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Biphonons in the $$\beta$$-Fermi-Pasta-Ulam model. (English) Zbl 1126.82023
The quantization of the beta-FPU model with boson quantization rules and the analysis of the two quanta sector within the boson conserving approximation leads to the appearance of biphonons. These states may be considered, as the lowest states arising from the acoustic nonlineanty of the Hamiltonian and may be thought of as quantum counterparts of the classical FPU discrete breathers. Analytical calculations showed that two types of states may appear within the two-quanta sector, corresponding to on-site biphonons as well as adjacent-site biphonons. The latter states have higher energy than former ones, as expected. The presence of two types of biphonons may result in higher mobility for the two-quanta states compared with the case, where only a single on-site two-boson state existed. The analysis shows that biphonon states appear in the number conserving beta-FPU model below the band of free two-phonon states in the case of attractive nonlinearity; while for repulsive nonlinearity they appear above the free band. It is found that both attraction and repulsion may lead to effective binding of single quanta states.

##### MSC:
 82C20 Dynamic lattice systems (kinetic Ising, etc.) and systems on graphs in time-dependent statistical mechanics
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