Mathematical Physics Seminar
Organizer: Joel L. Lebowitz, lebowitz@math.rutgers.edu
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Speaker: Yuri Suhov, University of Cambridge, UK
Date/Time/Place: Thursday, April 3, 2008 @12:00PM Hill 705
Title: Localization in the Anderson tight binding model with several particles
Abstract: The Anderson model (which will celebrate its 50th anniversary in 2008) is among most popular topics in the random matrix and operator theory. However, so far the attention here was concentrated on single-particle models, where the random external potential is either IID or has a rapid decay of spatial correlations. Multi-particle models remained out of scope in mathematical (and, surprisingly, physical) literature. Recently, Chulaevsky and Suhov (2007) proposed a version of the multi-scale analysis (MSA) scheme tackling the multi-particle case. I'll discuss one of results in this direction: localisation in the lattice (tight binding) multi-particle models for large values of the amplitude (coupling) constant.
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Speaker: Sagun Chanillo, Rutgers University
Date/Time/Place: Thursday, April 3, 2008 @ 2:00pm Hill 705
Title: The Composite Membrane Problem
Abstract: The problem is to build a body of given shape and of a given mass out of materials of varying density so as to minimize the first Dirichlet eigenvalue with fixed boundary. Existence, uniqueness of the configuration and the regularity of the free boundary which is the interface between the materials are the obvious questions. We shall give answers to these issues and discuss many open questions that arise in this mathematically rich problem.
Speaker: Stefano Olla, University of Paris - Dauphine, France
Date/Time/Place: Thursday, April 17, 2008 @12:00pm Hill 705
Title: Title: Macroscopic energy diffusion in a system of weakly coupled anharmonic oscillators with energy conserving noise.
Abstract: We consider a chain of weakly coupled oscillators whose Hamiltonian dynamics is
perturbed by stochastic terms that conserve energy of each particle. In a large-time weak-coupling limit, the energy of the particles evolves autonomously following a (non-gradient) stochastic Ginzburg-Landau dynamics. Then a non linear heat equation can be deduced from this stochastic dynamics under a hydrodynamic diffusive limit. This is a joint work with Carlangelo Liverani.
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Speaker: Alessandro Giuliani, University of Rome III, Italy
Date/Time/Place: Thursday, April 17, 2008 @2:00pm Hill 705
Title: Periodic ground states of spin models with long range competing interactions.
Abstract: We shall review some recent results on the existence of periodic ground states for a class of 1D and 2D discrete or continuum spin systems. These models are all characterized by a competition between a short range attractive interaction, favoring a homogeneous ordered state, and a long range repulsive interaction, opposing such ordering on the scale of the whole sample. The case of long range repulsive Kac interactions will be considered. In the limit of infinite range interactions, the repulsive nature of the long range interaction implies that at the mean field level there is no phase transition in the thermodynamic sense. However, for long but finite
range, it is expected that the repulsive Kac potential causes the distinct homogeneous phases to break into mesoscopic droplets (or "froth"). The relevance of our results for the problem of understanding the micrscopic structure of this froth will be discussed.