Long range interactions enhance global stability in 1-D Hamiltonian lattices (T. Bountis, 10/1/2023)
Channel: Academy of Athens
Date: 17/05/2023

Tassos Bountis
CRANS-Center for Research and Applications in Nonlinear Systems, University of Patras

Abstract: Local and global stability properties of 1-D Hamiltonian lattices of N interacting particles have been studied extensively, in view of their important implications to many problems of mathematical physics [1]. A wealth of important results published since the pioneering numerical results of Fermi, Pasta, Ulam and Tsingou (FPUT) in the early 1950’s, have greatly enhanced our understanding of such lattices in the case of nearest neighbor interactions. On the other hand, the importance of long-range forces to statistical physics has also been pointed out in many works (see for example [2]). 

More recently, the non-extensive statistical analysis of FPUT 1-D lattices has revealed that long-range forces increase the global stability of the dynamics and lead to a novel view of their phase transition diagram [3,4]. In the last few years, this has further been supported by studies of the remarkable supratransmission phenomenon, where the first particle of a 1-D lattice is subjected to sinusoidal forcing: The critical amplitude for destabilizing the system increases as the interaction range goes to zero, except in the presence of local potentials!