Mathematical Physics Seminar
Rutgers University
Hill Center, Room 705

November Schedule

Organized by: Joel L. Lebowitz
lebowitz@math.rutgers.edu




Please join us for coffee and cookies in the kitchen of Hill 705 at 11:45am.


Speaker: S. Olla, Universite Paris Dauphine
Date/Time/Place: Thursday, Nov. 6, 2008, 12:00pm, Hill 705
Title: Pressure models: non-equilibrium behavior
Abstract: Pressure models, i.e., one dimensional chains of unpinned anharmonic oscillators, are the simplest non-linear mechanical model for the study of 'macroscopic' equilibrium and non-equilibrium statistical mechanics. The equilibrium statistical mechanics is particularly simple since it reduces here to the study of the properties of sums of independent variables. Non-equilibrium macroscopic evolution, in hyperbolic and diffusive space time scale, and non-equilibrium stationary states, provide very challenging problems also in this simplified context. I will translate for this model, some old and new results, and open problems.

THERE WILL BE A BROWN BAG LUNCH FROM 1PM - 2PM


Speaker: E. Lieb, Princeton University
Date/Time/Place: Thursday, Nov. 6, 2008, 2:00pm, Hill 705
Title: Some extensions of Lieb-Thirring inequalities of eigenvalues of the Shroedinger operator
Abstract: The LT inequalities bound sums of negative eigenvalues by certain integrals of the potential energy function. Extensions of these inequalities (obtained in joint work with R. Frank and R. Seiringer) to matrix valued potentials and to complex-valued potentials will be described.

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PLEASE NOTE: THE SEMINAR FOR THURSDAY, NOVEMBER 13TH HAS BEEN CANCELED.


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Speaker: R. McPherson, IAS
Date/Time/Place: Thursday, Nov. 20, 2008, 12:00pm, Hill 705
Title: The geometry of polycrystalline materials
Abstract: A metal or ceramic is naturally decomposed into cells called "grains", each of which is a single crystal. The geometry of this cell complex influences the properties of the material. Some interesting mathematical problems arise in trying to understand the time evolution of these grains. In 1952, Von Neumann gave a simple formula for the growth rate of a grain in 2 dimensions, which has been used as the basis for much of the work on grain evolution. This formula will be generalized to 3 (and higher) dimensions (joint work with David Srolovitz).

THERE WILL BE A BROWN BAG LUNCH FROM 1PM - 2PM


Speaker: R. Seiringer, Princeton University
Date/Time/Place: Thursday, Nov. 20, 2008, 2:00pm, Hill 705
Title: Coherent States in Quantum Statistical Mechanics
Abstract: Coherent states go back to the early days of quantum mechanics and have found use in many problems in quantum physics. We shall discuss their application in problems in quantum statistical mechanics and dilute Bose gases in particular. Coherent states can be used to rigorously justify part of Bogoliubov's theory, where creation and annihilation operators get replaced by c-numbers. Moreover, they are essential for understanding the emergence of effective theories on the macroscopic scale, like the Gross-Pitaevskii equation for rotating Bose gases in traps.

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Speaker: A. Short, University of Cambridge, UK
Date/Time/Place: Tuesday, Nov. 25, 2008, 12:00pm, Hill 705
Title: A quantum approach to thermal equilibrium
Abstract: One of the biggest challenges in understanding statistical mechanics is its use of probabilities, which are usually introduced through ignorance or time-averaging. Here, I will describe an alternative approach, also pursued here at Rutgers, in which probabilities arise as an objective consequence of quantum entanglement. In this context, I will offer a general and rigorous proof of canonical typicality (that small subsystems appear canonical for almost all states), and show that even non-canonical initial states evolve towards equilibrium under very general conditions.

THERE WILL BE A BROWN BAG LUNCH FROM 1PM-2PM


Speaker: P.Garrido, Universidad de Granada
Date/Time/Place: Tuesday, Nov. 25, 2008, 2:00pm, Hill 705
Title: A test of the additivity principle for current fluctuations in a model of heat conduction
Abstract:The additivity principle allows to compute the current distribution in many one-dimensional (1D) nonequilibrium systems. Using simulations, we confirm this principle in the 1D Kipnis-Marchioro- Presutti model of heat conduction. In this case the current distribution shows both Gaussian and non-Gaussian regimes, and obeys the Gallavotti-Cohen fluctuation theorem. We confirm the existence of a well-defined temperature profile associated to a given current fluctuation. This profile is independent of the current sign, and this symmetry extends to higher-order profiles and spatial correlations. We also show that finite-time joint fluctuations of the current and the temperature profile are described by the additivity functional. These results confirm the additivity hypothesis as a general and powerful tool to compute current distributions in many 1D nonequilibrium systems.

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Date/Time/Place: Thursday, Nov. 27, 2008, 12:00pm, Hill 705
PLEASE NOTE: THERE WILL NOT BE A SEMINAR THIS DAY IN OBSERVANCE OF THANKSGIVING HOLIDAY