THE FIRST AND SECOND MOMENTS FOR THE QUANTUM BROWNIAN PLANAR ROTATOR IN EXTERNAL HARMONIC CLASSICAL FIELD

Abstract

We derive explicit expressions for the first and second moments as well as the correlation function for a planar (one-dimensional) quantum Brownian rotator placed in the external harmonic potential. Our results directly provide the standard deviations for the azimuthal angle and the canonically conjugate angular momentum for the rotator. We find that there are some significant physical differences between this model and the free rotator model, which is well investigated in the literature. HIGHLIGHTS Expressions were derived for the first and second moments, and the correlation function for a planar (one-dimensional) quantum Brownian rotator placed in the external harmonic potential. In comparison with the well-known free Brownian rotator, we observe the existence of the stationary state in the asymptotic limit (). Significantly smaller standard deviations and the correlation-function for the rotator exerted to the external harmonic potential we established.