Statistical Mechanics Seminar, P. Kleban, "Crossing probabilities, their densities, and modular forms"
Wed, Dec 14, 2011, 2:00 pm – 3:30 pm
Abstract: A crossing probability is the probability of finding a critical cluster that touches specified boundary arcs. We consider formulas for the prototypical example, the horizontal crossing probability Ph, which gives the probability of connecting the left and right sides of a rectangle containing a system at the two-dimensional…
Statistical Mechanics Seminar, V. Mastropietro, "Universal conductivity in graphene; some rigorous results and open problems"
Wed, Dec 7, 2011, 2:00 pm – 3:30 pm
Abstract: Recent experiments have found an universal value for the dynamic conductivity in graphene, fully confirming theoretical predictions based on a non interacting tight binding model. This however poses a problem since one could expect a many body renormalization of the non interacting value of the conductivity due to the interaction. In…
CANCELED Statistical Mechanics Seminar, J Yngvason, "Interacting Bosons in Random Potentials Interacting Bosons in"
Wed, Nov 30, 2011, 2:00 pm – 3:30 pm
Abstract: : In contrast to the cases of single particle Schrödinger operators and ideal Bose gases the effects of random external potentials on many-body systems of interacting particles is still poorly understood. In the lecture the effects of random scatterers on the ground state of the one-dimensional Lieb-Liniger model of interacting…
Statistical Mechanics Seminar, M. Lewin, "The thermodynamic limit of disordered quantum Coulomb systems"
Wed, Nov 23, 2011, 2:00 pm – 3:30 pm
Abstract: In this talk I will explain how to prove the existence of the thermodynamic limit for a many-body quantum crystal in which the electrons are quantum and the nuclei are classical point particles, with disordered charges and locations around a lattice. This is a collaboration with Xavier Blanc, based on previous work with Christian…
Statistical Mechanics Seminar, Rupert Frank, "A microscopic derivation of Ginzburg-Landau theory of superconductivity"
Wed, Nov 16, 2011, 2:00 pm – 3:30 pm
Abstract: We describe the first rigorous derivation of the celebrated Ginzburg-Landau (GL) theory, starting from the microscopic Bardeen-Cooper-Schrieffer (BCS) model. Close to the critical temperature, GL arises as an effective theory on the macroscopic scale. The relevant scaling limit is semiclassical in nature, and semiclassical analysis…
Statistical Mechanics Seminar, D.Ruelle, "A mechanical model for Fourier's law for heat conduction"
Wed, Nov 9, 2011, 2:00 pm – 3:30 pm
Abstract: Nonequilibrium statistical mechanics close to equilibrium is a physically satisfactory theory centered on the linear response formula of Green-Kubo. This formula results from a formal first order perturbation calculation without rigorous justification. A rigorous derivation of Fourier's law for heat conduction from the laws of mechanics…
Statistical Mechanics Seminar, D. Brydges, "The renormalisation group and recent applications"
Wed, Oct 26, 2011, 2:00 pm – 3:30 pm
Abstract: I will review a method to control irrelevant terms in the renormalisation group and describe an application to self-repelling walk in four dimensions.
Statistical Mechanics Seminar, R, Car, "Entangled protons in ice"
Wed, Oct 19, 2011, 2:00 pm – 3:30 pm
Abstract: Quantum fluctuations can drive phase transitions in ice. This happens when the protons tunnel between the two equivalent sites on a hydrogen bond. The corresponding dynamics is collective and dominated by strong local correlations originating from the ice rules. As a result, the state of the proton is entangled, an effect that can be…
Statistical Mechanics Seminar, G. Gallavotti, "Time Evolution and Stationary States of Classical and Quantum"
Wed, Oct 12, 2011, 2:00 pm – 3:30 pm
ABSTRACT: A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
J.L. Lebowitz, Time Evolution and Stationary States of Classical and Quantum
Wed, Oct 5, 2011, 2:00 pm – 3:30 pm
Abstract: I will review both old and recent work about the time dependence and steady states of isolated macroscopic systems as well as those in contact with infinite thermal reservoirs. The emphasis will be on quantum systems and will include a discussion of the micro/macro connection in isolated ones and the derivation of a master equation…
Statistical Mechanics Seminar - Philip W. Anderson, Some new results on the ground state of the strong coupling (solid)limit of the Bose-Hubbard Mod
Wed, Sep 28, 2011, 2:00 pm – 3:30 pm
Abstract: The Mott insulator is accepted as the appropriate ground manifold for the strongly interacting Fermion Hubbard model, with solid He-3 as the simplest exemplar. It is a manifold because of the spin degrees of freedom, which order antiferromagneticallly due to atom exchange, below a critical temperature. No corresponding effect…
Giovanni Gallavotti , Title: Nonequilibrium: Thermostats, BBGKY Hierarchy, Fourier's Equation
Wed, Dec 8, 2010, 2:00 pm – 6:00 pm
Abstract: Review of rigorous results on thermostats. Families of exact formal solutions of the BBGKY hierarchy for hard sphere systems with free boundary conditions at collisions and Fourier equation emergence, to first order in the temperature difference, after boundary conditions are imposed. Formal means that the solutions are given by…
Peter Kleban, University of Maine
Wed, Dec 1, 2010, 2:00 pm – 6:00 pm
Title“Hidden Symmetries at the Percolation Point in Two Dimensions
Michael Aizenman, Princeton University
Wed, Nov 24, 2010, 2:00 pm – 6:00 pm
Title: "Rounding of 1st Order Quantum Phase Transitions in Low- Dimensional Systems with Quenched Disorder " Abstract: The addition of quenched disorder has a rounding effect on 1st order phase trans ition in systems of sufficiently low dimension (d=2, and up to ï¿½ 4 in case of co ntinuous symmetry). The talk will focus on the recent…
Wed, Nov 17, 2010, 2:00 pm – 6:00 pm
Title: Critical velocites in rotating Bose gases Abstract: Some of the remarkable phenomena that emerge when a trapped, ultracold Bose gas is set in rapid rotational motion will be reviewed. In anharmonic traps, where the rotational velocity can in principle be arbitrarily large, one can distinguish three critical velocities at which the…
Wed, Nov 10, 2010, 2:00 pm – 6:00 pm
Title: Bethe-Ansatz for the two species totally asymmetric diffusion Model Abstract: We study the two species asymmetric diffusion model that describes two species and vacancies diffusing asymmetrically on a one-dimensional lattice. Our method is the algebraic Bethe Ansatz. We will explain this technique which we use to find the finite-size…
David Ruelle, IHES, France
Wed, Oct 27, 2010, 2:00 pm – Fri, Oct 8, 2010, 6:00 pm
Title: Characterization of Lee-Yang polynomials Abstract: I shall give a characterization of the multi-affine polynomials in n variables that occur in the proof of the Lee-Yang Circle Theorem. In particular, it will be seen that the spin interactions for which the Circle Theorem holds at all temperatures must be the ferromagnetic pair…
David Ruelle, IHES, France
Wed, Oct 27, 2010, 2:00 pm – 6:00 pm
Title: Characterization of Lee-Yang polynomials AAbstract: I shall give a characterization of the multi-affine polynomials in n variables that occur in the proof of the Lee-Yang Circle Theorem. In particular, it will be seen that the spin interactions for which the Circle Theorem holds at all temperatures must be the ferromagnetic pair…
Stefano Olla, Universite Paris-Dauphine
Wed, Oct 20, 2010, 2:00 pm – 6:00 pm
Title: From microscopic hamiltonian dynamics to heat equation Abstract: One of the main problems in non-equilibrium statistical mechanics is to derive, by space-time rescaling, macroscopic irreversible diffusive evolution for the co nserved quantities of an (large) hamiltonian system. I will describe the mathematical setup of the problem,…
Joel Liebowitz -- Rutgers University
Wed, Oct 13, 2010, 2:00 pm – 6:00 pm
Title: "Microscopic Models of Macroscopic Transport: A Selective Overview" Abstract: I will describe various attempts to derive, heuristically or rigorously, diffusive behavior of energy (particle) transport, i.e. Fourier's law (Fick's law) from classical microscopic models (mostly deterministic). Computer simulations showing presence or…
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