Some open questions in "wave chaos"
St\'ephane Nonnenmacher (IPHT)
TL;DR
This paper discusses unresolved questions in wave chaos, a field connecting quantum physics, mathematics, and geometry, highlighting its interdisciplinary nature and ongoing research challenges.
Contribution
It provides an overview of open problems in wave chaos, emphasizing the interdisciplinary connections and historical context of these unresolved questions.
Findings
Identification of key open questions in wave chaos
Historical perspective on unresolved issues
Connections between wave chaos and various mathematical fields
Abstract
The subject area referred to as "wave chaos", "quantum chaos" or "quantum chaology" has been investigated mostly by the theoretical physics community in the last 30 years. The questions it raises have more recently also attracted the attention of mathematicians and mathematical physicists, due to connections with number theory, graph theory, Riemannian, hyperbolic or complex geometry, classical dynamical systems, probability etc. After giving a rough account on "what is quantum chaos?", I intend to list some pending questions, some of them having been raised a long time ago, some others more recent.
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