Seminars and Colloquia by Series

Transition lines for Almost Mathieu Operator

Series
Math Physics Seminar
Time
Wednesday, November 7, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Fan YangGeorgia Tech
I will talk about what happens on the spectral transition lines for the almost Mathieu operator. This talk is based on joint works with Svetlana Jitomirskaya and Qi Zhou. For both transition lines \{\beta(\alpha)=\ln{\lambda}\} and \{\gamma(\alpha,\theta)=\ln{\lambda}\} in the positive Lyapunov exponent regime, we show purely point spectrum/purely singular continuous spectrum for dense subsets of frequencies/phases.

Strongly dissipative systems with a quasi-periodic forcing term

Series
Math Physics Seminar
Time
Wednesday, October 24, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guido GentileUniversita di Roma 3
We consider a class of singular ordinary differential equations, describing systems subject to a quasi-periodic forcing term and in the presence of large dissipation, and study the existence of quasi-periodic solutions with the same frequency vector as the forcing term. Let A be the inverse of the dissipation coefficient. More or less strong non-resonance conditions on the frequency assure different regularity in the dependence on the parameter A: by requiring a non-degeneracy condition on the forcing term, smoothness and analyticity, and even Borel-summability, follow if suitable Diophantine conditions are assumed, while, without assuming any condition, in general no more than a continuous dependence on A is obtained. We investigate the possibility of weakening the non-degeneracy condition and still obtaining a solution for arbitrary frequencies.

TBA David Borthwick

Series
Math Physics Seminar
Time
Wednesday, October 10, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
David BorthwickDept. of Math. and Comp. Science, Emory University
TBA

Distribution of Resonances for Hyperbolic Surfaces

Series
Math Physics Seminar
Time
Wednesday, October 10, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
David BorthwickDept. of Math. and Comp. Science, Emory University
Non-compact hyperbolic surfaces serve as a model case for quantum scattering theory with chaotic classical dynamics. In this talk I’ll explain how scattering resonances are defined in this context and discuss our current understanding of their distribution. The primary focus of the talk will be on some recent conjectures inspired by the physics of quantum chaotic systems. I will introduce these and discuss the numerical evidence as well as recent theoretical progress.

Localization of orthonormal functions in spectral clusters

Series
Math Physics Seminar
Time
Wednesday, October 3, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rupert FrankLMU Munich/Caltech
We generalize the Lp spectral cluster bounds of Sogge for the Laplace-Beltrami operator on compact Riemannian manifolds to systems of orthonormal functions. We show that these bounds are optimal on any manifold in a very strong sense. These spectral cluster bounds follow from Schatten-type bounds on oscillatory integral operators and their optimality follows by semi-classical analysis.

A Quantum Kac Model

Series
Math Physics Seminar
Time
Wednesday, September 19, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Michael LossSchool of Mathematics, Georgia Tech
We introduce a quantum version of the Kac Master equation,and we explain issues like equilibria, propagation of chaos and the corresponding quantum Boltzmann equation. This is joint work with Eric Carlen and Maria Carvalho.

Autonomous evolution of electron speeds in a thermostatted system: exact results

Series
Math Physics Seminar
Time
Wednesday, September 12, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Federico BonettoGeorgia Tech
We investigate a dynamical system consisting of $N$ particles moving on a $d$-dimensional torus under the action of an electric field $E$ with a Gaussian thermostat to keep the total energy constant. The particles are also subject to stochastic collisions which randomize direction but do not change the speed. We prove that in the van Hove scaling limit, $E\to 0$ and $t\to t/E^2$, the trajectory of the speeds $v_i$ is described by a stochastic differential equation corresponding to diffusion on a constant energy sphere.Our results are based on splitting the system's evolution into a ``slow'' process and an independent ``noise''. We show that the noise, suitably rescaled, converges to a Brownian motion. Then we employ the Ito-Lyons continuity theorem to identify the limit of the slow process.

The discrete Bethe-Sommerfeld Conjecture

Series
Math Physics Seminar
Time
Wednesday, September 5, 2018 - 16:00 for 1 hour (actually 50 minutes)
Location
Skiles room 005
Speaker
Rui HanGeorgia Tech
We will talk about discrete versions of the Bethe-Sommerfeld conjecture. Namely, we study the spectra of multi-dimensional periodic Schrödinger operators on various discrete lattices with sufficiently small potentials. In particular, we provide sharp bounds on the number of gaps that may perturbatively open, we characterize those energies at which gaps may open, and we give sharp arithmetic criteria on the periods that ensure no gaps open. We will also provide examples that open the maximal number of gaps and estimate the scaling behavior of the gap lengths as the coupling constant goes to zero. This talk is based on a joint work with Svetlana Jitomirskaya and another work with Jake Fillman.

Quantum simulation in Rydberg media

Series
Math Physics Seminar
Time
Friday, April 27, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles 202
Speaker
Brian KennedySchool of Physics, Georgia Tech
Electrons possess both spin and charge. In one dimension, quantum theory predicts that systems of interacting electrons may behave as though their charge and spin are transported at different speeds.We discuss examples of how such many-particle effects may be simulated using neutral atoms and radiation fields. Joint work with Xiao-Feng Shi

Scratching the surface of many-body localization

Series
Math Physics Seminar
Time
Friday, April 6, 2018 - 15:00 for 1 hour (actually 50 minutes)
Location
Skiles Room 202
Speaker
Günter StolzUniversity of Alabama, Birmingham
Localization properties of quantum many-body systems have been a very active subject in theoretical physics in the most recent decade. At the same time, finding rigorous approaches to understanding many-body localization remains a wide open challenge. We will report on some recent progress obtained for the case of quantum spin chains, where joint work with A. Elgart and A. Klein has provided a proof of several manifestations of MBL for the droplet spectrum of the disordered XXZ chain.

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