Few-body and many-body chaos
june 4 and 5
While many of the essential features of classical mechanics were developed centuries ago, chaos was the exception, rising to prominence only relatively recently. It has now permeated disparate areas of science: from weather forecasting to statistical mechanics, from population dynamics to chemical reactions. The focus of these lectures will be on some of the recent developments in chaos in quantum many-body systems.
The two-body problem is one of the simplest mechanics problems. Yet, adding just one additional body proves incredibly challenging. As is now recognized, the difficulty is not merely technical but conceptual: the three-body problem exhibits chaos. Nevertheless, our experience with the sun-earth-moon system tells us that the chaos can be weak. For many-body problems, such as a gas of hard spheres in a box, chaos is essential, and forms the basis of statistical mechanics: chaos gives rise to the ergodic mixing of phase space that justifies the use of the Boltzmann distribution. If the gas is made up of microscopic particles, classical mechanics must be replaced with quantum mechanics. And if the particles are relativistic, they can create and annihilate, and one is in the realm of quantum field theory. At each stage in the progression, from few-body classical chaos to many-body quantum chaos, the conceptual and technical challenges multiply: How should we characterize many-body chaos? Can we see order within chaos? And, ultimately, how can we make predictions (statistical, by necessity) for observables in chaotic systems?
In the first lecture we will give a rapid review of some of the essential features of classical chaos, illustrated with canonical examples of simple chaotic systems: the baker’s map, the Lorenz system, and pinball scattering. In the second lecture we will discuss some of the recent developments in quantum many-body chaos, including: out-of-time-order correlators and bounds on quantum chaos, chaos in black holes, and the Sachdev-Ye-Kitaev model.
About the lecturer
Vladimir Rosenhaus is a member at the Institute for Advanced Study, and Assistant Professor of Physics at the Graduate Center, CUNY (starting Fall 2020). He has worked on problems at the interface of quantum field theory, gravity, and chaos.
Vladimir can be reached with questions and comments at vladr@ias.edu