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 consider a minimal model to describe the quantum phases of ultracold dipolar bosons in two-dimensional (2D) square optical lattices. The model is a variation of the extended Bose-Hubbard model and apt to study the quantum phases arising from the variation in the tilt angle θ of the dipolar bosons. At low tilt angles 0 • θ 25 • , the ground state of the system are phases with checkerboard order, which could be either checkerboard supersolid or checkerboard density wave. For high tilt angles 55 • θ 35 • , phases with striped order of supersolid or density wave are preferred. In the intermediate domain 25 • θ 35 • an emulsion or SF phase intervenes the transition between the checkerboard and striped phases. The attractive interaction dominates for θ 55 • , which renders the system unstable and there is a density collapse. For our studies we use Gutzwiller mean-field theory to obtain the quantum phases and the phase boundaries. In addition, we calculate the phase boundaries between an incompressible and a compressible phase of the system by considering second order perturbation analysis of the mean-field theory. The analytical results, where applicable, are in excellent agreement with the numerical results.
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