Dynamics of coupled modes for sliding particles on a fluctuating landscape

Abstract

The recently developed formalism of nonlinear fluctuating hydrodynamics (NLFH) has been instrumental in unraveling many new dynamical universality classes in coupled driven systems with multiple conserved quantities. In principle, this formalism requires knowledge of the exact expression of locally conserved current in terms of local density of the conserved components. However, for most nonequilibrium systems an exact expression is not available and it is important to know what happens to the predictions of NLFH in these cases. We address this question for the first time here in a system with coupled time evolution of sliding particles on a fluctuating energy landscape. In the disordered phase this system shows short-ranged correlations, this system shows short-ranged correlations, the exact form of which is not known, and so the exact expression for current cannot be obtained. We use approximate expressions based on mean-field theory and corrections to it, to test the prediction of NLFH using numerical simulations. In this process we also discover important finite size effects and show how they affect the predictions of NLFH. We find that our system is rich enough to show a large variety of universality classes. From our analytics and simulations we have been able to find parameter values which lead to diffusive, Kardar-Parisi-Zhang (KPZ), 5/3 Lévy and modified KPZ universality classes. Interestingly, the scaling function in the modified KPZ case turns out to be close to the Prähofer-Spohn function which is known to describe usual KPZ scaling. Our analytics also predict the golden mean and the 3/2 Lévy universality classes within our model but our simulations could not verify this, perhaps due to strong finite size effects.

A lattice Gas Model for Generic One-Dimensional Hamiltonian Systems

“…where J is the current Jacobian (17). The matrix product J K is symmetric as has been proved in [16], thus linking the purely static compressibility K with the dynamics encoded in J .…”

“…Monte Carlo simulations are performed for a periodic system of very large length L = 10 6 with fixed particle numbers N λ . Hereby, large periodic systems allow to suppress finite size effects [17] while the translational invariance increases the quality of the estimator. Further, fixing the particle numbers allow a better control of finite size effects which are of order…”

Light and heavy particles on a fluctuating surface: Bunchwise balance, irreducible sequences and local density-height correlations

“…2 (C)). Kinematic waves propagate across the particle and tilt sub-lattices in steady state [39], and the nature of their decay changes across the disordered phase [35], giving rise to several new dynamical universality classes [18][19][20][21][22][23].…”

“…The rich phenomena displayed by a system comprising two coupled fields provided the motivation for the LH model, which was introduced and studied in [24][25][26]35]. It is a simple lattice model of light (L) and heavy (H) particles interacting with the local slopes of a fluctuating surface.…”

“…The disordered phase arises when the back-action of particles on the surface goes opposite to the action of surface slopes on the particles. The dynamics is then dominated by mixed-mode kinematic waves, and a recent numerical study [35] shows that several of the new universality classes that characterize their decay, predicted in [18][19][20][21][22][23], are achieved by choosing coupling constants appropriately. On the other hand, when the back-action of the particles on the surface is in consonance with the action of surface slopes on the particles, there is a tendency to form large H particle clusters residing on large sloping segments.…”