiferromagnets in two dimensions. Despite the very different broken symmetries in the two phases we show that a generic second order transition is possible. The corresponding critical theory is unusual and is not simply expressed in terms of the natural order parameters of either phase. Rather it involves new `fractionalized' degrees of freedom that are specific to the critical point and are absent (i.e confined) in either phase. These fractional particles interact with an emergent gauge field that is `deconfined' in a precise sense that will be explained. Physical consequences and implications of this unusual kind of criticality will be discussed. |
G. Slade, University of British Columbia Title: "Phase Transition in High-Dimensional Networks" Abstract: It has been known since the work of Erdos and Renyi that random subgraphs of the complete graph undergo a phase transition, with a low density phase with small connected components and a high density phase with a giant component. We formulate a condition for a general transitive graph which implies that its phase transition obeys the same scaling observed by Erdos and Renyi, and we verify the condition for several high-dimensional graphs including the n-cube {0,1}n. This is joint work with Christian Borgs, Jennifer Chayes, Remco van der Hofstad and Joel Spencer. |
S. Solla, Northwestern University Title: "Self-Sustained Activity and Failure in a Small-World Network of Excitable Neurons", by Alex Roxin, Hermann Riecke, and SARA A. SOLLA Abstract: We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities p of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief transient followed by failure. Averages over the quenched ensemble reveal that the probability of failure changes from 0 to 1 over a narrow range in p; this failure transition can be described analytically through an extension of an existing mean-field description of the topology of small-world networks. At higher densities p, long transients of activity emerge; their patterns are disordered, in contrast to the mostly periodic persistent patterns observed at low p. The times at which such patterns die out follow a stretched-exponential distribution, which depends sensitively on the propagation velocity of the excitation. |
E. Sontag, Rutgers University Title: "Interconnections of Monotone Systems with Steady-State Characteristics" Abstract: One of the key ideas in control theory is that of viewing a complex dynamical system as an interconnection of simpler subsystems, thus deriving conclusions regarding the complete system from the properties of its building blocks. Following this paradigm, and originally motivated by questions in cell signal transduction modeling, we recently developed with D. Angeli an approach based on components which are monotone systems with respect to partial orders in state and signal spaces and have well-defined steady-state characteristics. The talk will present a brief exposition of recent results, with an emphasis on small gain theorems for negative feedback and on the emergence of multi-stability and associated hysteresis effects under positive feedback. We will also explain how one would apply these theorems in practical experimental situations, as discussed in our recent work with J. Ferrell. |
S. Todadri, MIT Title: "Deconfined Quantum Criticality" Abstract: Following up on the previous talk by S. Sachdev, we consider the zero temperature transition between Neel and valence bond solid phases of spin-1/2 quantum antiferromagnets in two dimensions. Despite the very different broken symmetries in the two phases we show that a generic second order transition is possible. The corresponding critical theory is unusual and is not simply expressed in terms of the natural order parameters of either phase. Rather it involves new `fractionalized' degrees of freedom that are specific to the critical point and are absent (i.e confined) in either phase. These fractional particles interact with an emergent gauge field that is `deconfined' in a precise sense that will be explained. Physical consequences and implications of this unusual kind of criticality will be discussed. |
D. Vanderbilt, Rutgers University Title: "Electronic Structure of an Insulator in a Finite Electric Field: What to Do When There Is No Ground State" Abstract: I will discuss two related problems: (i) how to compute the electric polarization of a (non-centrosymmetric) crystalline insulator, even in zero electric field; and (ii) how to compute the properties of a crystalline insulator in a finite homogeneous electric field. It might be thought that both of these problems should have standard textbook solutions, but in fact it is only in the last few years that these two problems have been adequately resolved. The electric-field problem is quite subtle because even for a small field, the Hamiltonian eigenstates lose their Bloch symmetry, the potential energy for the electrons is not bounded from below, and there is no ground state. I will give a flavor of recent developments, showing how a Berry phase figures prominently in the solution to (i), and explaining how the solution to (i) also provides the solution to (ii). |
J. Wang, SUNY at Stony Brook Title: "Energy Landscape and Specificity of Biomolecular Bindings" Abstract: Biomolecular recognition is one of the most important problems in molecular biology. There are two important issues involved, one is the affinity measuring the degree of association and the other is the specificity measuring the discrimination of one with the other. In this study, we establish an energy landscape description of binding, and quantify the specificity. We found that the specifity is closely related to the key parameters describing the shape of the underling landscape. Further more, high specificity leads to both thermodynamic stability and discrimination as well as faster kinetics. |