We demonstrate particle clustering on macroscopic scales in a coupled nonequilibrium system where two species of particles are advected by a fluctuating landscape and modify the landscape in the process. The phase diagram generated by varying the particle-landscape coupling, valid for all particle density and in both one and two dimensions, shows novel nonequilibrium phases. While particle species are completely phase separated, the landscape develops macroscopically ordered regions coexisting with a disordered region, resulting in coarsening and steady state dynamics on time scales which grow algebraically with size, not seen earlier in systems with pure domains.PACS numbers: 64.75.Gh, 68.43.Jk Particle clustering is important in many natural physical and biological phenomena, for instance, the formation of sediments [1] and protein clustering on a biological membrane [2]. Evidently, it is important to understand processes that cause clustering in different physical contexts, and how these processes influence the properties of the cluster and the time taken to form it. Often, large-scale clustering is driven by interactions with an external medium which itself has correlations in space and time [3][4][5]. An important physical effect in such systems is the back-influence of the particles on the medium. This interaction can aid clustering, or destroy it. If a cluster does form, it may be compact and robust, or a dynamic object that undergoes constant reorganization. The formation time may grow exponentially with the size, or as a power law. Given this wealth of possibilities, it is important to look for an understanding, within simple models, of the circumstances under which different sorts of macroscopically clustered states occur.In this letter, we derive the phase diagram of a simple model system as we vary the interaction between the environment and particles. In the process, we unmask a novel non-equilibrium phase of particles with compact clustering and rich and rapid dynamics coexisting with a macroscopically organized landscape. The model has partial overlap with the lattice gas model of Lahiri and Ramaswamy (LR) for sedimenting colloidal crystals [6,7], but the new phases manifest themselves outside the LR regime. Our results hold in both one and two dimensions.The model consists of two sets of particles moving stochastically in a fluctuating potential energy landscape. Particles try to minimize their energy by (a) moving along the local potential gradient of the landscape and (b) modifying the landscape around them in such a way as to lower the energy further. The model is generic but we discuss it in the language of particles confined to move on a fluctuating surface in the presence of gravity, where the particles can locally distort the surface shape to further lower the energy (see Fig. 1). One of the particle species is considered lighter and the other is heavier; we use the name LH (Light-heavy) model to describe the system. Process (b) affects the landscape dynamics quite differently in parts...

We study a coupled driven system in which two species of particles are advected by a fluctuating potential energy landscape. While the particles follow the potential gradient, each species affects the local shape of the landscape in different ways. As a result of this two-way coupling between the landscape and the particles, the system shows interesting new phases, characterized by different sorts of long-ranged order in the particles and in the landscape. In all these ordered phases, the two particle species phase separate completely from each other, but the underlying landscape may either show complete ordering, with macroscopic regions with distinct average slopes, or may show coexistence of ordered and disordered regions, depending on the differential nature of effect produced by the particle species on the landscape. We discuss several aspects of static properties of these phases in this paper, and we discuss the dynamics of these phases in the sequel.

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.

We study the dynamical properties of the ordered phases obtained in a coupled nonequilibrium system describing advection of two species of particles by a stochastically evolving landscape. The local dynamics of the landscape also gets affected by the particles. In a companion paper we have presented static properties of different phases that arise as the two-way coupling parameters are varied. In this paper we discuss the dynamics. We show that in the ordered phases macroscopic particle clusters move over an ergodic time-scale growing exponentially with system size but the ordered landscape shows dynamics over a faster time-scale growing as a power of system size. We present a scaling ansatz that describes several dynamical correlation functions of the landscape measured in steady state.2

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