Abstracts for the Moshe Flato Lecture Series 2011

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.

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 experimentalists and practical band-structure calculators had not spotted despite years of study 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 disorder. I will review the history of the idea and recent developments, as well as concrete realizations in electronic and photonic systems, that may have important technological applications.

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.

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.

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 conceptual revolutions.