Structural transitions and dynamical regimes for directional locking of vortices and colloids driven over periodic substrates

We examine collective dynamical locking effects for superconducting vortices and colloids interacting with square and triangular substrate arrays under a slowly rotated dc drive. A rich variety of lattice configurations associated with a series of steps in the velocity-force curves occur during the locking transitions. These include triangular, square, smectic, and disordered particle arrangements that can be identified using the structure factor. We show that the step widths vary with the ratio of the number of particles to the number of pinning sites. Unlike a static system, where matching effects occur at simple integer commensuration ratios, we find dynamical commensuration effects that arise when an integer number of particle chains flow between rows of pins. We identify two distinct types of locking as a function of substrate strength, distinguished by whether the particles flow along or between the pinning rows.     

Hydrodynamic Synchronisation of Model Microswimmers

We define a model microswimmer with a variable cycle time, thus allowing the possibility of phase locking driven by hydrodynamic interactions between swimmers. We find that, for extensile or contractile swimmers, phase locking does occur, with the relative phase of the two swimmers being, in general, close to 0 or π, depending on their relative position and orientation. We show that, as expected on grounds of symmetry, self T-dual swimmers, which are time-reversal covariant, do not phase-lock. We also discuss the phase behaviour of a line of tethered swimmers, or pumps. These show oscillations in their relative phases reminiscent of the metachronal waves of cilia.     

Ballistic transport in aperiodic Labyrinth tiling proven through a new convolution theorem

In this article, we report a distinct convolution theorem developed for the Kubo-Greenwood formula in Labyrinth tiling by transforming the two-dimensional lattice into a set of independent chains with rescaled Hamiltonians. Such transformation leads to an analytical solution of the direct-current conductance spectra, where quantized steps with height of 2g₀ are found in Labyrinth tiling with periodic order along the applied electric field direction, in contrast to the step height of g₀ observed in the corresponding square lattices, being g₀ the conductance quantum. When this convolution theorem is combined with the real-space renormalization method, we are able to address in non-perturbative way the electronic transport in macroscopic aperiodic Labyrinth tiling based on generalized Fibonacci chains. Furthermore, we analytically demonstrate the existence of ballistic transport states in aperiodic Labyrinth tiling. This finding suggests that the periodicity should not be a necessary condition for the single-electron ballistic transport even in multidimensional fully non-periodic lattices.     

Charge frustration and quantum criticality for strongly correlated fermions

We study a model of strongly correlated electrons on the square lattice which exhibits charge frustration and quantum critical behavior. The potential is tuned to make the interactions supersymmetric. We establish a rigorous mathematical result which relates quantum ground states to certain tiling configurations on the square lattice. For periodic boundary conditions this relation implies that the number of ground states grows exponentially with the linear dimensions of the system. We present substantial analytic and numerical evidence that for open boundary conditions the system has gapless edge modes.     

Moving Wigner glasses and smectics: dynamics of disordered Wigner crystals

We examine the dynamics of driven classical Wigner solids interacting with quenched disorder from charged impurities. For strong disorder, the initial motion is plastic, in the form of crossing winding channels. For increasing drive, there is a reordering into a moving Wigner smectic with the electrons moving in separate 1D channels. These different dynamic phases can be related to the conduction noise and I(V) curves. For strong disorder, we show criticality in the voltage onset just above depinning. We obtain the dynamic phase diagram for driven Wigner solids and demonstrate a finite threshold of force for transverse sliding, recently observed experimentally.     

Brownian ratchets driven by asymmetric nucleation of hydrolysis waves

We propose a stochastic process wherein molecular transport is mediated by asymmetric nucleation of domains on a one-dimensional substrate, in contrast with molecular motors that hydrolyze nucleotide triphosphates and undergo conformational change. We show that asymmetric nucleation of hydrolysis waves on a track can also result in directed motion of an attached particle. Asymmetrically cooperative kinetics between hydrolyzed and unhydrolyzed states on each lattice site generate moving domain walls that push a particle sitting on the track. We use a novel fluctuating-frame, finite-segment mean field theory to accurately compute steady-state velocities of the driven particle and to discover parameter regimes yielding maximal domain wall flux, leading to optimal particle drift.     

Berry Phases and Entanglement of a Two Spin-1/2 Model with Dzyaloshinski-Moriya Interaction in Magnetic Fields

We show that the entanglement (as quantified by the concurrence) and Berry phases of the adiabatic quantum states vanish for a two spin-1/2 system with Dzyaloshinski-Moriya (DM) interaction, while one of the spins is driven by a time-varing rotating magnetic field and the other one is coupled with a strong static magnetic field. The system is described by the Heisenberg XX model and the static field is in the direction of the rotation axis. We also investigate that how the concurrence and Berry phases depend on the DM interaction, coupling coefficient and the static magnetic field. In addition, we show that reversing the sign of the static magnetic field can cause exchange of the Berry phases and entanglement between the adiabatic states. Finally it is shown that each energy level approach causes jumps or cusp-like behaviour in the Berry phases and the concurrences.     

Charge Stripes Due to Electron Correlations in the Two-Dimensional Spinless Falicov—Kimball Model

We calculate the restricted phase diagram for the Falicov–Kimball model on a two-dimensional square lattice. We consider the limit where the average conduction electron density is equal to the average localized electron density, which is the limit related to the S _z =0 states of the Hubbard model. After considering over 20,000 different candidate phases (with a unit cell of 16 sites or less) and their thermodynamic mixtures, we find only about 100 stable phases in the ground-state phase diagram, where the ground state is usually the phase separated mixture of two or three stable phases, that often have different electron densities than in the Maxwell-constructed mixture. We analyze these phases to describe where stripe phases occur and relate these discoveries (were appropriate) to the physics behind stripe formation in the Hubbard model.     

Dynamics, rectification, and fractionation for colloids on flashing substrates

We show that a rich variety of dynamic phases can be realized for mono- and bidisperse mixtures of interacting colloids under the influence of a symmetric flashing periodic substrate. With the addition of dc or ac drives, phase locking, jamming, and new types of ratchet effects occur. In some regimes we find that the addition of a nonratcheting species increases the velocity of the ratcheting particles. We show that these effects occur due to the collective interactions of the colloids.     

Nonadiabatic Geometric Phase and Induced Persistent Current in Mesoscopic Square Circuit with Tilted Magnetic Field at Edges

We investigate the geometric phase produced by nonadiabatic transition of spin states at corners of mesoscopic square circuit with tilted magnetic field at its edges, From the Schrodlnger equation, the transitions of electron spin state at corners are described by the transfer matrices. The eigenenergies and eigenstates are obtained from the cyclic condition and the multiplying of the transfer matrices. We show that there exist persistent charge and spin currents in such a system due to the lift of degeneracy between the opposite moving directions in the presence of the tilted magnetic field. The dependences of eigenenergies, geometric phase, charge and spin persistent currents on the tilting angles of magnetic field are analysed.     

Archimedean-like colloidal tilings on substrates with decagonal and tetradecagonal symmetry

Two-dimensional colloidal suspensions subjected to laser interference patterns with decagonal symmetry can form an Archimedean-like tiling phase where rows of squares and triangles order aperiodically along one direction (J. Mikhael et al., Nature 454, 501 (2008)). In experiments as well as in Monte Carlo and Brownian dynamics simulations, we identify a similar phase when the laser field possesses tetradecagonal symmetry. We characterize the structure of both Archimedean-like tilings in detail and point out how the tilings differ from each other. Furthermore, we also estimate specific particle densities where the Archimedean-like tiling phases occur. Finally, using Brownian dynamics simulations we demonstrate how phasonic distortions of the decagonal laser field influence the Archimedean-like tiling. In particular, the domain size of the tiling can be enlarged by phasonic drifts and constant gradients in the phasonic displacement. We demonstrate that the latter occurs when the interfering laser beams are not ideally adjusted.     

Quantum accelerator modes from the Farey tree

We show that mode locking finds a purely quantum nondissipative counterpart in atom-optical quantum accelerator modes. These modes are formed by exposing cold atoms to periodic kicks in the direction of the gravitational field. They are anchored to generalized Arnol'd tongues, parameter regions where driven nonlinear classical systems exhibit mode locking. A hierarchy for the rational numbers known as the Farey tree provides an ordering of the Arnol'd tongues and hence of experimentally observed accelerator modes.     

Collective multivortex states in periodic arrays of traps

We examine the vortex states in a 2D superconductor interacting with a square array of pinning sites. As a function of increasing pinning size or strength we find a series of novel phases including multivortex and composite superlattice states such as aligned dimer and trimer configurations at individual pinning sites. Interactions of the vortices give rise to an orientational ordering of the internal vortex structures in each pinning site. We also show that these vortex states can give rise to a multistage melting behavior.     

Possible test of the thermodynamic approach to granular media

We study the steady state distribution of the energy of the Sherrington-Kirkpatrick model driven by a tapping mechanism which mimics the mechanically driven dynamics of granular media. The dynamics consists of two phases: a zero temperature relaxation phase which leads the system to a metastable state, then a tapping which excites the system thus reactivating the relaxational dynamics. Numerically, we investigate whether the distribution of the energies of the blocked states obtained agrees with a simple canonical form of the Edwards measure. It is found that this canonical measure is in good agreement with the dynamically measured energy distribution. A possible experimental test of the Edwards measure based on the study here is proposed.     

A slow-light laser radar system with two-dimensional scanning

We propose a multi-aperture slow-light laser radar with two-dimensional scanning. We demonstrate experimentally that we can use two independent slow-light mechanisms, namely dispersive delay and stimulated Brillouin scattering, to dynamically compensate the group delay mismatch among different apertures, while we use optical phase locking to control the relative phases of the optical signals emitted from different apertures, as the system steers the beam in two dimensions.     

Notes on infinite layer quantum Hall systems

We study the fractional quantum Hall effect in three-dimensional systems consisting of infinitely many stacked two-dimensional electron gases placed in transverse magnetic fields. This limit introduces new features into the bulk physics such as quasiparticles with non-trivial internal structure, irrational braiding phases, and the necessity of a boundary hierarchy construction for interlayer correlated states. The bulk states host a family of surface phases obtained by hybridizing the edge states in each layer. We analyze the surface conduction in these phases by means of sum rule and renormalization group arguments and by explicit computations at weak tunneling in the presence of disorder. We find that in cases where the interlayer electron tunneling is not relevant in the clean limit, the surface phases are chiral semi-metals that conduct only in the presence of disorder or at finite temperature. We show that this class of problems which are naturally formulated as interacting bosonic theories can be fermionized by a general technique that could prove useful in the solution of such “one and a half” dimensional problems.     

光腔耦合阵列中四模方形Cluster态的制备

提出一种四模方形cluster态的制备方案,方案选用四个分别包含一个原子系综的独立单模光腔,光腔之间用短光纤实现耦合.讨论证明在合适外加激光脉冲的驱动下,可确定性的制备得到稳定的四模方形cluster态.通过调节驱动激光的频率和相位,该方案可以拓展到多模和其他形cluster态的制备.     

光腔耦合阵列中四模方形Cluster态的制备

提出一种四模方形cluster态的制备方案,方案选用四个分别包含一个原子系综的独立单模光腔,光腔之间用短光纤实现耦合.讨论证明在合适外加激光脉冲的驱动下,可确定性的制备得到稳定的四模方形cluster态.通过调节驱动激光的频率和相位,该方案可以拓展到多模和其他形cluster态的制备.     

Representations of Canonical Commutation Relations Describing Infinite Coherent States

We investigate the infinite volume limit of quantized photon fields in multimode coherent states. We show that for states containing a continuum of coherent modes, it is mathematically and physically natural to consider their phases to be random and identically distributed. The infinite volume states give rise to Hilbert space representations of the canonical commutation relations which we construct concretely. In the case of random phases, the representations are random as well and can be expressed with the help of Itô stochastic integrals. We analyze the dynamics of the infinite state alone and the open system dynamics of small systems coupled to it. We show that under the free field dynamics, initial phase distributions are driven to the uniform distribution. We demonstrate that coherences in small quantum systems, interacting with the infinite coherent state, exhibit Gaussian time decay. The decoherence is qualitatively faster than the one caused by infinite thermal states, which is known to be exponentially rapid only. This emphasizes the classical character of coherent states.     

Classical driven transport in open systems with particle interactions and general couplings to reservoirs

We study nonequilibrium steady states of lattice gases with nearest-neighbor interactions that are driven between two reservoirs. Density profiles in these systems exhibit oscillations close to the reservoirs. We demonstrate that an approach based on time-dependent density functional theory copes with these oscillations and predicts phase diagrams of bulk densities to a good approximation under arbitrary boundary-reservoir couplings. The minimum or maximum current principles can be applied only for specific bulk-adapted couplings. We show that they generally fail to give the correct topology of phase diagrams but can still be useful for getting insight into the mutual arrangement of different phases.