2014/01/31 by Juan G. Restrepo, James D. Meiss
Computer Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Classical mechanics #Condensed matter physics #Coupling (piping) #Coupling strength #Hamiltonian (control theory) #Inertia #Materials science #Mathematics #Mean field theory #Mechanics #Nonlinear Dynamics and Pattern Formation #Physics #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Statistical physics #cond-mat.stat-mech #nlin.CD
paper · pdf · doi:10.1103/physreve.89.052125
published as Phys. Rev. E 89: 052125 (2014) · 5 pages, 5 figures
arxiv created 2014/05/12 · openalex publication_date 2014/05/19 · arxiv updated 2014/06/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the Hamiltonian mean field (HMF) model of coupled Hamiltonian rotors with a heterogeneous distribution of moments of inertia and coupling strengths. We show that when the parameters of the rotors are heterogeneous, finite-size fluctuations can greatly modify the coupling strength at which the incoherent state loses stability by inducing correlations between the momenta and parameters of the rotors. When the distribution of initial frequencies of the oscillators is sufficiently narrow, an analytical expression for the modification in critical coupling strength is obtained that confirms numerical simulations. We find that heterogeneity in the moments of inertia tends to stabilize the incoherent state, while heterogeneity in the coupling strengths tends to destabilize the incoherent state. Numerical simulations show that these effects disappear for a wide, bimodal frequency distribution.