# University of Virginia Mathematical Physics Seminar 2011-12

 September 7 Speaker: Israel Klich Title: Quantum Noise and the Entanglement Entropy Abstract: Entanglement entropy is a measure of quantum many body correlations between the parts of a many body system. It has emerged as a useful quantity in broad areas of theoretical physics, from cosmology to condensed matter and quantum information. In this talk I will discuss the problem of entanglement entropy of fermions and it's relation to Widom's conjecture. I will also describe a universal relation between entanglement entropy and statistics of current flowing through a quantum point contact. This relation provides a way to experimentally measure entanglement entropy, and test seminal results of conformal field theory such as the prediction of Holzhey, Larsen and Wilczek for entanglement entropy of fermions. September 14 Speaker: John Imbrie Title: Diagonalizing a Matrix a la Newton Abstract: Newton showed how to solve an equation f(x)=0 by constructing a sequence of approximate solutions that converge rapidly to the answer. A similar idea can be used to solve nonlinear functional equations, as in Nash-Moser and KAM theorems. I will use Newton's method to diagonalize a symmetric NxN matrix with small off-diagonal entries. This will be an elementary talk which will lay the foundation for subsequent lectures applying the idea to Anderson localization. September 21 Speaker: John Imbrie Title: Newton's Method for Anderson Localization Abstract: I will present an eigenfunction-based scheme for proving Anderson localization. September 28 Speaker: John Imbrie Title: Newton's Method for Anderson Localization Abstract: I continue with a discussion of how to control both resonant and non-resonant regions. October 7 NOTE CHANGE IN DAY--FRIDAY AND ROOM--KER 317 Speaker: David Hasler, College of William and Mary Title: Anderson localization for Schroedinger operators with a random magnetic field Abstract: We consider a two dimensional Schroedinger operator with a spatially stationary random magnetic field in the plane and on the lattice. We prove a Wegner estimate, which can be used to establish localization at the band edges of the spectrum. October 12 Speaker: John Imbrie Title: Newton's Method for Anderson Localization Abstract: I conclude the series with a discussion of key issues for controlling long-range resonances. October 19 Speaker: Julianne Rama Title: Time asymptotics of exp(ith(\kappa)) for analytic matrices Abstract: The results I will present are a joint work with Markus Klein. Our interest in this problem has its origin in quantum resonance theory. I will analyze the time evolution of exp(ith(\kappa)), where h(\kappa) is an analytic matrix family. I shall derive asymptotic expansions with error bounds which are uniform in t and \kappa. In particular, these error bounds apply to the simultaneous limit t -> \infty, \kappa -> 0. October 26 Speaker: Larry Thomas Title: Stochastic wave equation model for heat-flow in non-equilibrium statistical mechanics Abstract: We consider the problem of constructing an invariant measure for a one-dimensional non-linear stochastic wave equation. The invariant measure serves to describe steady state heat flow in a simple model in non-equilibrium statistical mechanics. November 2 Speaker: Larry Thomas Title: Stochastic wave equation model for heat-flow in non-equilibrium statistical mechanics, cont. Abstract: We consider the problem of constructing an invariant measure for a one-dimensional non-linear stochastic wave equation. The invariant measure serves to describe steady state heat flow in a simple model in non-equilibrium statistical mechanics. November 9 Speaker: Abdelmalek Abdesselam Title: Rigorous quantum field theory functional integrals over the p-adics Abstract: I will present the results of joint work with Ajay Chandra and Gianluca Guadagni regarding the construction of probability measures on the space of distributions over a three-dimensional p-adic space-time. The main ingredient is an extension of the renormalization group methods by Brydges and collaborators to the case of nonuniform potentials. November 16 Speaker: Abdelmalek Abdesselam Title: Rigorous quantum field theory functional integrals over the p-adics, cont. Abstract: I will present the results of joint work with Ajay Chandra and Gianluca Guadagni regarding the construction of probability measures on the space of distributions over a three-dimensional p-adic space-time. The main ingredient is an extension of the renormalization group methods by Brydges and collaborators to the case of nonuniform potentials. November 23 THANKSGIVING RECESS November 30 Speaker: Abdelmalek Abdesselam Title: Rigorous quantum field theory functional integrals over the p-adics, cont. Abstract: I will present the results of joint work with Ajay Chandra and Gianluca Guadagni regarding the construction of probability measures on the space of distributions over a three-dimensional p-adic space-time. The main ingredient is an extension of the renormalization group methods by Brydges and collaborators to the case of nonuniform potentials. February 8 Speaker: Abdelmalek Abdesselam Title: Rigorous quantum field theory functional integrals over the p-adics, cont. Abstract: I will present the results of joint work with Ajay Chandra and Gianluca Guadagni regarding the construction of probability measures on the space of distributions over a three-dimensional p-adic space-time. The main ingredient is an extension of the renormalization group methods by Brydges and collaborators to the case of nonuniform potentials. February 15 Speaker: Ajay Chandra Title: Rigorous quantum field theory functional integrals over the p-adics, cont. Abstract: I will continue this sequence of talks by describing how one controls the flow of observables in our theory. If time permits I will give a sketch of how studying the flow of one fairly simple observable shows that the measure constructed is non-trivial (non-Gaussian). This is joint work with Abdelmalek Abdesselam and Gianluca Guadagni. February 22 Speaker: Ajay Chandra Title: Rigorous quantum field theory functional integrals over the p-adics, cont. May 2 Speaker: Juliane Rama Title: Instability of resonances in the Stark effect for a simple model Abstract: This is joint work with Ira Herbst. For a simple matrix Schroedinger operator we present some (preliminary) results on the instability of a resonance under the influence of a small electric field in the weak field limit (DC Stark effect).

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