2017/11/03 by Kaïs Ammari, Gilles Lebeau, Ammari, Kaïs +1
Mathematics · Physics and Astronomy · #35A08 #35C05 #35L05 #35R02 #Acoustics #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Bethe ansatz #Bethe lattice #Biology #Condensed matter physics #Evolutionary biology #FOS: Mathematics #Function (biology) #Lattice (music) #Mathematical physics #Mathematics #Physics #Quantum chaos and dynamical systems #Quantum electrodynamics #Spectral Theory in Mathematical Physics #math.AP #msc:35A08 #msc:35C05 #msc:35L05 #msc:35R02
paper · pdf · doi:10.48550/arxiv.1711.01363
arxiv created 2017/11/03 · openalex publication_date 2017/11/03 · arxiv updated 2017/11/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we compute an explicit analytic expression for the Green function of the wave operator on the 2-regular lattice called the "Bethe lattice" equipped with its standard metric. In particular, we exhibit a phenomena of abnormal speed of propagation for waves: the effective speed of propagation of energy for large time is c_*=2√ 2/3 <1, and there exists a true propagation at any speed c