Abstracts for the Moshe Flato Lecture Series 2011
Prof. Étienne Ghys
Chirality in dynamics
Consider a dynamical system in 3-space, induced by some vector
field. Its trajectories, the phase portrait, may present some asymmetry
with respect to a mirror image.
I would like to discuss some examples of such "chiral vector fields".
I'll introduce a family of "fully chiral" dynamics and explain some
consequences on the topology of periodic orbits.
Prof. F. Duncan M. Haldane
The very topical experimental field of "topological insulators"
is a rare example of a subfield that started as an abstract theoretical
or mathematical idea that exposed a striking effect that both
practical band-structure calculators had not spotted despite years of
the materials exhibiting it!. Topologically-stable conducting edge states
occur at the boundaries between
insulators that belong to incompatible classes, which cannot be destroyed by
I will review the history of the idea and recent developments, as well as
realizations in electronic and photonic systems, that may have important
Prof. Mordechai Heiblum
Entangled Electrons in the Solid State: Quantum Interference and Dephasing
I will describe two connected experiments, where pairs of
electrons were entangled in a solid state Mach-Zehnder Interferometer
(MZI), leading to entirely different outcomes. In one experiment electrons
in a 'which path' detector were entangled with electrons in a MZI,
leading to total dephasing of the interference. Under these conditions,
the interference that was lost had been recovered by doing a 'post
selection' type measurement (via cross-correlating currents); proving that
the phase information stayed in the system. In another experiment, making
use of two MZIs (in a novel 'two particle interferometer'), two
remote, indistinguishable, electrons were entangled only due to their
exchange statistics, namely, without ever interacting with each other (in
a similar fashion to the Hanbury Brown - Twist photonic experiment).
Though each electron's paths did not enclose a flux, cross correlating the
current fluctuations in the two separate detectors revealed Aharonov-Bohm
flux dependent oscillations.
Prof. Subir Sachdev
Quantum criticality and the gauge-gravity duality
Quantum critical points (or phases) are special locations in
parameter space where the ground state wavefunction has long-range
and scale-invariant quantum entanglement between the local
degrees of freedom. Such points are also the key to explaining
a wide variety of experiments on many modern electronic materials.
In recent years, ideas from string theory on the duality between
quantum gauge and gravity theories have provided a new physical
perspective on quantum criticality. I will give an overview of these developments
and their future prospects.
Prof. Cédric Villani
Landau damping, or relaxation without entropy production: the limits of Boltzmann's paradigm
Boltzmann's statistical entropy, the notion of macroscopic
irreversibility and molecular chaos, and the Boltzmann equation were at
the basis of a little conceptual revolution at the end of the nineteenth
century. In 1946, Landau shocked the scientific community by finding
irreversibility where there did not seem to be. This ended the reign of
entropy as the dominant explanation for irreversible behavior. It took
another 2/3 of! century before Landau's contribution was fully justified,
and, unexpectedly, related to some of the other most famous paradoxes of
classical mechanics. The present talk will explain in simple terms these