1999/09/17 by K. Ø. Rasmussen, Thierry Cretegny, T. Cretegny +3 · 2 citations
Computer Science · Mathematics · Physics and Astronomy · #Classical mechanics #Discontinuity (linguistics) #Hamiltonian (control theory) #Hamiltonian mechanics #Mathematical analysis #Mathematics #Nonlinear Dynamics and Pattern Formation #Nonlinear Photonic Systems #Nonlinear system #Partition function (quantum field theory) #Phase space #Phase transition #Physics #Quantum chaos and dynamical systems #Quantum mechanics #Quantum statistical mechanics #Statistical mechanics #Statistical physics #cond-mat.stat-mech #nlin.PS #patt-sol
paper · pdf · doi:10.1103/physrevlett.84.3740
published as Phys. Rev. Lett. 84, 3740 (2000). · 4 pages, 3 figures
arxiv created 1999/09/17 · openalex publication_date 2000/04/24 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is demonstrated to manifest itself in the creation of breatherlike localized excitations. Interrelation between the statistical mechanics and the nonlinear dynamics of the system is explored numerically in both regimes.