Quantized breather excitations of Fermi-Pasta-Ulam lattices.

We have calculated the lowest energy quantized breather excitations of both the β and the α Fermi-Pasta-Ulam monoatomic lattices and the diatomic β lattice within the ladder approximation. While the classical breather excitations form continua, the quantized breather excitations form a discrete hierarchy labeled by a quantum number n. Although the number of phonons is not conserved, the breather excitations correspond to multiple bound states of phonons. The n=2 breather spectra are composed of resonances in the two-phonon continuum and of discrete branches of infinitely long-lived excitations. The nonlinear attributes of these excitations become more pronounced at elevated temperatures. The calculated n=2 breather and the resonance of the monoatomic β lattice hybridize and exchange identity at the zone boundary and are in reasonable agreement with the results of previous calculations using the number-conserving approximation. However, by contrast, the breather spectrum of the α monoatomic lattice couples resonantly with the single-phonon spectrum and cannot be calculated within a number-conserving approximation. Furthermore, we show that for sufficiently strong nonlinearity, the α lattice breathers can be observed directly through the single-phonon inelastic neutron-scattering spectrum. As the temperature is increased, the single-phonon dispersion relation for the α lattice becomes progressively softer as the lattice instability is approached. For the diatomic β lattice, it is found that there are three distinct branches of n=2 breather dispersion relations, which are associated with three distinct two-phonon continua. The two-phonon excitations form three distinct continua: One continuum corresponds to the motion of two independent acoustic phonons, another to the motion of two independent optic phonons, and the last continuum is formed by propagation of two phonons that are one of each character. Each breather dispersion relation is split off the top from of its associated continuum and remains within the forbidden gaps between the continua. The energy splittings from the top of the continua rapidly increase, and the dispersions rapidly decrease with the decreasing energy widths of the associated continua. This finding is in agreement with recent observations of sharp branches of nonlinear vibrational modes in NaI through inelastic neutron-scattering measurements. Furthermore, since the band widths of the various continua successively narrow as the magnitude of their characteristic excitation energies increase, the finding is also in agreement the theoretical prediction that breather excitations in discrete lattices should be localized in the classical limit.