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Dynamics, stability analysis and quantization of β-Fermi–Pasta–Ulam lattice

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Abstract

We study the well-known one-dimensional problem of N particles with nonlinear interaction. The β-Fermi–Pasta–Ulam model is the special case of quadratic and quartic interaction potential among nearest neighbours. We enumerate and classify the simple periodic orbits for this system and find the stability zones, employing Floquet theory. We quantize the nonlinear normal modes and construct a wavefunction for what we believe is a primitive nonlinear analogue of a ‘phonon’.

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Acknowledgements

This work was carried out under the collaboration scheme between Bhabha Atomic Research Centre and University of Pune. The authors thank Avinash Khare for important discussions and Aniruddha Kibey for his assistance and time.

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Authors and Affiliations

  1. Department of Physics, University of Pune, Pune, 411 007, India

    RUPALI L SONONE

  2. Nuclear Physics Division, Bhabha Atomic Research Centre, Mumbai, 400 085, India

    SUDHIR R JAIN

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  1. RUPALI L SONONE
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Correspondence to RUPALI L SONONE.

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SONONE, R.L., JAIN, S.R. Dynamics, stability analysis and quantization of β-Fermi–Pasta–Ulam lattice. Pramana - J Phys 83, 925–944 (2014). https://doi.org/10.1007/s12043-014-0829-z

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  • DOI: https://doi.org/10.1007/s12043-014-0829-z

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