Entropy of logarithmic modes

2021/02/26 by Eswarathasan, Suresh
#Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory (math.SP)

paper · doi:10.48550/arxiv.2102.13528

Abstract

Let (M,g) be a compact, boundaryless, Riemannian manifold whose geodesic flow on its unit sphere bundle is Anosov. Consider the (semiclassical) Laplace-Beltrami operator on M. Let ε>0. We study the semiclassical measures μ_sc of quasimodes spectrally supported in intervals of width ε(h)/(|log h|), a critical-type regime when considering ``delocalization". We derive a lower bound for the Kolmogorov-Sinai entropy of μ_sc that depends explicitly on ε, in the spirit of that given by Ananthamaran-Koch-Nonnenmacher.

Related

• Entropy of chaotic eigenstates
• Entropy of eigenfunctions
• Entropy rigidity for 3D conservative Anosov flows and dispersing billiards
• The logarithmic entropy formula for the linear heat equation on Riemannian manifolds
• Entropies of compact strictly convex projective manifolds