Abstract
Classical conservative systems that undergo a transition to chaos have very complex dynamical behavior, as we have seen in previous chapters. How much of this complex behavior remains in the corresponding quantum systems? That is the question we address in much of the remainder of this book. An essential new result has emerged: quantum systems, whose classical counterpart is chaotic, have spectra whose statistical properties are similar to those of random matrices that extremize information. Thus, any study of the quantum manifestations of chaos requires an analysis of information content of quantum systems using concepts from random matrix theory (RMT). We have attempted to give a complete grounding on random matrix theory in this book. Much of our discussion of random matrix theory is in the appendices, but we give an overview of key results in this chapter. Our analysis of quantum dynamics, the behavior of solutions of the Schrödinger equation, will actually begin in Chapter 6.
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Reichl, L.E. (2004). Random Matrix Theory. In: The Transition to Chaos. Institute for Nonlinear Science. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-4350-0_5
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