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Multifractality for Intermediate Quantum Systems by Ueberschaer, Henrik is a scholarly article available to read on EtoBox.

What is Multifractality for Intermediate Quantum Systems about?

While quantum multifractality has been widely studied in the physics literature and is by now well understood from the point of view of physics, there is little work on this subject in the mathematical literature. I will report on a proof of multifractal scaling laws for arithmetic \u{S}eba billiards. I will explain the mathematical approach to defining the Renyi entropy associated with a sequence of eigenfunctions and sketch how arithmetic methods permit us to obtain a precise asymptotic in the semiclassical regime and how this allows us to compute the fractal exponents explicitly. Moreover, I will discuss how the symmetry relation for the fractal exponent is related to the functional equation of certain zeta functions.

Author

Ueberschaer, Henrik

Published

2023

Language

EN