One aspect of this project dealt with the response of a system to an injection of energy. It is generally believed that after sufficient time, this energy spreads all over the system and heats it up uniformly - in a process called thermalization. Remarkably this common process is very poorly understood from first principles. In this project recent ideas which arose in String Theory have been used to uncover universal aspects of this dissemination of energy, i.e. aspects which are common to a large variety of systems. In particular we understood the mechanism behind a conjectured universal behavior when such energy injection happens near a phase transition.

A second aspect of this project dealt with the understanding of certain physical processes in cosmology which are special to situations when the universe is accelerating. Our universe is known to be of this kind. However it is rather puzzling to formulate the laws of physics in the simplest version of such a universe called de Sitter space. In this project, some of these questions were addressed by using a recently proposed novel description of physics in a de Sitter universe.

The project also investigated the fundamental question of whether it is possible for an object with minimal energy to move.  Normally, because of the usual relation between energy and velocity, this would not be possible. But by considering a modified relation, it was demonstrated that there are interesting systems - dubbed "time crystals" - where motion occurs even when the energy is minimized.  This is a form of perpetual motion, although no energy can be extracted from the system since it is already in a state of minimum energy.  Applications to condensed matter systems and cosmology are currently being explored.  It is possible that the Big Bang itself can be viewed as a time crystal.

A further investigation concerned the properties of the theories that describe scale-invariant systems in two dimensions.  Scale invariant systems arise in the vicinity of phase transitions, like the transition from a ferromagnet to a non-magnetic material, which occurs at a particular critical value of the temperature.  Generally, one finds that certain quantities (like the magnetization) behave in an especially simple way as the critical point is approached.  This work was able to put rigorous limits on how rapidly those quantities can change near the critical point.  These results are important because of their generality; they apply to an extremely broad class of phase transitions. 

The project had significant broader impacts. Two graduate students and  two postdocs received training during the execution of the project.  Seminars and lectures on these works at various institutions around the world helped to promote scientific culture. Some of the results of these investigations were reported in news articles in various media outlets, including Nature, Scientific American, Science News, New Scientist, Wired, and MSNBC. 

Last Modified: 10/30/2013
Modified by: Alfred Shapere