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Vibrational resonance in the Morse oscillator

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Abstract

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 ≫ 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.

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Acknowledgements

KA acknowledges the support from University Grants Commission (UGC), India in the form of UGC-Rajiv Gandhi National Fellowship. Financial support from the Spanish Ministry of Science and Innovation under Project No. FIS2009-09898 is acknowledged by MAFS.

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Authors and Affiliations

  1. School of Physics, Bharathidasan University, Tiruchirapalli, 620 024, India

    K ABIRAMI & S RAJASEKAR

  2. Nonlinear Dynamics, Chaos and Complex Systems Group, Departamento de Física, Universidad Rey Juan Carlos, Tulipán s/n, 28933, Móstoles, Madrid, Spain

    M A F SANJUAN

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  1. K ABIRAMI
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  2. S RAJASEKAR
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  3. M A F SANJUAN
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Correspondence to S RAJASEKAR.

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ABIRAMI, K., RAJASEKAR, S. & SANJUAN, M.A.F. Vibrational resonance in the Morse oscillator. Pramana - J Phys 81, 127–141 (2013). https://doi.org/10.1007/s12043-013-0546-z

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  • DOI: https://doi.org/10.1007/s12043-013-0546-z

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