Biphonons in the β-Fermi-Pasta-Ulam model

Discrete breathers or intrinsic localized modes are nonlinear localized states that appear in several classical extended systems, such as for instance the Fermi-Paste-Ulam (FPU) model. In order to probe the quantum states that correspond to discrete breathers, we quantize the β-FPU model using boson quantization rules, retain only number conserving terms, and analyze the two-quanta sector of the model. For both attractive and repulsive nonlinearity, we find the occurrence of biphonons in two forms, on-site and nearest-neighbor site, and analyze their properties. We comment on the use of this model as a minimal model for extended molecular and biomolecular systems.