Quantum Limits of Eisenstein Series and Scattering states
Yiannis N. Petridis, Nicole Raulf, Morten S. Risager
TL;DR
This paper investigates the asymptotic behavior of scattering states on the modular surface, revealing quantum limits of Eisenstein series and extending quantum ergodicity results.
Contribution
It introduces new insights into quantum limits of Eisenstein series and broadens the stability range of quantum unique ergodicity for scattering states.
Findings
Quantum limits of scattering states identified
Extended stability range for quantum unique ergodicity
Analysis of Eisenstein series away from the critical line
Abstract
We identify the quantum limits of scattering states for the modular surface. This is obtained through the study of quantum measures of non-holomorphic Eisenstein series away from the critical line. We provide a range of stability for the quantum unique ergodicity theorem of Luo and Sarnak.
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