Incoherent Inelastic Neutron Scattering data and new infrared spectra were acquired in order to examine both the external and internal vibrations in crystalline L-alanine. For the first time we observe a splitting of the NH3 + torsional band below a temperature of approximately 220 K as well as an overtone of this band. The intensity of both of these bands is strongly dependent on temperature. Birefringence and depolarization measurements performed with single crystals reveal a subtle breaking of symmetry around 220 K perhaps involving the hydrogen bond networks. We show that this instability cannot, however, be the origin of the observed splitting. Instead, the anomalous temperature dependence of the observed intensity and frequency of the torsional mode and its overtone may be explained on the basis of a nonlinear coupling of the NH3 + oscillator with lattice phonons. This leads to localization of vibrational energy, a so-called “breather” or “vibrational polaron”.

Abstract. An "exact discretization" of the Schrödinger operator is considered and its direct and inverse scattering problems are solved. It is shown that a differential-difference nonlinear evolution equation depending on two arbitrary constants can be solved by using this spectral transform and that for a special choice of the constants it can be considered an integrable discretization of the KdV equation at large times. An integrable difference-difference equation is also obtained.