Abstract
A nonlinear chain with sixth-order polynomial on-site potential is used to analyze the evolution of the total-to-kinetic-energy ratio during development of modulational instability of extended nonlinear vibrational modes. For the on-site potential of hard-type (soft-type) anharmonicity, the instability of \(q =\pi \) mode (\(q = 0\) mode) results in the appearance of long-living discrete breathers (DBs) that gradually radiate their energy and eventually the system approaches thermal equilibrium with spatially uniform and temporally constant temperature. In the hard-type (soft-type) anharmonicity case, the total-to-kinetic-energy ratio is minimal (maximal) in the regime of maximal energy localization by DBs. It is concluded that DBs affect specific heat of the nonlinear chain, and for the case of hard-type (soft-type) anharmonicity, they reduce (increase) the specific heat.
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Acknowledgements
The work of E.A.K. was supported by the Grant of the President of the Russian Federation for State support of young Russian scientists (No. MD-3639.2019.2). The work of D.X. is supported by NNSF (Grant No. 11575046) of China, NSF (Grant No. 2017J06002) of Fujian Province of China. The work of V.A.G. was supported by the MEPhI Academic Excellence Project. S.V.D. acknowledges the support of the Russian Foundation for Basic Research, Grant No. 19-02-00971. The work was partly supported by the State assignment of IMSP RAS No. AAAA-A17-117041310220-8. The work of O.B.N. was supported by the State Assignement of ICMM UB RAS, Government Contract No. AAAA-A19-119013090021-5.
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Communicated by Ram Ramaswamy.
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Singh, M., Morkina, A.Y., Korznikova, E.A. et al. Effect of Discrete Breathers on the Specific Heat of a Nonlinear Chain. J Nonlinear Sci 31, 12 (2021). https://doi.org/10.1007/s00332-020-09663-4
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DOI: https://doi.org/10.1007/s00332-020-09663-4
Keywords
- Crystal lattice
- Nonlinear chain
- Modulational instability
- Discrete breather
- Intrinsic localized mode
- Heat capacity
- Specific heat