A Low Temperature Analysis of the Boundary Driven Kawasaki Process

Low temperature analysis of nonequilibrium systems requires finding the states with the longest lifetime and that are most accessible from other states. We determine these dominant states for a one-dimensional diffusive lattice gas subject to exclusion and with nearest neighbor interaction. They do not correspond to lowest energy configurations even though the particle current tends to zero as the temperature reaches zero. That is because the dynamical activity that sets the effective time scale, also goes to zero with temperature. The result is a non-trivial asymptotic phase diagram, which crucially depends on the interaction coupling and the relative chemical potentials of the reservoirs.     

A self-organizing network in the weak-coupling limit

We prove the existence of spatially localized ground states of the diffusive Haken model. This model describes a self-organizing network whose elements are arranged on a d-dimensional lattice with short-range diffusive coupling. The network evolves according to a competitive gradient dynamics in which the effects of diffusion are counteracted by a localizing potential that incorporates an additional global coupling term. In the absence of diffusive coupling, the ground states of the system are strictly localized, i.e. only one lattice site is excited. For sufficiently small non-zero diffusive coupling , it is shown analytically that localized ground states persist in the network with the excitations exponentially decaying in space. Numerical results establish that localization occurs for arbitrary values of in one dimension but vanishes beyond a critical coupling _c(d), when d> 1. The one-dimensional localized states are interpreted in terms of instanton solutions of a continuum version of the model.     

Lattice limit cycle dynamics: Influence of long-distance reactive and diffusive mixing

The properties of global oscillations produced by coupled reactive stochastic discrete systems on a 2D lattice support are studied, taking into account the competitive influence of local and global mixing processes. Two types of global mixing are considered: reactive and diffusive. It is shown that in the case of diffusive mixing the increase in the diffusive coupling leads to a corresponding increase in the amplitude of the global oscillations. In the case of reactive mixing the competition of local-to-global effects leads to unexpected complex phenomena. Kinetic Monte Carlo simulations demonstrate that the amplitude of oscillations as a function of the mixing-reactive coupling presents an optimal value, which is attributed to the competitive effects between the local and global processes.     

Modulational Instability of Spinor Condensates in an Optical Lattice

We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.     

Quantum phase transition of cold atoms trapped in optical lattices

We review our recent theoretical advances in phase transition of cold atoms in optical lattices, such as triangular lattice, honeycomb lattice, and Kagomé lattice. By employing the new developed numerical methods called dynamical cluster approximation and cellular dynamical mean-field theory, the properties in different phases of cold atoms in optical lattices are studied, such as density of states, Fermi surface and double occupancy. On triangular lattice, a reentrant behavior of phase translation line between Fermi liquid state and pseudogap state is found due to the Kondo effect. We find the system undergoes a second order Mott transition from a metallic state into a Mott insulator state on honeycomb lattice and triangular Kagomé lattice. The stability of quantum spin Hall phase towards interaction on honeycomb lattice with spin-orbital coupling is systematically discussed. And we investigate the transition from quantum spin Hall insulator to normal insulator in Kagomé lattice which includes a nearest-neighbor intrinsic spin-orbit coupling and a trimerized Hamiltonian. In addition, we propose the experimental protocols to observe these phase transition of cold atoms in optical lattices.     

基于符号向量动力学的耦合映像格子参数估计

本文,将符号动力学推广到耦合映像格子中,以Logistic映射下耦合映像格子为研究对象,研究控制参数对符号向量序列动力学特性的影响.通过研究耦合映像格子逆函数,给出耦合映像格子的遍历条件.进一步,将给出系统初始向量,禁止字以及控制参数的符号向量序列描述方法,并最终给出基于符号向量动力学的耦合映像格子控制参数估计方法.实验结果表明,根据本文算法可以有效建立符号序列和耦合映像格子控制参数之间的对应关系,能够更好地刻画了实际模型的物理过程. 关键词： 符号向量动力学 耦合映像格子 参数估计 遍历性     

A coupled map lattice model for rheological chaos in sheared nematic liquid crystals

A variety of complex fluids under shear exhibit complex spatiotemporal behavior, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where the Reynolds number is very small. It must thus arise as a consequence of the coupling of the flow to internal structural variables describing the local state of the fluid. We propose a coupled map lattice model for such complex spatiotemporal behavior in a passively sheared nematic liquid crystal using local maps constructed so as to accurately describe the spatially homogeneous case. Such local maps are coupled diffusively to nearest and next-nearest neighbors to mimic the effects of spatial gradients in the underlying equations of motion. We investigate the dynamical steady states obtained as parameters in the map and the strength of the spatial coupling are varied, studying local temporal properties at a single site as well as spatiotemporal features of the extended system. Our methods reproduce the full range of spatiotemporal behavior seen in earlier one-dimensional studies based on partial differential equations. We report results for both the one- and two-dimensional cases, showing that spatial coupling favors uniform or periodically time-varying states, as intuitively expected. We demonstrate and characterize regimes of spatiotemporal intermittency out of which chaos develops. Our work indicates that similar simplified lattice models of the dynamics of complex fluids under shear should provide useful ways to access and quantify spatiotemporal complexity in such problems, in addition to representing a fast and numerically tractable alternative to continuum representations.     

Current Large Deviations in a Driven Dissipative Model

We consider lattice gas diffusive dynamics with creation-annihilation in the bulk and maintained out of equilibrium by two reservoirs at the boundaries. This stochastic particle system can be viewed as a toy model for granular gases where the energy is injected at the boundary and dissipated in the bulk. The large deviation functional for the particle currents flowing through the system is computed and some physical consequences are discussed: the mechanism for local current fluctuations, dynamical phase transitions, the fluctuation-relation.     

Fermions on a lattice at strong coupling

We study the pattern of dynamical symmetry breaking and its dependence on the choice made for the derivative on a lattice, including the possibility that it contains a term which couples a site to itself, in the strong coupling limit of a lattice gauge theory.     

Coupling Effect of Ion Channel Clusters on Calcium Signalling

Based on a modified intracellular Ca^2＋ model involving diffusive coupling of two calcium ion channel dusters, the effects of coupling on calcium signalling are numerically investigated. The simulation results indicate that the diffusive coupling of dusters together with internal noise determine the calcium dynamics of single duster, and for either homogeneous or heterogeneous coupled dusters, the synchronization of dusters, which is important to calcium signalling, is enhanced by the coupling effect.     

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The dynamics of cold atoms in conservative optical lattices obviously depends on the geometry of the lattice. But very similar lattices may lead to deeply different dynamics. In a 2D optical lattice with a square mesh, it is expected that the coupling between the degrees of freedom leads to chaotic motions. However, in some conditions, chaos remains marginal. The aim of this paper is to understand the dynamical mechanisms inhibiting the appearance of chaos in such a case. As the quantum dynamics of a system is defined as a function of its classical dynamics – e.g. quantum chaos is defined as the quantum regime of a system whose classical dynamics is chaotic – we focus here on the dynamical regimes of classical atoms inside a well. We show that when chaos is inhibited, the motions in the two directions of space are frequency locked in most of the phase space, for most of the parameters of the lattice and atoms. This synchronization, not as strict as that of a dissipative system, is nevertheless a mechanism powerful enough to explain that chaos cannot appear in such conditions.     

Lower bounds on the localisation length of balanced random quantum walks

Letters in Mathematical Physics - We consider the dynamical properties of Quantum Walks defined on the d-dimensional cubic lattice, or the homogeneous tree of coordination number 2d, with...     

Random walks interacting with evolving energy landscapes

We introduce a diffusion model for energetically inhomogeneous systems. A random walker moves on a spin-S Ising configuration, which generates the energy landscape on the lattice through the nearest-neighbors interaction. The underlying energetic environment is also made dynamic by properly coupling the walker with the spin lattice. In fact, while the walker hops across nearest-neighbor sites, it can flip the pertaining spins, realizing a diffusive dynamics for the Ising system. As a result, the walk is biased towards high energy regions, namely the boundaries between clusters. Besides, the coupling introduced involves, with respect the ordinary diffusion laws, interesting corrections depending on either the temperature and the spin magnitude. In particular, they provide a further signature of the phase-transition occurring on the magnetic lattice.     

Dynamical and static spin conductivities in the Heisenberg model on honeycomb lattice: The effects of magnetic long range ordering

We have studied both dynamical and static spin conductivities of Heisenberg antiferromagnet on honeycomb lattice in the presence of a magnetic long range ordering. The effects of spatial anisotropy as weak Dzyaloshinskii–Moriya interaction and next nearest neighbor exchange coupling on the behaviors of conductivities are discussed. A sublattice antiferromagnetic long range ordering has been considered for localized electrons on honeycomb lattice structure. Using Holstein–Primakoff bosonic transformations, the behaviors of spin transport properties have been studied by means of excitation spectrum of mapped bosonic gas. We have found the temperature dependence of static spin conductivity in the field induced gapped spin-polarized phase for various Dzyaloshinskii–Moriya interaction strengths. Furthermore we have studied the frequency dependence of dynamical spin conductivity for various Dzyaloshinskii–Moriya interaction strengths and different next nearest neighbor coupling constants. We find that the height of peak in the temperature dependence of static spin conductivity increases upon increasing the anisotropy parameter. The static spin conductivity is found to be monotonically increasing with anisotropy parameter due to increase of the energy gap in the excitation spectrum. Furthermore we have studied the temperature dependence of the spin conductivity for different next nearest neighbor coupling constants.     

A liquid-like picture for the interpretation of Raman scattering in superionic conductors

Raman spectra of superionic conductors are studied in a model which takes into account polarizability changes due to ionic motions between lattice sites. The scattered intensity is determined by a generalized dynamical structure factor at wave vectors depending on the periodicity of the lattice. The structure factor is evaluated in a model which for the mobile ions assumes Brownian motion in a sinusoidal potential. The results are compared with the spectrum of α-AgI. The observed broad Rayleigh wings can be explained by quasielastic scattering due to diffusive motions.     

Dynamical instability of a boson-fermion mixture at low dimensions

We examine theoretically the dynamical response of a homogeneous mixture of condensed bosons and spin-polarized fermions confined inside a quasi-two-dimensional or a quasi-one-dimensional geometry, considering quasi-three-dimensional boson-boson and boson-fermion interactions. We focus on the effects of low dimensions on the density response functions in the crossover from weak to strong boson-fermion coupling up to the onset of instability. The dynamical condition is found to be in agreement with a linear stability analysis at equilibrium.     

Self-organized memories in coupled map lattices

Spatially extended dynamical systems subjected to a periodic external input are able to store short-term memories as a result of self-organization. This phenomenon has been used to interpret sliding charge density wave experiments, and has been found in lattices of coupled maps and oscillators. In this paper, we aim to describe the influence of a stochastic perturbation in the self-organized memories in a lattice of coupled linear and weakly nonlinear maps. We consider the case in which the coupling between maps depends on the lattice distance as a power law.     

Renormalization Group for Strongly Coupled Maps

Systems of strongly coupled chaotic maps generically exhibit collective behavior emerging out of extensive chaos. We show how the well-known renormalization group (RG) of unimodal maps can be extended to the coupled systems, and in particular to coupled map lattices (CMLs) with local diffusive coupling. The RG relation derived for CMLs is nonperturbative, i.e., not restricted to a particular class of configurations nor to some vanishingly small region of parameter space. After defining the strong-coupling limit in which the RG applies to almost all asymptotic solutions, we first present the simple case of coupled tent maps. We then turn to the general case of unimodal maps coupled by diffusive coupling operators satisfying basic properties, extending the formal approach developed by Collet and Eckmann for single maps. We finally discuss and illustrate the general consequences of the RG: CMLs are shown to share universal properties in the space-continuous limit which emerges naturally as the group is iterated. We prove that the scaling properly ties of the local map carry to the coupled systems, with an additional scaling factor of length scales implied by the synchronous updating of these dynamical systems. This explains various scaling laws and self-similar features previously observed numerically.     

Gap formation and soft phonon mode in the Holstein model

We investigate electron-phonon coupling in many-electron systems using the dynamical mean-field theory in combination with the numerical renormalization group. This nonperturbative method reveals significant precursor effects to the gap formation at intermediate coupling strengths. The emergence of a soft phonon mode and very strong lattice fluctuations can be understood in terms of Kondo-like physics due to the development of a double-well structure in the effective potential for the ions.     

Atoms in double-delta-kicked periodic potentials: chaos with long-range correlations

We report an experimental and theoretical study of the dynamics of cold atoms subjected to pairs of closely spaced pulses in an optical lattice. For all previously studied delta-kicked systems, chaotic classical dynamics shows diffusion with short-time (2- or 3-kick) correlations; here, chaotic diffusion combines with new types of long-ranged global correlations, between all kick pairs, which control transport through trapping regions in phase space. Correlations are studied in the classical regime, but the diffusive behavior observed in experiment depends on the quantum dynamical localization.