Mathematical Physics Seminar
Rutgers University
Hill Center, Room 705

January & February Schedule

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






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Please join us for coffee and cookies in the kitchen of Hill 705 at 11:45am every Thursday before seminar
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Speaker: Cedric Villani, ENS, France
Date/Time/Place: Thursday, Jan. 29, 2009, 12:00pm, Hill 705
Title: Mathematical Theory of Landau Damping
Abstract: The Landau damping is a famous and mysterious phenomenon in plasma physics and galactic dynamics. Although well understood at the linear level, it has remained essentially untouched in the physically relevant nonlinear setting. I shall describe a current work with Clement Mouhot which is aimed at solving this problem.
Speaker: H. Brezis, Rutgers University
Date/Time/Place: Thursday, Feb. 5, 2009, 12:00pm, Hill 705
Title: On a Conjecture of J. Serrin
Abstract: In 1964 J. Serrin proposed the following conjecture. Let u be a weak solution (in W^{1,1}) of a second order elliptic equation in divergence form, with Holder continuous coefficients, then u is a classical solution. We announce a solution of this conjecture assuming even weaker conditions on u and on the coefficients.

THERE WILL BE A BROWN BAG LUNCH ON FEB. 5TH FROM 1:00-2:00PM BETWEEN SEMINARS - PLEASE JOIN US.


Speaker: Michael Aizenman, Princeton University
Date/Time/Place: Thursday, Feb. 5, 2009, 2:00pm, Hill 705
Title: Localization Bounds for Multiparticle Systems
Abstract: The talk will focus on the extension of the mathematical theory of Anderson localization to quantum systems of N interacting particles on lattices of arbitrary dimension. The main result is that for all N there are regimes of high disorder, and/or weak enough interactions, for which the system exhibits spectral and dynamical localization. The localization is expressed in terms of bounds on the transition amplitudes, and more generally eigenfunction correlators, which decay at exponential rate in terms of the Hausdorff distance in the configuration space, uniformly in the allotted time. The bounds are derived through the analysis of fractional moments of the N-particle Green function. (Joint work with Simone Warzel).
Speaker: Irene Gamba, University of Texas at Austin
Date/Time/Place: Thursday, Feb. 12, 2009, 12:00pm, Hill 705
Title: Kinetic Evolution for Complex Multi-linear Particle Interactions
Abstract: We present a generalized formulation of kinetic non-local collisional models of Maxwell type that cover a large class of global energy dissipative phenomena, such as inelastic collisions, mixtures and slowdown cooling processes, economics and social dynamics; in the setting of multiplicatively interactive stochastic processes. The working framework is in the space of characteristic functions of probabilities measures and is done for a class of equations of non-local multi linear form with basic symmetries and invariance, where is possible to recover the longtime dynamics as those of metrics evolution to stable laws characterized by self-similar states for finite or infinity energy initial data. These are states in probability space which can not have all moments bounded and even may admit singularities at the origin, while remaining integrable, as in a simple example of limit mixture model for a slow-down process.
Speaker: Pavel Dubovskiy, Stevens Institute of Technology, N.J.
Date/Time/Place: Thursday, Feb. 19, 2009, 12:00pm, Hill 705
Title: Solvability of the spatially inhomogeneous coagulation-fragmentation equation
Abstract: Existence and uniqueness of a continuous global solution is proved for the spatially inhomogeneous Smoluchowski coagulation equation with fragmentation taken into account. The coagulation kernels may be unbounded. The proof is based on new a priori estimates.
Speaker: Emil Yuzbashyan, Rutgers University
Date/Time/Place: Thursday, Feb. 26, 2009, 12:00pm, Hill 705
Title: The link between integrability, level crossings, and exact solution in quantum models
Abstract: I will discuss the connection between energy level crossings in integrable systems and their integrability. In particular, I will consider a general quantum Hamiltonian linear in the coupling u, H(u) = T + uV, and require that it has the maximum possible number of nontrivial commuting partners similarly linear in u. It turns out that this commutation requirement alone leads to: (1) an exact solution for the energy spectrum and (2) level crossings, which are always present in such Hamiltonians in violation of the famous Wigner-von Neumann non-crossing rule. Moreover, these Hamiltonians can be constructed explicitly by resolving the above commutation requirement and turn out to be equivalent to so-called Gaudin magnets. In contrast, fewer than the maximum number of conservation laws does not guarantee level crossings.