Vibrational Resonance in the Morse Oscillator
arXiv:1304.3988 · doi:10.1007/s12043-013-0546-z
Abstract
We investigate the occurrence of vibrational resonance in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. The biharmonic force consists of two forces of widely different frequencies ωand Ωwith Ω>>ω. In the damped and biharmonically driven classical Morse oscillator applying a theoretical approach we obtain an analytical expression for the response amplitude at the low-frequency ω. We identify the conditions on the parameters for the occurrence of the resonance. The system shows only one resonance and moreover at resonance the response amplitude is 1/(dω) where d is the coefficient of linear damping. When the amplitude of the high-frequency force is varied after resonance the response amplitude does not decay to zero but approaches a nonzero limiting value. We have observed that vibrational resonance occurs when the sinusoidal force is replaced by a square-wave force. We also report the occurrence of resonance and anti-resonance of transition probability of quantum mechanical Morse oscillator in the presence of the biharmonic external field.
21 pages, 10 figures