If we start with a quantum system in a particular state and let it evolve undisturbed according to the rules of quantum mechanics, usually it will not return to its initial state. However, there are exceptions, for example a simple harmonic oscillator. More generally the existence of such quantum revivals is associated with an infinite-dimensional algebra which generates the spectrum of the hamiltonian. Important examples are rational conformal field theories in two and higher dimensions. I discuss these in detail and show how an action of the modular group implies a complicated time-dependence for the return amplitude, including incomplete revivals at all rational multiples of the fundamental frequency.
In a quantum quench, system is prepared in some initial state (usually the ground state of some hamiltonian) and then allowed evolve in isolation with a different hamiltonian, for example, by rapidly quenching a parameter. This is most interesting for many-body systems where one can ask questions such as whether subsystems reach a stationary state, whether this state appears thermal, and how quickly does it reach this state. Although an obvious set of problems, they have only recently come to the fore with possibility of performing such experiments in ultra-cold atoms and other systems. In this talk I will try to address these questions in the context of some simple, and not-so-simple exactly solvable models.
Physicist Juan Maldacena of the Institute for Advanced Study will visit the University of Kentucky Friday and will deliver the 2014 van Winter Memorial Lecture in Mathematical Physics.
