Low-lying excitation spectrum of quantum anharmonic crystals

We analyze the low-lying excitation spectrum of some quantum anharmonic crystals. We determine the one-particle and two-particle bound state masses, and investigate the effects in the spectrum due to the anharmonicity and non-locality in the interaction. For the space dimension d=1, we show that, by increasing the non-locality in the anharmonic term, a bound state may appear even for the potential with positive coefficients. Moreover, for the case of the potential with a negative quartic coefficient, we show that we may have an interesting crossover phenomenon: the two-particle bound state mass may become smaller than the one-particle mass. Our results involve a perturbative analysis: e.g., for the computation of the bound state mass, we study the Bethe-Salpeter equation in a ladder approximation. We give some results for d>1 and comment on the reliability of the perturbative analysis