Ground states of coupled nonlinear oscillator systems

Abstract The dynamics of coupled nonlinear oscillator systems is often described by the classical discrete Schrodinger equation (DNLSE). In its simplest version, DNLSE made up two terms—a nearest-neighbor hopping term and an on-site cubic term. Each terms preceded a coefficient that can take on either positive or negative sign. versions derived from corresponding equivalent Hamiltonian. result small family four Hamiltonian, each with own associated ground state, all indeed scattered in myriad scientific publications. Here we present comprehensive picture for states systems, summarize existing results provide new insights. First classify Hamiltonians into pairs according to sign term—a “positive/negative Hamiltonian pair” if positive/negative respectively. Ground pair are plane waves ferromagnetic-like antiferromagnetic-like configuration, depending unstaggered staggered site-centered breathers. instantaneous state system set one-parameter complex functions amplitude phase. We show except phase, maximum energy sign-reversed (negative/positive) Next discuss some properties positive-Hamiltonian pair—entropy, temperature, correlations stability. extend our stability discussion include excited waves. propose engineer specific perturbation preserves both density energy—the conserved quantities system—and test wave's based entropy change. under such conserved-quantities-preserved perturbation, entropy-unstable. For breathers—the negative-Hamiltonian pair—we have divided nonlinearity ranges wrote very good analytic approximations breathers range. Lastly, dedicated section, briefly implementation fields magnetism, optics, ultracold atoms, emphasizing states. example, following 2002 article, 1d optically-trapped bosonic rather wide range densities nonlinearities, be particular version here-discussed DNLSEs.