Directional ordering of fluctuations in a two-dimensional compass model

In the Mott insulating phase of the transition metal oxides, the effective orbital-orbital interaction is directional both in orbital space and in real space. We discuss a classical realization of directional coupling in two dimensions. Despite extensive degeneracy of the ground state, the model exhibits partial orbital ordering in the form of directional ordering of fluctuations at low temperatures stabilized by an entropy gap. Transition to the disordered phase is shown to be in the Ising universality class through exact mapping and multicanonical Monte Carlo simulations.     

神经系统的简并性与序空间编码分析

Edelman提出了神经系统中存在简并现象,但并未说明简并在神经系统中的具体形式和作用.文中从序空间理论出发,以神经回路为讨论基础,具体讨论了双耳定向的神经回路中可能出现的简并网络,以及各种网络被简并的方法.把简并现象的讨论和编码的讨论结合起来,对神经网络中的简并现象有了一个具体的认识.文中虽然是由纯理论推导的结果,但所得回路包含了被广泛承认的Jeffress模型,因此也间接证明了该理论也有一定的生物学基础. 关键词： 简并 神经编码 序空间 双耳声源定向     

Anisotropic Interface Roughness Scattering in a Lateral Superlattice

A novel interface roughness due to the perturbation of the periodic interface structure is studied theoretically for a lateral superlattice realized by an interface corrugated quantum well. It is found by numerical simulation that the correlation function for interface roughness can be well modeled by a sinusoidal function with an exponential decay in the direction of corrugation. Such a feature makes the correlation function far from a Gaussian function which is extensively used as a theoretical approximation of the correlation function for interface roughness. With such a correlation function, the influence of interface roughness scattering on electronic transport in the lateral superlattice is investigated. Consequently, it gives rise to a high anisotropy of electronic transport both in the absence and presence of a magnetic field, by which the relevant experiments can be well explained.     

Anisotropic Interface Roughness Scattering in a Lateral Superlattice

A novel interface roughness due to the perturbation of the periodic interface structure is studied theoretically for a lateral superlattice realized by an interface corrugated quantum well. It is found by numerical simulation that the correlation function for interface roughness can be well modeled by a sinusoidal function with an exponential decay in the direction of corrugation. Such a feature makes the correlation function far from a Gaussian function which is extensively used as a theoretical approximation of the correlation function for interface roughness. With such a correlation function, the influence of interface roughness scattering on electronic transport in the lateral superlattice is investigated.Consequently, it gives rise to a high anisotropy of electronic transport both in the absence and presence of a magnetic field, by which the relevant experiments can be well explained.     

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.     

The phase diagram and susceptibility of LiNiO2

The phase diagram and the temperature dependence of the susceptibility of a four-site spin system with orbital degeneracy have been calculated by taking into account the triangular lattice symmetry. The results indicate that the ground state of the spin–orbital system can be spin disordered even in the case of the large Hund's interaction and the anisotropic orbital hopping. The susceptibility and the short correlation show antiferromagnetic in low temperature, but ferromagnetic in high temperature. These conclusions are in agreement with the recent experimental observations on the material LiNiO₂.     

Degeneracy of Resonances: Branch Point and Branch Cuts in Parameter Space

The rich phenomenology of crossings and anticrossings of energies and widths, observed in an isolated doublet of resonances when one control parameter is varied, is fully explained in terms of the topological properties of the energy hypersurfaces close to the degeneracy point. The hypersurface representing the complex resonance eigenvalues, as functions of the control parameters, has an algebraic branch point of rank one, and branch cuts in its real and imaginary parts, in parameter space. Associated with this singularity in parameter space, the scattering matrix, S _ℓ (E), and the Green’s function, G _ℓ ⁽⁺⁾(k; r,r'), have one double pole in the unphysical sheet of the complex energy plane. We characterize the universal unfolding or deformation of any degeneracy point of two unbound states in parameter space by means of a universal 2-parameter family of functions which is contact equivalent to the pole position function of the isolated doublet of resonances at the exceptional point and includes all small perturbations of the degeneracy condition up to contact equivalence.     

Ten-fold degenerate d-electron correlation and the metal-nonmetal transition in a disordered binary system: Inclusion of Hund's rule coupling

The Yonezawa-Watabe (YW) study of the metal-nonmetal transitions in nondegenerate, s-electron disordered binary systems: doped semiconductors, metal-ammonia solutions, liquid metals and mixed crystals (alloys), is generalized to include ten-fold d-electron (hole) degeneracy. Such degeneracy automatically includes Hund's rule d-electron coupling and intra-site enhanced Coulomb and exchange interactions. Such a calculation is specifically relevant only to transition metal alloys, transition metal oxides and mixed transition metal oxides. It is seen that potential fluctuations exist in these systems and the possibility of Anderson localization in these disordered degenerate binary transition metal systems is explored. The YW CPA treatment of the effect of substitutional disorder (alloying) upon the mobility gap and quasiparticle states of the density of states at the extreme band edges and localization due to random spin configuration are generalized to these degenerate d-electron systems and it is shown that the disappearance of the mobility gap, not the density of states gap, causes the metal-nonmetal transition for degenerate d-electrons.     

Orbital liquid in three-dimensional mott insulator: LaTiO3

We present a theory of spin and orbital states in Mott insulator LaTiO3. The spin-orbital superexchange interaction between d(1)(t(2g)) ions in cubic crystal suffers from a pathological degeneracy of orbital states at the classical level. Quantum effects remove this degeneracy and result in the formation of the coherent ground state, in which the orbital moment of t(2g) level is fully quenched. We find a finite gap for orbital excitations. Such a disordered state of local degrees of freedom on unfrustrated, simple cubic lattice is highly unusual. Orbital liquid state naturally explains observed anomalies of LaTiO3.     

Energy landscape of a simple model for strong liquids

We calculate the statistical properties of the energy landscape of a minimal model for strong network-forming liquids. Dynamic and thermodynamic properties of this model can be computed with arbitrary precision even at low temperatures. A degenerate disordered ground state and logarithmic statistics for the local minima energy distribution are the landscape signatures of strong liquid behavior. Differences from fragile liquid properties are attributed to the presence of a discrete energy scale, provided by the particle bonds, and to the intrinsic degeneracy of topologically disordered networks.     

The influence of the surface roughness on dielectric function of two-dimensional electron gas: a Lindhard model approach

Low field response function calculations have been performed on a two-dimensional electron gas with well-defined electron-surface roughness scattering. The Lindhard model was employed to compute the response function. In particular, detailed investigations were made on the system searching for an interplay between surface roughness with well-defined correlation function, (characterizes by asperity height and correlation length) spatial confinement and the dielectric function. We analyze to what extent the normal behavior and functionality of dielectric function of two-dimensional devices are modified by random scattering events caused by the contribution from the surface roughness. Results of the current work indicate that contribution of the surface roughness on scattering and absorption process could not be considered as an underestimating effect. We find, however, that functionality of the dielectric function seems to be quite independent of the particular roughness features.     

New effective-field theory with correlations; application to disordered magnets

The Ising model of spin 1/2 with nearest-neighbour interaction is investigated. Within the effective-field theory introduced by Honmura and Kaneyoshi, a new type of decoupling approximation is introduced for treating the multispin correlation functions. The critical temperature, the spontaneous magnetization, and the two-site spin c correlation function are calculated for a two- (or three-) dimensional lattice. The present formalism yields results better than those of Bethe-Peierls approximation and is extended to disordered magnets. The thermodynamical quantities of quenched random-bond magnets, such as magnetization, susceptibility and so on, are studied, We find that in particular the twosite spin correlation functions of the disordered magnets exhibit some interesting behavior.     

Wetting, spreading, and adsorption on randomly rough surfaces

The wetting properties of solid substrates with customary (i.e., macroscopic) random roughness are considered as a function of the microscopic contact angle of the wetting liquid and its partial pressure in the surrounding gas phase. Analytic expressions are derived which allow for any given lateral correlation function and height distribution of the roughness to calculate the wetting phase diagram, the adsorption isotherms, and to locate the percolation transition in the adsorbed liquid film. Most features turn out to depend only on a few key parameters of the roughness, which can be clearly identified. It is shown that a first-order transition in the adsorbed film thickness, which we term "Wenzel prewetting", occurs generically on typical roughness topographies, but is absent on purely Gaussian roughness. It is thereby shown that even subtle deviations from Gaussian roughness characteristics may be essential for correctly predicting even qualitative aspects of wetting.     

Density matrix renormalization group numerical study of the kagome antiferromagnet

We numerically study the spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice using the density-matrix renormalization group method. We find that the ground state is a magnetically disordered spin liquid, characterized by an exponential decay of spin-spin correlation function in real space and a magnetic structure factor showing system-size independent peaks at commensurate magnetic wave vectors. We obtain a spin triplet excitation gap DeltaE(S=1)=0.055+/-0.005 by extrapolation based on the large size results, and confirm the presence of gapless singlet excitations. The physical nature of such an exotic spin liquid is also discussed.     

A New Probe: AFM Measurements for Random Disorder Systems

We study the quenched random disorder(QRD) effects created by aerosil dispersion in the octylcyanobiphenyl(8CB) liquid crystal(LC) using atomic force microscopy technique. Gelation process in the 8CB+aerosil gels yields a QRD network which also changes the surface topography. By increasing the aerosil concentration, the original smooth pattern of LC sample surfaces is suppressed by the emergence of a fractal aerosil surface effect and these surfaces become more porous, rougher and they have more and larger crevices. The dispersed aerosil also serves as pinning centers for the liquid crystal molecules. It is observed that via the diffusion-limitedaggregation process, aerosil nano-particles yield a fractal-like surface pattern for the less disordered samples. As the aerosil dispersion increases, the surface can be described by more aggregated regions, which also introduces more roughness. Using this fact, we show that there is a net correlation between the short-range ordered x-ray peak widths(the results of previous x-ray diffraction experiments) and the calculated surface roughness. In other words, we show that these QRD gels can also be characterized by their surface roughness values.     

Many-Body Localization Transition in the Heisenberg Ising Chain

In this paper, we use exact matrix diagonalization to explore the many-body localization (MBL) transition of the Heisenberg Ising spin-1/2 chain with nearest neighbor couplings and disordered external fields. It demonstrates that the fidelity, magnetization and spin-spin space correlation can be used to characterize the many-body localization transition in this closed spin system which is also in agreement with previous analytical and numerical results. We test the properties for the middle third many-body eigenstates. It shows that for this model with random-field, the excited-state fidelity exhibits a pronounced drop at the transition and then gradually tends to be stable in the localized phase, the critical point and the final value of averaged fidelity are all size dependent. It demonstrates that disordered external fields drive the occurrence of the MBL transition. Moreover, we investigate the magnetization and spin-spin space correlation in this model to verify the conclusion we got and further explore the properties of ergodic phase and localized phase.

     

Roughness and correlation-length determination of rough-surface objects using the speckle contrast

A method using the speckle contrast for the determination of both the roughness and the correlation length of surface-height variations of a rough-surface object is proposed on the basis of the statistical properties of the Gaussian speckle field in the image region. The expression for the speckle contrast is first theoretically derived in the optical imaging system as a function of the defocus distance and the surface parameters of the object. By solving the equations expressing the speckle contrasts at the image and defocus planes, a unique solution is found to exist for the roughness and the correlation length. In particular, a useful approximate relation that the roughness depends only on the contrast ratio is derived for relatively small values of the roughness. The experiments were performed to confirm the validity of the proposed method. The present method has an advantage of the simplicity in a measuring procedure where the contrasts at only the two points are required to determine the surface parameters.     

Measurement of surface roughness properties using speckle patterns with non-gaussian statistics

The surface roughness properties (i.e. the rms surface roughness and the correlation length) of strong diffuse objects are investigated by using the speckle patterns which obeys the non-gaussian statistics. The intimate linear relation is found to exist between the rms surface roughness of objects and the maximum contrast obtained from the varying curves of the average image speckle contrast as a function of the point spread of an optical imaging system. The correlation length of surface roughness of objects is related to the averaged intensity distribution of speckle patterns produced at the far-field diffraction plane. It now becomes clear that the rms roughness and the correlation length of strong diffuse objects are determined, respectively, from the maximum speckle contrast at the image plane and the averaged speckle intensity distribution at the far-field diffraction plane.