Title: Quantum Revivals and the Modular Group
Abstract: 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.
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