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Morse oscillator; biharmonic force; vibrational resonance.

The occurrence of vibrational resonance is investigated 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 $𝛺 \gg 𝜔$. In the damped and biharmonically driven classical Morse oscillator, by applying a theoretical approach, an analytical expression is obtained for the response amplitude at the low-frequency 𝜔. Conditions are identified on the parameters for the occurrence of 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. It is observed that vibrational resonance occurs when the sinusoidal force is replaced by a square-wave force. The occurrence of resonance and antiresonance of transition probability of quantum mechanical Morse oscillator is also reported in the presence of the biharmonic external field.

K Abirami¹ S Rajasekar¹ M A F Sanjuan²

1. School of Physics, Bharathidasan University, Tiruchirapalli 620 024, India
2. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933 Móstoles, Madrid, Spain

Manuscript received

21 June 2012

Manuscript revised

8 February 2012

Accepted

26 February 2013