Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chain
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chain Elena A. Korznikova 1,2 , Alina Y. Morkina 2 , Mohit Singh 3 , Anton M. Krivtsov 4,5 , Vitaly A. Kuzkin 4,5 , Vakhid A. Gani 6,7 , Yuri V. Bebikhov 8 and Sergey V. Dmitriev 1,9,a 1
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Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa 450054, Russia Ufa State Aviation Technical University, Ufa 450008, Russia Indian Institute of Technology Kharagpur, Kharagpur 721302, India Peter the Great Saint Petersburg Polytechnical University, Polytechnicheskaya Street 29, Saint Petersburg, Russia Institute for Problems in Mechanical Engineering RAS, Bolshoy pr. V.O. 61, Saint Petersburg, Russia Department of Mathematics, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow 115409, Russia Institute for Theoretical and Experimental Physics of National Research Centre “Kurchatov Institute”, Moscow 117218, Russia North-Eastern Federal University, Polytechnic Institute (branch) in Mirny, 678170 Mirny, Sakha (Yakutia), Russia Institute of Mathematics with Computing Centre, UFRC, Russian Academy of Sciences, Ufa 450008, Russia Received 2 April 2020 Published online 1 July 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. The effect of discrete breathers (DBs) on macroscopic properties of the Fermi-Pasta-Ulam chain with symmetric and asymmetric potentials is investigated. The total to kinetic energy ratio (related to specific heat), stress (related to thermal expansion), and Young’s modulus are monitored during the development of modulational instability of the zone boundary mode. The instability results in the formation of chaotic DBs followed by the transition to thermal equilibrium when DBs disappear due to energy radiation in the form of small-amplitude phonons. It is found that DBs reduce the specific heat for all the considered chain parameters. They increase the thermal expansion when the potential is asymmetric and, as expected, thermal expansion is not observed in the case of symmetric potential. The Young’s modulus in the presence of DBs is smaller than in thermal equilibrium for the symmetric potential and for the potential with a small asymmetry, but it is larger than in thermal equilibrium for the potential with greater asymmetry. Our results can be useful for setting experiments on the identification of DBs in crystals by measuring their macroscopic properties.
1 Introduction Discovery of discrete breathers (DBs), or intrinsic localized modes (ILMs) – spatially localized large-amplitude oscillatory modes in nonlinear lattices free of defects – three decades ago [1–3] has triggered extensive studies devoted to the phenomenon of vibrational energy localization [4,5]. Experimentally DBs have been excited in the physical systems of different nature, including macroscopic periodic systems [6–8], nonlinear me
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