Biphonons in the -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.