Mathematical Physics Seminar
Rutgers University
Hill Center, Room 705

September Schedule

Organized by: Joel L. Lebowitz

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  • Speaker- L. Rey-Bellet, University of Massachussets
  • Time/Place- Thursday 9/1/05, 12-1pm in Hill 423(NOTE RM. CHANGE)
  • Title- "Large Deviations in Quantum Lattice Systems"
  • Abstract- We prove large deviation estimates for quantum lattice systems (spin or fermions) in one dimension and at high temperature. We discuss as well open questions. This is a joint work with Marco Lenci.

  • Speaker- R. Seiringer, Princeton University
  • Time/Place- Thursday 9/8/05, 12-1pm in Hill 705
  • Title- "Derivation of the Gross-Pitaevskii Equation for Rotating Bose Gases" leaf5
  • Abstract- We prove that the Gross-Pitaevskii equation correctly describes the ground state energy and corresponding one-particle density matrix of rotating, dilute, trapped Bose gases with repulsive two-body interactions. We also show that there is 100% Bose-Einstein condensation. While a proof that the GP equation correctly describes non-rotating or slowly rotating gases was known for some time, the rapidly rotating case was unclear because the Bose (i.e., symmetric) ground state is not the lowest eigenstate of the Hamiltonian in this case. We have been able to overcome this difficulty with the aid of coherent states. Our proof also conceptually simplifies the previous proof for the slowly rotating case. In the case of axially symmetric traps, our results show that the appearance of quantized vortices causes spontaneous symmetry breaking in the ground state.



    There will be no seminar Thursday 9/15/05. Please attend the Solitons, Singularities, Surreals and Such: A Conference in Honor of Martin Kruskal's Eightieth Birthday. Hill Center, Room 705



    Coffee and cookies will be provided at 11:40A

  • Speaker - V. Vu, Rutgers University
  • Time/Place - Thursday, 9/22/05, 12:15-1PM - Hill 705
  • Title - Singularity of random symmetric matrices
  • Abstract - Let Qn denote the n by n random symmetric matrix, whose upper triangle entries are i.i.d Bernoulli random variables (taking value 0 or 1 with probability 1/2). We are going to show that Qn is almost surely singular, answering a question of Weiss. If time allows, I will discuss several related questions.
    Joint work with Terrence Tao (UCLA) and Kevin Costello (UCSD).



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    Coffee and cookies will be provided before the first talk at 11:40A

  • Speaker - E. Carlen, Georgia Tech.
  • Time/Place - Thursday, 9/29/05. 12-1PM - Hill 705
  • Title - "Problems in the calculus of variations associated to droplet formation.
  • Abstract - On a mesoscopic scale, the equilibrium configurations of statistical meachanical systems in contact with a heat bath are found by minimizing a free energy function that is non convex if the system has a phase transition. Determining the geoemtric nature of the minimizers is a problem of considerable mathematical and physical interest. Detailed solutions will be provided for certain well known models in this talk, which is based on joint work with Carvalho, Esposito, Lebowitz and Marra.

  • Speaker - P. Ferrari, Technische Universitaet Muenchen
  • Time/Place - Thursday, 9/29/05 2-3pm HILL 705
  • Title - "Scaling limit for the space-time covariance of the stationary TASEP"
  • Abstract - We consider the stationary totally asymmetric simple exclusion process (TASEP), with Bernoulli \rho measure as initial condition. We analyze the 2-point function and obtain, for large time t, its the limiting expression. It is given in term of generalization of the GUE Tracy-Widom distribution of random matrices.