Abstract
We describe the connection between quantum systems which have a chaotic classical counterpart and random matrix theory. As is well-known, it consists in the fact that the statistical properties of the spectra of such systems in the semiclassical limit are equivalent to those of random matrix theory. Here, we first briefly review some properties of random matrices, and then proceed to justify the above-mentioned connection in two different ways: First, according to the classic work of Berry, we show how the result can be derived from periodic orbit theory, of which we give a rapid overview; second, we show how the same result can be obtained with greater generality but in a more speculative manner using the concept of structural invariance.
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