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Series: Other Talks

Thesis defense:
Advisors: Turgay Uzer and Cristel Chandre
Summary:
Thirty years after the demonstration of
the production of high laser harmonics through nonlinear laser-gas
interaction, high harmonic generation (HHG) is being used to probe
molecular dynamics in real time and is realizing its
technological potential as a tabletop source of attosecond pulses in the
XUV to soft X-ray range. Despite experimental progress, theoretical
efforts have been stymied by the excessive computational cost of
first-principles simulations and the difficulty of
systematically deriving reduced models for the non-perturbative,
multiscale interaction of an intense laser pulse with a macroscopic gas
of atoms. In this thesis, we
investigate first-principles reduced models for HHG using
classical mechanics. On the microscopic level, we examine the
recollision process---the laser-driven collision of an ionized electron
with its parent ion---that drives HHG. Using nonlinear dynamics, we
elucidate the indispensable role played by the ionic
potential during recollisions in the strong-field limit. On the
macroscopic level, we show that the intense laser-gas interaction can be
cast as a classical field theory. Borrowing a technique from plasma
physics, we systematically derive a hierarchy of
reduced Hamiltonian models for the self-consistent interaction between
the laser and the atoms during pulse propagation. The reduced models
can accommodate either classical or quantum electron dynamics, and in
both cases, simulations over experimentally-relevant
propagation distances are feasible. We build a classical model based on
these simulations which agrees quantitatively with the quantum model
for the propagation of the dominant components of the laser field.
Subsequently, we use the classical model to trace
the coherent buildup of harmonic radiation to its origin in phase
space. In a simplified geometry, we show that the anomalously high
frequency radiation seen in simulations results from the delicate
interplay between electron trapping and higher energy recollisions
brought on by propagation effects.

Series: Other Talks

Oral Comprehensive Exam

<p>The purpose of this work is approximation of generic Hamiltonian dynamical systems by those with a finite number of islands. In this work, we will consider a Lemon billiard as our Hamiltonian dynamical system apparently with an infinitely many islands. Then, we try to construct a Hamiltonian dynamical system by deforming the boundary of our lemon billiard to have a finite number of islands which are the same or sub-islands of our original system. Moreover, we want to show elsewhere in the phase space of the constructed billiard is a chaotic sea. In this way, we will have a dynamical system which preserves some properties of our lemon billiards while it has much simpler structure.</p>

Series: Other Talks

Cristobal Guzman will discuss his employment experience as an ACO alummus. The conversations will take place over coffee.

Series: Other Talks

Thermodynamics
provides a robust conceptual framework and set
of laws that govern the exchange of energy and matter. Although these
laws were originally articulated for macroscopic objects, it is hard to
deny that nanoscale systems, as well, often exhibit “thermodynamic-like”
behavior. To what extent can the venerable
laws of thermodynamics be scaled down to apply to individual microscopic
systems, and what new features emerge at the nanoscale? I will review
recent progress toward answering these questions, with a focus on the
second law of thermodynamics. I will argue
that the inequalities ordinarily used to express the second law can be
replaced by stronger equalities, known as fluctuation relations, which
relate equilibrium properties to far-from-equilibrium fluctuations. The
discovery and experimental validation of these
relations has stimulated interest in the feedback control of small
systems, the closely related Maxwell demon paradox, and the
interpretation of the thermodynamic arrow of time. These developments
have led to new tools for the analysis of non-equilibrium experiments
and simulations, and they have refined our understanding of
irreversibility and the second law.
Bio
Chris
Jarzynski received an AB degree in physics from Princeton
University in 1987, and a PhD in physics from the University of
California, Berkeley in 1994. After postdoctoral positions at the
University of Washington in Seattle and at Los Alamos National
Laboratory in New Mexico, he became a staff member in the Theoretical
Division at Los Alamos. In 2006, he moved to the University of Maryland,
College Park, where he is now a Distinguished University Professor in
the Department of Chemistry and Biochemistry, with joint appointments in
the Institute for Physical Science and Technology
and the Department of Physics. His research is primarily in the area of
nonequilibrium statistical physics, where he has contributed to an
understanding of how the laws of thermodynamics apply to nanoscale
systems. He has been the recipient of a Fulbright Fellowship,
the 2005 Sackler Prize in the Physical Sciences, and the 2019 Lars
Onsager Prize in Theoretical Statistical Physics. He is a Fellow of the
American Physical Society and the American Academy of Arts and Sciences.
Contact: Professor Jennifer Curtis Email: <a rel="noopener noreferrer" href="mailto:jennifer.curtis@physics.gatech.edu" target="_blank">jennifer.curtis@physics.gatech.edu</a>

Series: Other Talks

This talk is organized by the Association for Women in Math (AWM). Everyone is welcome to attend.

In 1968, Mader showed that for every integer $p = 1, 2, …, 7$, agraph on $n \geq p$ vertices and at least $(p-2)n - \binom{p-1}{2} + 1$ edgeshas a $K_p$ minor. However, this result is false for $p = 8$ with the counter-example K2,2,2,2,2. In this talk, we will discuss this function presented byMader for $K_p$ where $p$ is bigger. We will also discuss related resultsproved using probabilistic methods and the relation of this problem toHadwiger’s conjecture.

Series: Other Talks

I
will discuss chaos in quantum many-body systems, specifically how it is
relates
to thermalization and how it fails in many-body localized states. I will
conjecture a new universal form for the spreading of chaos in local
systems, and discuss evidence for the conjecture from a variety of
sources including new large-scale simulations of
quantum dynamics of spin chains.

Series: Other Talks

Thanks are due to our colleague, Vladimir Koltchinskii, for arranging this visit. Please write to Vladimir if you would like to meet with Professor Gabor Lugosi during his visit, or for additional information.

In these lectures we discuss some statistical problems with an interesting combinatorial structure behind. We start by reviewing the "hidden clique" problem, a simple prototypical example with a surprisingly rich structure. We also discuss various "combinatorial" testing problems and their connections to high-dimensional random geometric graphs. Time permitting, we study the problem of estimating the mean of a random variable.

Series: Other Talks

Series: Other Talks

What to do if the measurements that you took were
corrupted by a malicious spy? We will see how the natural geometric
approach to the problem leads to a geometry where lines are crooked, and
triangles are square.

Series: Other Talks