The quasi-equilibrium phase of nonlinear chains

Linearity stabilizes discrete breathers

“…When α = 0, β = 1, such a perturbation results in both a stable propagating compression pulse (solitary wave), and an identical and opposite propagating dilation pulse (anti-solitary wave). The solitary and anti-solitary waves interact among themselves and with the boundaries leading to the eventual formation of an equilibrium-like state with excitations made up of a Gaussian energy distributed collection of only solitary and anti-solitary waves and hence with sustained large energy fluctuations [35][36][37]. In all our studies with α = 1 and β = 0, 1, the system eventually slipped into a state where energy is equipartitioned.…”

“…In an earlier study, we have reported about the dynamics of systems described by eq. (2) when perturbed by a δ-function velocity perturbation imparted to any particle at an initial time t = 0 [36]. Velocity perturbations lead to very different system dynamics compared to that seen when the dynamics is initiated by displacement perturbations (see below).…”

“…Velocity perturbations lead to very different system dynamics compared to that seen when the dynamics is initiated by displacement perturbations (see below). We explored the system dynamics for both periodic boundary conditions and fixed boundary conditions [36]. In the former case, v 1 = v N +1 while, in the latter case, the particle velocities were simply reversed during collisions with a boundary.…”

“…For α = 0, β = 1, the bond vibration(s) can be identified as DBs and are localized and sustained across many decades in time with the system eventually beginning to slip into an equilibrium-like state with the qualification that the excitations in this state are comprised of solitary and anti-solitary waves (as opposed to harmonic modes). We have referred to this kind of state which may show unusually large kinetic energy (and hence temperature) fluctuations, as the quasiequilibrium state [19,26,[34][35][36][37][38]. Dynamics of the system when α = 1, β = 1 is a well-studied problem [1,5,6,13,[34][35][36][37][38].…”

“…Much theoretical, simulational and experimental work has been done in the context of unloaded, discrete granular systems in acoustic vacua [22][23][24][25][26][27][28][29][30]. In 1D, these systems admit solitary waves, allow the formation of secondary solitary waves when solitary waves collide [31][32][33][34] and exhibit the recently suggested quasiequilibrium phase in finite systems [35][36][37][38].…”