Vibrational resonance in the Morse oscillator

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 ω and Ω with 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. 46.40.Ff.

Vibrational resonance in a harmonically trapped potential system

“…It is important to investigate the role of shape of potentials on vibrational resonance. In this direction, the occurrence of vibrational resonance has been examined in bistable [16][17][18][21][22][23][24] , monostable [25] , asymmetric [26] , spatially periodic [27] and spatially extended single-well [28] potentials systems. It has also been analyzed in an excitable system [29] and in a system with signum nonlinearity [30] .…”

Coexistence of Multiple Attractors, Hysteresis, and Vibrational Resonance in the Classical Morse Oscillator Driven by an Amplitude Modulated Signa

“…In recent years, many studies were focused within the classical, semiclassical, and quantum mechanical methods on the Morse oscillator dynamics. In particular, Abirami et al [9] investigated recently the occurrence of a vibrational resonance in both classical and quantummechanical Morse oscillators driven by a biharmonic force. Behnia et al [10] studied the control over chaos via a slave-master feedback in the classical Morse oscillator.…”

“…Stochastic resonance [20] is one of such phenomena in which an enhancement of the signal amplitude is observed at an optimum noise intensity. It has been shown both theoretically and experimentally that the amplification of a resonance can be achieved when noise is replaced by a high-frequency periodic force, and the associated effect is called the vibrational resonance(VR) [9,16,17]. The analysis of vibrational resonances has attracted a considerable interest in recent years because of its wide variety of applications.…”

Vibrational Resonance in the Classical Morse Oscillator Driven by Narrow-Band and Wide-Band Frequency Modulated Signals

“…de Lima [32] studied the control of chaotic photodissociation in the classical driven Morse oscillator by means of bichromatic pulses. Recently, Abirami et al [33] have investigated the occurrence of vibrational resonance in both classical and quantum mechanical Morse oscillators driven by a biharmonic force. This paper is organized as follows.…”