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.

Graphical abstract

中文翻译：

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离散呼吸对费米-帕斯塔-乌拉姆链宏观性质的影响

摘要

研究了离散通气（DBs）对具有对称和不对称电势的Fermi-Pasta-Ulam链的宏观性能的影响。在区域边界模式的调制不稳定性的发展过程中，要监视总动能比（与比热有关），应力（与热膨胀有关）和杨氏模量。这种不稳定性导致混沌DB的形成，随后当DB以能量的形式以小振幅声子的形式辐射而消失时，DB过渡到热平衡。发现对于所有考虑的链参数，DB降低了比热。当电位不对称时，它们会增加热膨胀，并且正如预期的那样，在对称电位的情况下不会观察到热膨胀。对于对称电势和具有较小不对称性的电势，在存在DB的情况下，杨氏模量小于在热平衡状态下的对称性，但对于具有较大不对称性的电势，其杨氏模量则大于在热平衡状态下的模量。我们的结果对于通过测量晶体的宏观性质来进行鉴定晶体中DB的实验很有用。

图形概要