String Theory Journal Club

Understanding the time evolution of quantum operators is hardly a new topic in physics. In fact, for simple systems such as the harmonic oscillator this is a problem reserved for undergraduate students. However, what happens when we consider more complex systems that are, for example, described by many body dynamics or QFTs? How can we approach the same type of problem in the case of chaotic theories for which the tools at our disposal are limited? In my talk I will discuss a general method, called the Lanczos algorithm, which allows us to make progress in these directions by providing us with a clever way of decomposing a quantum operator in a convenient basis. I will then show that for systems with symmetry we can obtain analytical results for an operator at arbitrary times by combining the Lanczos algorithm with the formalism of coherent states. This turns out to be an efficient way of treating chaotic systems (and not only!), since it makes information about the operator evolution that is generally difficult to access readily available. In this sense we obtain a way to "tame" quantum chaos through symmetry considerations.