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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