ABSTRACT
We present a nonlinear model that allows exploration of the relationship between energy relaxation, thermal conductivity and the excess of low-frequency vibrational modes (LFVMs) that are present in glasses. The model is a chain of the Fermi-Pasta-Ulam (FPU) type, with nonlinear second neighbour springs added at random. We show that the time for relaxation is increased as LFVMs are removed, while the thermal conductivity diminishes. These results are important in order to understand the role of the cooling speed and thermal conductivity during glass transition. Also, the model provides evidence for the fundamental importance of LFVMs in the FPU problem.
ABSTRACT
Glasses exist because they are not able to relax in a laboratory time scale toward the most stable structure: a crystal. At the same time, glasses present low-frequency vibrational-mode (LFVM) anomalies. We explore in a systematic way how the number of such modes influences thermal relaxation in one-dimensional models of glasses. The model is a Fermi-Pasta-Ulam chain with nonlinear springs that join second neighbors at random, which mimics the adding of bond constraints in the rigidity theory of glasses. The corresponding number of LFVMs decreases linearly with the concentration of these springs, and thus their effect upon thermal relaxation can be studied in a systematic way. To do so, we performed numerical simulations using lattices that were thermalized and afterwards placed in contact with a zero-temperature bath. The results indicate that the time required for thermal relaxation has two contributions: one depends on the number of LFVMs and the other on the localization of modes due to disorder. By removing LFVMs, relaxation becomes less efficient since the cascade mechanism that transfers energy between modes is stopped. On the other hand, normal-mode localization also increases the time required for relaxation. We prove this last point by comparing periodic and nonperiodic chains that have the same number of LFVMs.
