FEATURES OF PHASE DIAGRAMS OF A TWO-FREQUENCY PENDULUM IN JAN-TELLER POTENTIAL AND HEAT CAPACITY OF WATER

Abstract

A simulation of rotational vibrations of a water molecule was carried out using a model of a two-frequency pendulum in a simple Jahn–Teller potential (JTP), which has a minimum potential at a certain angle of deviation of the pendulum from the axis (the bending angle of the intermolecular hydrogen bond of the water molecule). It has been established that at low initial speeds for a given potential a new type of oscillations is observed - transverse oscillations of the pendulum inside the circular gutter JTP, at medium speeds - two-frequency independent oscillations (IO) along two axes, and at large ones - ellipse-like oscillations (ELO) at a single frequency. The work examines phase diagrams (PD) and mixed PD (MPD) in two coordinates for these two-dimensional oscillations. A significant difference between these diagrams in the JTP and standard PD is shown. The appearance of additional ellipses, loops and waves on the PD due to the appearance of transverse vibrations in the nuclear fuel gutter was discovered. To obtain ellipses in phase diagrams from all transverse oscillations of the pendulum, it is proposed to construct a PD versus radius (PDR) for the oscillation trajectory. It is shown that ellipses on the PDR for transverse oscillations of the pendulum are clearly observed at low initial speeds, but for medium and high speeds the transverse part of speed is not independently distinguished from the total speed. The presence of stable transverse vibrations in the JTP gutter for rotational vibrations of hydrogen atoms of water molecules around the axes of intermolecular bonds can be considered as new degrees of freedom for its new collectivized transverse vibrations in this potential. Their existence may lead to an explanation for the contribution of these types of oscillations to the anomalously large heat capacity of water in the liquid phase. However, for the presence of such new degrees of freedom for transverse vibrations of water molecules, it is necessary that their vibrations always take place in the region of “small” velocities - in the JTP gutter. To do this, it is necessary to increase this range of vibrations so that the maximum value of the potential on the axis of the intermolecular bond would be large. This should ensure the existence of transverse rotational oscillations in the JTP gutter for water molecules in all liquid phase temperatures.