Disordered FPUT-α Hamiltonian Lattices: Recurrence breakdown and chaotic behavior

This paper studies a modified Fermi–Pasta–Ulam-Tsingou (FPUT)-$\alpha$ Hamiltonian lattice, where variability is introduced to the system through the potential parameters. By a transformation, the system is equivalent to the FPUT-$\alpha$ lattice with random masses. We fix the energy level and investigate how energy recurrences disappear as the percentage of variability increases from zero. We observe that the disappearance of energy recurrences leads to either localization or thermalization of normal-mode energy. When energy localization occurs, we derive a two-mode system by using multiple-scale expansions to explain the route to localization as the percentage of variability increases. Furthermore, we investigate the chaotic behavior of the system by computing the maximum Lyapunov exponent for different percentages of variability. Our results show that the number of particles increases the chances of observing chaotic dynamics for small percentages of variability. Meanwhile, the effect reverses as the percentage of variability introduced to the system rises from zero.