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Variation of the Specific Heat in the Fermi–Pasta–Ulam Chain due to Energy Localization

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Abstract

The influence of discrete breathers (DBs) on the macroscopic properties of the Fermi–Pasta–Ulam chain with symmetric and asymmetric single-well potentials is investigated. The ratio of the total energy to the kinetic energy (which determines the specific heat) was monitored during the development of modulation instability of the short-wavelength vibrational mode with the wavenumber at the boundary of the Brillouin zone. Instability leads to the formation of chaotic DBs with subsequent transition to thermal equilibrium when DBs disappear due to the emission of energy in the form of low-amplitude phonons. The localization parameter, the number of DBs in the chain, and the average energy per one DB are given as functions of time. The number of DBs is close to the maximum at the point in time when the energy localization parameter reaches its maximum. It is found that DBs reduce the heat capacity for all considered parameters of the chain potential. This is due to the fact that the chain under consideration has a hard type of anharmonicity, at which the DB frequency increases with an increase in the amplitude. In the energy localization regime, the DB oscillation frequencies increase, which leads to an increase in the particle velocities and, accordingly, in their kinetic energy. An increase in the kinetic energy in the presence of DBs in the chain leads to a decrease in the ratio of total energy to kinetic energy, that is, to a decrease in the specific heat capacity. In chains with soft anharmonicity, the DB frequency decreases with an increase in the amplitude, and the opposite effect is obtained, i.e., DBs increase the heat capacity in this case. The obtained results can be useful for setting up experiments on the identification of discrete breathers in crystals by measuring their macroscopic properties.

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Funding

This work was supported by the Russian Science Foundation (project no. 21-12-00229).

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Authors and Affiliations

  1. Center for Design of Functional Materials, Ufa University of Science and Technology, 450008, Ufa, Russia

    A. Yu. Morkina, E. A. Korznikova & S. V. Dmitriev

  2. Indian Institute of Technology Kharagpur, 721302, Kharagpur, India

    M. Singh

  3. Mirnyi Polytechnic Institute, Branch of North-Eastern Federal University, 678174, Mirnyi, Russia

    Yu. V. Bebikhov

  4. Institute of Molecule and Crystal Physics, UFRC of Russian Academy of Sciences, 450001, Ufa, Russia

    S. V. Dmitriev

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  1. A. Yu. Morkina
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Morkina, A.Y., Singh, M., Bebikhov, Y.V. et al. Variation of the Specific Heat in the Fermi–Pasta–Ulam Chain due to Energy Localization. Phys. Solid State 64, 446–454 (2022). https://doi.org/10.1134/S1063783422090050

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