2020/10/26 by Víctor Arnaiz, Arnaiz, Víctor, Fabricio Macià +1 · 1 citation
Computer Science · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #Spectral Theory (math.SP) #Spectroscopy and Quantum Chemical Studies
paper · pdf · doi:10.48550/arxiv.2010.13436
openalex publication_date 2020/10/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We characterize quantum limits and semi-classical measures corresponding to sequences of eigenfunctions for systems of coupled quantum harmonic oscillators with arbitrary frequencies. The structure of the set of semi-classical measures turns out to depend strongly on the arithmetic relations between frequencies of each decoupled oscillator. In particular, we show that as soon as these frequencies are not rational multiples of a fixed fundamental frequency, the set of semi-classical measures is not convex and therefore, infinitely many measures that are invariant under the classical harmonic oscillator are not semi-classical measures.