Mathematical Physics
Seminar
November Schedule
Organizer: Joel L. Lebowitz
lebowitz@math.rutgers.edu

• Speaker- N. Zanghi, INFN, Italy
• Title-New Directions in Bohmian Mechanics
• Time/place-Thursday 11/6/03, 11:30am in Hill 423
• Abstract-Bohmian Mechanics is a precise formulation of quantum mechanics which provides an explanation and a precise characterization of the range of validity of various quantum laws. Aim of the seminar is to present some novel developments of relevance for the foundations of quantum field theory and quantum statistical mechanics.
  
  Please note there will be a brown bag lunch between the 2 seminars this morning. Bring your sandwich.
  Coffee and homemade cookies will be available.
  
  
• Speaker- T. Kuna, University of Rome/Rutgers University
• Title-Phase Transition for a Quantum Mechanical System of Interacting Particles
• Time/place-Thursday 11/6/03, 1:30pm in Hill 423
• Abstract-In the talk we will consider a system of particles interacting via scaled Kac potentials. The existence of a gas-liquid type phase transition with the particle density as the order parameter was shown by Lebowitz, Mazel, and Presutti. Using the Feynman-Kac representation we verify that this result also holds for the corresponding quantum system obeying Maxwell-Boltzmann statistic. In particular, we developed a variant of Dobrushin's uniqueness theorem suitable for Pirogov-Sinai scheme. The main steps and there adjustments to the quantum mechanical case are pointed out.
  The talk is based on a joint work with F. Baffioni, T. Merola and E. Presutti.

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• Speaker- N. Menon, University of Massachusetts
• Title-Experimental Studies of a Vibrated Inelastic Gas
• Time/place-Thursday 11/13/03, 11:30am in Hill 423
• Abstract-Under the action of external forces, sand can flow like a fluid. An important question is whether there is an appropriate continuum description of flowing sand. A related question is whether the statistical physics of conventional fluids may be adapted to granular fluids. In our experiments, we drive granular media into homogenous, stationary states to consider these questions in relatively simple settings. I will describe an intensely vibrated 2D system in which we study the validity and usefulness of a variable analogous to temperature. Our results show that this granular temperature determines a spectrum of velocity fluctuations that is not Maxwellian, but is well defined over a broad regime. I will also describe experimental results that bear upon equipartition in this system. Finally, I will discuss the statistics of the power flux into the system in the light of the Gallavotti-Cohen fluctuation theorem.
  
  Please note there will be a brown bag lunch between the 2 seminars this morning. Bring your sandwich.
  Coffee and homemade cookies will be available.
  
  
• Speaker-A. Guiliani, INFN, Italy
• Title-Anisotropic Ashkin-Teller model: Anomalous Renormalization of the Critical Temperatures
• Time/place-Thursday 11/13/03, 1:30pm in Hill 423
• Abstract-The 2d Ashkin-Teller (AT) model can be formulated as a system of two 2d Ising layers (with couplings $J_1$ and $J_2$) interacting via a four spin term (of strength $\lambda$). We study the weakly anisotropic AT ($0<J_1-J_2<<J_1+J_2$) at criticality, for small interaction $\lambda$, via renormalization group methods. We find that the system admits two critical temperatures, whose difference is renormalized by an anoumalous critical exponent (w.r.t. the noninteracting case). The specific heat is found to diverge logarithmically at criticality, but the coefficient of the logarithm is found to be anomalous (i.e. diverging or going to zero for $J_1\to J_2$).

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• Speaker- S. Tanveer, Ohio State University
• Title-Two Interacting Bubbles in Stokes Flow (Joint work with D.G. Crowdy and G.L. Vasconcelos).
• Time/place-Thursday 11/20/03, 11:30am in Hill 423
• Abstract- The problem of evolving bubbles in 2-D Stokes Flow (highly viscous regime of fluid flow) is considered with nonzero surface tension. The problem has a rich mathematical structure that allows one to determine exact solutions for an entire class of initial conditions, even for two bubbles. Cauchy transform, which is the generating function of moments of a given domain, turn out to preserve an iniitial meromorphic form with finite number of poles for these class of solutions. Further, though the system is dissipative, it has an infinite number of conserved quanitities when surface tension is ignored. With surface tension, in a normal form, the equations have an interesting triangular structure so that any truncated representation is an exact solution. Some interesting shape computations will also be presented.
  
  Please note there will be a brown bag lunch between the 2 seminars this morning. Bring your sandwich.
  Coffee and homemade cookies will be available.
  
  
• Speaker- O. Costin, Rutgers University
• Title-Nonperturbative Methods and Results in the Time-dependent Schrodinger Equation
• Time/place-Thursday 11/20/03, 1:30pm in Hill 423
• Abstract-The talk focuses on new methods in the analysis of large time behavior of the wave function of a particle in time-periodic or quasiperiodic fields. The methods allow for the study of fields which are not necessarily small and which bring about surprising effects. We present recent results we obtained in the problem of ionization in R^d.
  I will also briefly explain how similar methods apply to the study of existence, uniqueness, regularity of solutions as well as formation of singularities, in general classes of nonlinear evolution PDEs in C^d.
  Joint work with R. D. Costin, J. L. Lebowitz and S. Tanveer
  
  

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• Speaker- H. Furstenberg, Yale University
• Title-Ergodic Geometry, Nilpotent Groups, and Nonconventional Ergodic Averages
• Time/place-Tuesday 11/25/03(please note day), 11:30am in Hill 423
• Abstract-This talk will be an introduction to recent work of B. Host and B. Kra establishing a mean ergodic theorem for "non-conventional" ergodic averages such as
  
  1/N sigma f_1(T^n x)f_2(T^2n x)...f_k(T^kn x).
  In their proof an important role is played by nilpotent groups, and we will try to explain the connection in terms of an "ergodic" analog of the notions of parallelism and congruence in ordinary geometry.
  
  
  
  

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