1The use of the electric curtain (EC) has been proposed for manipulation and control of particles in various applications. The EC studied in this paper is called the 2-phase EC, which consists of a series of long parallel electrodes embedded in a thin dielectric surface. The EC is driven by an oscillating electric potential of a sinusoidal form where the phase difference of the electric potential between neighboring electrodes is 180 degrees. We investigate the one-and two-dimensional nonlinear dynamics of a particle in an EC field. The form of the dimensionless equations of motion is codimension two, where the dimensionless control parameters are the interaction amplitude (A) and damping coefficient (β). Our focus on the one-dimensional EC is primarily on a case of fixed β and relatively small A, which is characteristic of typical experimental conditions. We study the nonlinear behaviors of the one-dimensional EC through the analysis of bifurcations of fixed points in the Poincaré sections. We analyze these bifurcations by using Floquet theory to determine the stability of the limit cycles associated with the fixed points in the Poincaré sections. Some of the bifurcations lead to chaotic trajectories where we then determine the strength of chaos in phase space by calculating the largest Lyapunov exponent. In the study of the two-dimensional EC we independently look at bifurcation diagrams of variations in A with fixed β and variations in β with fixed A. Under certain values of β and A, we find that no stable trajectories above the surface exists; such chaotic trajectories are described by a chaotic (strange) attractor, for which the the largest Lyapunov exponent is found. We show the well-known stable oscillations between two electrodes come into existence for variations in A and the transitions between several distinct regimes of stable motion for variations in β.

We introduce the quantum dimer-pentamer model (QDPM) on the square lattice. This model is a generalization of the square lattice quantum dimer model as its configuration space comprises fullypacked hard-core dimer coverings as well as dimer configurations containing pentamers, where four dimers touch a vertex. Thus in the QDPM, the fully-packed, hard-core constraint of the quantum dimer model is relaxed such that the local dimer number at each vertex is fixed modulo 3, resulting in an exact local Z3 gauge symmetry. We construct a local Hamiltonian for which the Rokhsar-Kivelson (RK) equal superposition state is the exact ground state and has a 9-fold topological degeneracy on the torus. Using Monte Carlo calculations, we find no spontaneous symmetry breaking in the RK wavefunction and that its dimer-dimer correlation function decays exponentially. By doping the QDPM RK state with a pair of monomers, we demonstrate that Z3 electric charges are deconfined. Additionally, we introduce a Z3 magnetic string operator that we find decays exponentially and shows no signatures of magnetic vortex condensation and with correlations. These numerical results suggest that the ground state of the QDPM is a dimer liquid with Z3 topological order.

In this paper, we investigate the equilibrium and non-equilibrium properties of a model that shares several important characteristics with charged particles interacting in an Electric Curtain (EC) device. An EC comprises a periodic array of parallel electrodes, applied to each is an alternating electric potential. Depending on the applied potentials and the geometry of the electrodes, a wide variety of field structures above the plane of the electrodes are possible. The EC has multiple applications in the control and manipulation of small particles, but is under utilized in industry and science because of difficulties in predicting and understanding the particle dynamics. One particular challenge in understanding the dynamics is the many-body coulomb interactions. To better understand the role of the interactions, we study a one-dimensional analytically tractable model that encapsulates their long-range nature. Specifically, we study a Hamiltonian similar to that of the Hamiltonian mean field model but with the inclusion of an index dependent phase in the interaction term that, as we show, reflects the periodic structure of an EC field. We solve for the canonical partition function and also investigate some of the non-equilibrium behaviors. In the study of the non-equilibrium behaviors, we find an interesting property, namely that a quasistationary (lifetime diverges as the number of particles is increased) clustered state can exist when an initial configuration is ordered by the particle indices.

The spatio-temporally periodic (STP) potential is interesting in Physics due to the intimate coupling between its time and spatial components. In this paper, we begin with a brief discussion of the dynamical behaviors of a single particle in a STP potential and then examine the dynamics of multiple particles interacting in a STP potential via the electric Coulomb potential. For the multiple particles' case, we focus on the occurrence of bifurcations when the amplitude of the STP potential varies. It is found that the particle concentration of the system plays an important role; the type of bifurcations that occur and the number of attractors present in the Poincar e sections depend on whether the number of particles in the simulation is even or odd. In addition to the nonlinear dynamical approach, we also discuss dependence of the squared fractional deviation of particles' kinetic energy of the multiple particle system on the amplitude of the STP potential which can be used to elucidate certain transitions of states; this approach is simple and useful particularly for experimental studies of complicated interacting systems. V C 2014 AIP Publishing LLC.