# Statistical Physics

Statistical Physics deals with analyzing the effects of fluctuations of systems. It provides the major tools used to bridge the gap between the microscopic world described by classical and quantum mechanics and the macroscopic behavior of many particle systems. As such, it is the theoretical basis not only of equilibrium thermodynamics, its first major application, but also deals with fluctuations of systems far out of equilibrium. Statisical physicsis a powerful tool describing vast phenomena ranging from gases, liquids, solids, to phase transitions, transport and diffusion processes, Bose and Fermi statistics and much more.A major theme underlying much of modern statistical physics is that of scaling, along with such ancillary topics as fractals and power-law distributions.

Two major current applications where fluctuations play an essential role are communications, where noise needs to be filtered out to allow successful data transfers, and biology, where the small scales involved imply that significant fluctuations are often inescapable. Another major research focus, which cuts across many subdisciplines, is the study of random networks, whether of Internet connections, electricity distribution networks, or infection transmission pathways.

Prof. Kanter's group focuses mainly on theoretical and experimental properties of synchronization and their application to problems in communication, information theory and brain modes of activity. They study issues of error correction and data compression using deep analogies to the fundamental laws of thermodynamics as well as the properties of interacting spin systems. Another recent direction is the efficient production of ultra-high speed random number streams based on chaotic lasers, so crucial in modern data security protocols. In addition they also study the synchronization properties of networks of coupled lasers with an eye to applications of public channel cryptography. Very recently synthetic reverberating activity patterns embedded in neural networks were analyzed theoretically andin a spontaneously active network of cortical cells in-vitro.

Prof. Rabin's group works at the interface of polymer physics and biology, with focus on the most important polymer of all, DNA. They analyze the mechanical and topological properties of these polymers and the effect of these properties on the binding of proteins. One major interest is the passage of polymers through nanopores, whether natural (as in cell membrane channels) or artificial (proposed as a method of DNA sequencing). Another is the study of self-assembled DNA monolayers on solid surfaces. Yet another area of study deals with "hairy" (i.e., protein-coated) nanopores, both synthetic and natural (the nuclear pore complex). Prof. Rabin also studies the structure and dynamics of intra-nuclear chromatin (DNA-protein complex). Finally, the group is working on materials science related problems such as phase transitions in polymer gels.

A major focus of Prof. Havlin's group is the properties of random networks, especially scale-free networks where various nodes have a wide distribution of outgoing or incoming links. The applications span a wide range of problems, from computer virus transmission to climate to economics. A recent new direction is the study of the effects of failures in one network, say the electricity network, on other networks, such as the telephone network, and the backreaction on the original network. These works build on the basic physics of the percolation phase transition as the number of links in a network increase.

Prof. Barkai and his group focus on problems related to anomalous diffusion, generalizing the classic case of Brownian motion with the toolbox of the fractional calculus, involving derivatives of non-integer order. In anomalous diffusion, the spreading of a spatial distribution differs from the classical sqrt(t) behavior. They study the implications of this for such fundamental issues as ergodicity breaking, where time averages do not reproduce ensemble averages, and aging, where the system does not forget its initial state. Among the physical systems they study are the blinking of quantum dots, the diffusion of cold atoms in atomic traps, Levy flights for light in a fractal glass and the diffusion of single molecules within a cell. Barkai's group also investigates the relation between weak chaos, i.e. deterministic dynamics with zero Lyapunov exponents which still appears random, infinite invariant measures and weak ergodicity breaking.

The group of Prof. Shnerb deals with varied problems in population dynamics. One principle application is in ecology, trying to use statistical measures of the spatial distributions of trees in a forest to uncover the underlying dynamical processes. The question of the relative weight of deterministic (fitness) effects versus stochastic effects is also of prime concern. Yet another focus is on using genomic data to determine the dynamics of a population over time. The group also studies the role of diffusion in shielding a population from possible extinction due to random fluctuations.

Prof. Gitterman studies the phenomenon of stochastic resonance, wherein an increase in the "noise" results in a larger signal. He works on trying to understand the essential features of this phenomon, which has been encountered in many different physical situations, including the neural tissue of the sensory systems in various organisms. For example, he has shown that various aspects which have been thought to be essential to see stochastic resonance, for example nonlinearity, are not in fact crucial.

Prof. Gitterman also studies various other extensions of simple Brownian motion, stochastic resonance being related to a variable frequency of oscillation. One extension is where the particle has a fluctuating mass, due to the attachment and disattachment of particles from the surrounding medium. Another is where the damping is a fluctuating variable.

Prof. Kessler and his group study a wide range of problems. One area is the role of noise in the functioning of biological systems, particularly in the sensing of external signals. Another question is the optimal strategy for dispersal of a population, where the intrinsic fluctuations of a population (so-called demographic noise) are a key factor. This ties into general questons of the statistics of diversity in a growing population. The modelling of biological evolution is a key concern. The diffusive behavior of cold atoms in an optical lattice is another problem of interest.

Prof. Rapaport and his group are involved in projects that include molecular dynamics simulation of complex fluids and hydrodynamic instabilities, computer modeling of supramolecular and surfactant self-assembly, simulation of granular flow phenomena and segregation, general simulation methodology, algorithm design for advanced computers (including GPUs), and interactive simulation with animated computer graphics.

Dr. Sloutskin's group studies experimentally the properties of aggregating colloids, micron-sized particles suspended in a fluid. The interactions between the particles can be tuned by adjusting the chemical composition both of the colloidal particles and of the solvent. The process is studied using confocal microscopy, giving a real-time visualization in three spatial dimensions. The ultimate goal is to understand the connection between the microscopic properties of the system, e.g. the interactions, shape of the colloidal particles, the colloid density, and the macroscopic properties of the aggregate.

Prof. Taitelbaum and his group experimentally study the statistical properties of the reactive wetting interface that is formed when a drop of mercury is placed upon a silver substrate. The behavior of the front is monitored in real time with a microscope. In particular, they study the scaling of the interfacial roughness over different lengthscales and the persistence behavior, a measure of how long-lived fluctuations of a given sign are at a particular point on the interface.