# Authorisation

# IRREVERSIBLE DYNAMICS OF THE ANGULAR MOMENTUM OF A QUANTUM PENDULUM

Author: Archil UgulavaCo-authors: Z. Toklikishvili, S. Chkhaidze

Keywords: quantum pendulum; irreversibility of motion

Annotation:

The dynamics of the quantum pendulum, described by the Mathieu-SchrÃ¶dinger equation, which has symmetries of the Klein quadruple group, is considered. The dependence of the average value and quantum fluctuations of the angular momentum on the problem parameter (the length of the pendulum filament) for different symmetry groups is studied. It is shown that the mean values of the pulse moments for nondegenerate quantum states (the symmetry region of the quadruple group) tend to zero, and the mean-square fluctuations for the same states are non-zero and, therefore, overlap the mean values. In the region of fluctuation overlap, different quantum states become indistinguishable. In this case, quantum fluctuations play the role of those small errors in the initial conditions from which dynamic stochasticity grows and the irreversibility of motion is formed when considering classical systems. Therefore, it can be argued that the mean value of the angular momentum is irreversible with respect to changing the direction of the parameter.