Regular Article

Effect of discrete breathers on macroscopic properties of the Fermi-Pasta-Ulam chain

¹ Institute of Molecule and Crystal Physics, Ufa Federal Research Centre of the Russian Academy of Sciences, Ufa 450054, Russia
² Ufa State Aviation Technical University, Ufa 450008, Russia
³ Indian Institute of Technology Kharagpur, Kharagpur 721302, India
⁴ Peter the Great Saint Petersburg Polytechnical University, Polytechnicheskaya Street 29, Saint Petersburg, Russia
⁵ Institute for Problems in Mechanical Engineering RAS, Bolshoy pr. V.O. 61, Saint Petersburg, Russia
⁶ Department of Mathematics, National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), Moscow 115409, Russia
⁷ Institute for Theoretical and Experimental Physics of National Research Centre “Kurchatov Institute”, Moscow 117218, Russia
⁸ North-Eastern Federal University, Polytechnic Institute (branch) in Mirny, 678170 Mirny, Sakha (Yakutia), Russia
⁹ Institute of Mathematics with Computing Centre, UFRC, Russian Academy of Sciences, Ufa 450008, Russia

^a e-mail: dmitriev.sergey.v@gmail.com

Received: 2 April 2020
Published online: 1 July 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.