Control and characterization of spatio-temporal disorder in parametrically excited surface waves

The nonlinear interactions of parametrically excited surface waves have been shown to yield a rich family of nonlinear states. When the system is driven by two commensurate frequencies, a variety of interesting superlattice type states are generated via a number of different 3-wave resonant interactions. These states occur either as symmetry-breaking bifurcations of hexagonal patterns composed of a single unstable mode or via nonlinear interactions between the two different unstable modes generated by the two forcing frequencies. Near the system’s bicritical point, a well-defined region of phase space exists in which a highly disordered state, both in space and time, is observed. We first show that this state results from the competition between two distinct nonlinear super-lattice states, each with different characteristic temporal and spatial symmetries. After characterizing the type of spatio-temporal disorder that is embodied in this disordered state, we will demonstrate that it can be controlled. Control to either of its neighboring nonlinear states is achieved by the application of a small-amplitude excitation at a third frequency, where the spatial symmetry of the selected pattern is determined by the temporal symmetry of the third frequency used. This technique can also excite rapid switching between different nonlinear states.     

Symmetries of multifractal spectra and field theories of Anderson localization

We uncover the field-theoretical origin of symmetry relations for multifractal spectra at Anderson transitions and at critical points of other disordered systems. We show that such relations follow from the conformal invariance of the critical theory, which implies their general character. We also demonstrate that for the Anderson localization problem the entire probability distribution for the local density of states possesses a symmetry arising from the invariance of correlation functions of the underlying nonlinear σ model with respect to the Weyl group of the target space of the model.     

Oscillating viscosity in a lyotropic lamellar phase under shear flow

We report some time-dependent behavior of lyotropic lamellar phase under shear flow. At fixed stress, near a layering instability, the system presents an oscillating shear rate. We build up a new stress versus shear rate diagram that includes temporal behavior. This diagram is made of two distinct branches of stationary states which correspond, respectively, to disordered and ordered multilamellar vesicle phases. When increasing the shear stress, prior to the transition to the ordered structural state, sustained oscillations of the viscosity are recorded. They correspond to periodic structural change of the entire sample between a disordered and a ordered state of multilamellar vesicles.     

Quantifying the complexity of excised larynx vibrations from high-speed imaging using spatiotemporal and nonlinear dynamic analyses

In this paper, we investigate the biomechanical applications of spatiotemporal analysis and nonlinear dynamic analysis to quantitatively describe regular and irregular vibrations of twelve excised larynges from high-speed image recordings. Regular vibrations show simple spatial symmetry, temporal periodicity, and discrete frequency spectra, while irregular vibrations show complex spatiotemporal plots, aperiodic time series, and broadband spectra. Furthermore, the global entropy and correlation length from spatiotemporal analysis and the correlation dimension from nonlinear dynamic analysis reveal a statistical difference between regular and irregular vibrations. In comparison with regular vibrations, the global entropy and correlation dimension of irregular vibrations are statistically higher, while the correlation length is significantly lower. These findings show that spatiotemporal analysis and nonlinear dynamic analysis are capable of describing the complex dynamics of vocal fold vibrations from high-speed imaging and may potentially be helpful for understanding disordered behaviors in biomedical laryngeal systems.     

Higher-order solitons in amplitude-disordered waveguide arrays

We investigate the existence and stability of different families of spatial solitons in optical waveguide arrays whose amplitudes obey a disordered distribution. The competition between focusing nonlinearity and linearly disordered refractive index modulation results in the formation of spatial localized nonlinear states. Solitons originating from Anderson modes with few nodes are robust during propagation. While multi-peaked solitons with in-phase neighboring components are completely unstable, multipole-mode solitons whose neighboring components are out-of-phase can propagate stably in wide parameter regions provided that their power exceeds a critical value. Our findings, thus, provide the first example of stable higher-order nonlinear states in disordered systems.     

单核子在具有八极形变的平均势场中的混沌运动(I)相干态在势场中传播的理论表示

单核子在具有八极以上形变的平均势场中发现有混沌运动．通过研究系统非定态波函数的时间演化特征,而使研究量子混沌与研究经典混沌的思路更趋一致,特别是能体现量子状态对初始条件的敏感性。给出了当初态选为二维不对称谐振子动力学对称条件下的、满足坐标动量最小测不准关系的相干态时,八极形变耦合作用下量子状态正则变量的期望值及测不准度随时间演化的理论表示．     

Localized bifurcations and defect instabilities in the convection of a nematic liquid crystal

The stationary and the time-dependent homogeneous ordered states in convection may both become unstable against localized perturbations. Defects are then created and they may contribute to the disorganization of the homogeneous state. We present an experimental study of defects in some homogeneous stationary structures as well as in the traveling-wave states of convection of a nematic liquid crystal. We show that the core of the defects is a germ of the unstable state and it can become unstable under the external stress. Then, either fully homogeneous states with the symmetry of the core, or complex disordered states can develop from the local instability of defects in processes quite similar to displacive transitions in solids. Some of the main features are qualitatively similar to numerical simulations of an appropriate Landau-Ginzburg equation.     

Chaotic Motion of a Nucleon in Mean Field Potential With Octupole Deformation (I) The Formalism of the Propagation of Coherent States in Potential

The temporal variation characteristics of nonstationary wave functions are investigated, which enables us to carry out the study of quantum chaotic dynamics with the same starting point as in corresponding classical case, especially to realize the sensitivity of the quantum state with respect to the initial condition. Here the coherent states under the dynamical symmetry of asymmetrical two dimensional harmonic oscillator, in which the minimum uncertainty Principle is satisfied, are usedas an initial state. The formalism of the temporal variation of the expectation values and the uncertainty measurements of canonical variables of the quantum state under the broken symmetry by the additional octupole deformed potential is fulfilled.     

Square-lattice algebraic spin liquid with SO(5) symmetry

We propose a critical spin liquid ground state for S=1/2 antiferromagnets on the square lattice. In a renormalization group analysis of the "staggered flux" algebraic spin liquid, we examine perturbations, present in the antiferromagnet, which break its global SU(4) symmetry to SO(5). At physical parameter values, we find an instability towards a fixed point with SO(5) symmetry. We discuss the possibility that this fixed point describes a transition between the Néel and valence bond solid states, and the relationship to the SO(5) nonlinear sigma model of Tanaka and Hu.     

Nonlinear Coherent States and Some of Their Properties

We construct nonlinear coherent states by the application of a deformed displacement operator acting upon the vacuum state and as approximate eigenstates of a deformed annihilation operator. These states are used to evaluate the temporal evolution of the average value of the momentum and the diplacement coordinate as well as their dispersions. We also construct even and odd combinations of these nonlinear coherent states and compute their second order correlation function in order to analyze their statistical behavior.     

Bott Periodicity for {\mathbb{Z}_2} Symmetric Ground States of Gapped Free-Fermion Systems

Building on the symmetry classification of disordered fermions, we give a proof of the proposal by Kitaev, and others, for a “Bott clock” topological classification of free-fermion ground states of gapped systems with symmetries. Our approach differs from previous ones in that (i) we work in the standard framework of Hermitian quantum mechanics over the complex numbers, (ii) we directly formulate a mathematical model for ground states rather than spectrally flattened Hamiltonians, and (iii) we use homotopy-theoretic tools rather than K-theory. Key to our proof is a natural transformation that squares to the standard Bott map and relates the ground state of a d-dimensional system in symmetry class s to the ground state of a (d + 1)-dimensional system in symmetry class s + 1. This relation gives a new vantage point on topological insulators and superconductors.     

Nonlinear sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry

A novel nonlinear sigma model method is proposed for the two-dimensional J1-J2 model, which is extended to include plaquette-type distortion. The nonlinear sigma model is properly derived without spoiling the original spin degrees of freedom. The method shows that a single disordered phase continuously extends from a frustrated uniform regime to an unfrustrated distorted regime. By the continuity and Oshikawa's commensurability condition, the disordered ground states for the uniform J1-J2 model are plaquette states with fourfold degeneracy.     

基于弱非线性实现非破坏性测量两光子Bell态及三光子Greenberger-Horne-Zeilinger态

基于弱非线性及线性光学元件提出非破坏性测量两光子Bell态及三光子 Greenberger-Horne-Zeilinger (GHZ)态方案. 方案中, 首先应用光束分束器及交叉克尔非线性介质对两光子Bell态进行对称性分析, 进而结合控制非门提出三光子分析方案实现对八个三光子GHZ态完全且非破坏性区分. 关键词： Bell态测量 Greenberger-Horne-Zeilinger态测量 弱非线性 量子非破坏性测量     

Spectrum and nature of surface states

With the help of an approximative E(k) relation in the forbidden gap N(E) distributions for localized states are calculated. A potential fluctuation model gives energy distributions of states in the gap which exhibit features of surface state spectra or spectra of disordered systems. Binding and nonbinding states are coupled to pairs by the E(k) relation and characteristic properties of surface and interface state spectra like symmetry, acceptordonor character, minimum of the N(E) distribution may be described. Dangling bonds of preferential 111 character are the proper chemical picture. Approximative energy calculations show a preferential energy range for isolated interface states at a distance of 0.1–0.2 eV distance from the band edges. Comparison with experimental termspectra shows a good agreement with the treated model. Common characteristics of clean, ordinary and oxidized surfaces and the metal semiconductor contact are revealed.     

Two dimensional interacting electrons on a torus in a strong magnetic field: Symmetry properties and the effect of disorder

We discuss the symmetry properties of two dimensional interacting electrons on a torus in a strong magnetic field. Invariance under magnetic translations of the center of mass leads to a decomposition of the Hilbert space into a direct sum of subspaces. The degenerate ground states are out of one of these subspaces. This is used to calculate the energy splitting of the ground state energy due to a disordered background potential. The energy splitting is small and vanishes in thermodynamic limit if the denominator of the filling factor is odd and small. Numerical calculations confirm our results.     

RADIAL SOLUTIONS OF THE DIRAC EQUATION IN A LEMAITRE METRIC

In this paper the radial solutions of the Dirac equation in a metric with spheroidal symmetry are given.It is shown that there exists no quantum bound states of Fermions about the Schwarzschild black hole.Some cases are discussed,one is a soliton wave of the temporal state,which provides a new insight for checking the existence of a black hole,the other is a solution of the stationary state which describes the accretion and vaporization of the black hole.     

Details of disorder matter in 2D d-wave superconductors

Within numerically exact solutions of the Bogoliubov-de Gennes equations, we demonstrate that discrepancies between predicted low-energy quasiparticle properties in disordered 2D d-wave superconductors occur because of the unanticipated importance of disorder model details and normal state particle-hole symmetry. For the realistic case, which is best described by a binary alloy model without particle-hole symmetry, we predict density-of-state suppression below an energy scale which appears to be correlated with the corresponding single impurity resonance.     

Resonant formation and control of 2D symmetric vortex waves

It is shown that m-fold symmetric vortex waves in two dimensions ( V states) preserve their functional form in a weak straining flow having appropriate symmetry, but arbitrary time dependence. This phenomenon is used in driving the V states into a highly nonlinear excitation by subjecting a circular vortex patch to rotation and strain with oscillating strain rate and varying the rotation angular velocity. The effect is due to autoresonance in the system as the excited vortex state boundary self-adjusts its aspect ratio to synchronize with the external flow.     

Ordered and disordered dynamics in monolayers of rolling particles

We consider the ordered and disordered dynamics for monolayers of rolling self-interacting particles modeling water molecules. The rolling constraint represents a simplified model of a strong, but rapidly decaying bond with the surface. We show the existence and nonlinear stability of ordered lattice states, as well as disturbance propagation through and chaotic vibrations of these states. We study the dynamics of disordered gas states and show that there is a surprising and universal linear connection between distributions of angular and linear velocity, allowing definition of temperature.     

Mixed symmetry states and electromagnetic transition in the N=Z nucleus ~(28)Si

The interacting boson model with isospin (IBM-3) has been used to study mixed symmetry states and electromagnetic transitions at low-lying states for a ²⁸Si nucleus. The theoretical calculations show that the 2₄⁺ state is the lowest mixed symmetry state in ²⁸Si and the 4₃⁺ state is also a mixed symmetry state.