Nodal domain statistics for quantum maps, percolation, and stochastic Loewner evolution

We develop a percolation model for nodal domains in the eigenvectors of quantum chaotic torus maps. Our model follows directly from the assumption that the quantum maps are described by random matrix theory. Its accuracy in predicting statistical properties of the nodal domains is demonstrated for perturbed cat maps and supports the use of percolation theory to describe the wave functions of general Hamiltonian systems. We also demonstrate that the nodal domains of the perturbed cat maps obey the Cardy crossing formula and find evidence that the boundaries of the nodal domains are described by stochastic Loewner evolution with diffusion constant close to the expected value of 6, suggesting that quantum chaotic wave functions may exhibit conformal invariance in the semiclassical limit.     

Moment-wavelet quantization: a first principles analysis of quantum mechanics through continuous wavelet transform theory

The space of polynomials is invariant under affine maps. This suggests that a moment based analysis can facilitate a first principles incorporation of continuous wavelet transform (CWT) theory into quantum mechanics. We show that this is indeed the case for a large class of Hamiltonians and mother wavelet functions. We establish the equivalence between moment quantization (MQ) and CWT. By so doing, we clearly demonstrate the inherent multiscale structure of MQ analysis with regards to determining the physical energies and corresponding wavefunctions.     

A Novel Moment Approach for Calculation of the Perron–Frobenius Spectrum

The spectral properties of the Perron–Frobenius operator of the one-dimensional maps are studied by using the moment. In this paper we make an investigation into the properties of self-similar measures related to the theory of orthogonal polynomials. Numerical investigation of a particular family of maps shows that the spectrum generates the invariant measure. Analytical considerations generalize the results to a broader class of the maps. Some examples of this method are presented through out the paper.     

Lyapunov exponent for chaotic 1D maps with uniform invariant distribution

Some properties of iterative functions of 1D chaotic maps that provide uniform invariant distribution are formulated. A method for synthesizing strictly nonlinear maps with uniform invariant distribution is demonstrated. The Lyapunov exponents for such maps are analyzed and it is shown that, among the maps with a specified number of full branches, piecewise linear maps with branches characterized by equal moduli of angular coefficients have the maximum Lyapunov exponent.     

A first-principle study of the magnetic,electronic and elastic properties of the hypothetical YFe5 compound

We present a DFT-based study of the magnetic properties, electronic structure and bulk modulus of YFe₅ at ambient and higher hydrostatic pressures. The LSDA and GGA approximations, as implemented in the electronic structure code FPLO-09, are used throughout the scalar relativistic calculation in this work. Charge and spin density maps using the WIEN2k are also reported for the equilibrium lattice constants. Our study shows that the magnetic phase of this hypothetical compound is more stable than the nonmagnetic phase, and that the application of pressure on magnetic YFe₅ has a prominent effect on its magnetic and electronic properties, e.g. the reduction of the magnetic moment and finally the disappearance of ferromagnetism.     

Random walks with nonnearest-neighbor transitions. II. Analytic one-dimensional theory for exponentially distributed steps in systems with boundaries

Exact analytic results for symmetric, nonnearest-neighbor random walks in one-dimensional finite and semiinfinite lattices are presented. Random walks with exponentially distributed step lengths are considered such that variation of a single parameter permits one to cover the whole range of step lengths from nearest-neighbor transitions to steps of aribtrary length. The generating functions for such lattices are derived and used to calculate a number of moment properties (mean first passage times, dispersion in the mean recurrence time). Since explicit expressions for the generating functions for these walks are obtained, additional moment properties can readily be calculated. The results found here for a finite system are compared to results found previously for a system with periodic boundary conditions. Two different semiinfinite systems are also considered.     

WAVE FUNCTIONS WITHOUT SU6 SYMMETRY IN THE STRATON MODEL AND THEIR APPLICATIONS

On the basis of the straton model^[1],using the general groundstate wave functionsof mesons and baryons given in ref.[2],we have constructed under some specific as-sumptions the meson and baryon wave functions without SU₆ symmetry.We applythese wave functions to explain the mesonic and baryonic properties of the electroma-gnetic and weak interactions;many results obtained are in agreement with the experi-ments.By using the 1/2⁺-baryon wave functions without SU₆ symmetry,we obtain ananomalous magnetic moment for the proton.There is no need to introduce an ano-malous magnetic moment for the straton in the effective Hamiltonian of electromag-netic interaction between stratons.Similarly,the magnetic moment of the neutroncan also be explained.     

Nonergodicity of blinking nanocrystals and other Lévy-walk processes

We investigate the nonergodic properties of blinking nanocrystals modeled by a Lévy-walk stochastic process. Using a nonergodic mean field approach we calculate the distribution functions of the time averaged intensity correlation function. We show that these distributions are not delta peaked on the ensemble average correlation function values; instead they are W or U shaped. Beyond blinking nanocrystals our results describe ergodicity breaking in systems modeled by Lévy walks , for example, certain types of chaotic maps and spin dynamics to name a few.     

Moment maps at the quantum level

We introduce the notion of moment maps for quantum groups acting on their module algebras. When the module algebras are quantizations of Poisson manifolds, we prove that the construction at the quantum level is a quantization of that at the semi-classical level. We also prove that the corresponding smashed product algebras are quantizations of the semi-direct product Poisson structures.Research partially supported by NSF grant DMS-89-07710     

Aperiodic magnetic models on the Wheatstone hierarchical lattice

Aperiodic Ising models on Wheatstone hierarchical lattices, induced by two-letter substitution sequences, are analyzed within a transfer matrix framework. The numerical iteration of the set of maps leads to values for the thermodynamical properties as functions of the temperature, from which the critical properties are evaluated. Relevant geometric fluctuations in the distribution of bonds induced by substitution rules play an essential role for the occurrence of changes in the critical behavior of the aperiodic model in comparison with its homogeneous counterpart. We have found both irrelevant and relevant fluctuations already for the first two members of this family. Results are important to the understanding of the behavior of aperiodic Ising model on planar lattices.     

Local and global statistical properties of deterministic chaos

Summary Locla and global statistical properties of a class of one-dimensional dissipative chaotic maps and a class of 2-dimensional conservative hyperbolic maps are investigated. This is achieved by considering the spectral properties of the Perron-Frobenius operator (the evolution operator for probability densities) acting on two different types of function space. In the first case, the function space is piecewise analytic, and includes functions having support over local regions of phase space. In the second case, the function space essentially consists of functions which are “globally? analytic,i.e. analytic over the given systems entire phase space. Each function space defines a space of measurable functions or observables, whose statistical moments and corresponding characteristic times can be exactly determined. Paper presented at the International Workshop ?Fluctuations in Physics and Biology: Stochastic Resonance, Signal Processing and Related Phenomena?, Elba, 5–10 June 1994.     

The Influence of Dynamical Screening on the Transport Properties of Dense Plasmas

We investigate the effects of dynamical screening on the static transport properties. We review the low density expansion for the electron‐electron and electron‐ion correlation functions and give results for a 6‐moment approach within linear response theory. The expansion coefficients are given. The convergence of thermoelectric transport coefficients is examined in dependence of the rank of the collision term determinant. The results are compared with previous calculations and experiments. Effective Debye screening radii derived from the Gould‐DeWitt scheme for the inclusion of strong collisions as well as dynamical effects are discussed. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

利用高分辨同步辐射衍射研究氨苄青霉素三水合物的电荷密度分布:密度泛函理论和多极模型之间的相关性

实验研究了氨苄青霉素三水合物的电荷密度分布,并与用密度泛函理论的量子计算结果进行比较.计算了电荷导出性质,Mulliken原子电荷,偶极矩和分子静电势.另外用多极分析对实验总体参数的进行细化.用多极处理获得的结构因子构建了傅立叶图.同时讨论电荷分布的拓扑性质,分析了（3,-1）临界点的特性.     

Inverse moment analysis of time dependent autocorrelation functions

We apply inverse moment techniques to analyse certain time dependent autocorrelation functions. The experimentally measured values are interpreted as moments of a probability distributionf(x) which is calculated numerically. For this purpose we use Chebychev's algorithm. By means of the inverse algorithm we can reproduce the original data within numerical precision. The ill-conditioning of the inverse moment problem is circumvented by making an ansatz for the unknown higher order moments. We discuss in particular exponentially and algebraically decaying correlation functions.     

An analytical construction of the SRB measures for Baker-type maps

For a class of dynamical systems, called the axiom-A systems, Sinai, Ruelle and Bowen showed the existence of an invariant measure (SRB measure) weakly attracting the temporal average of any initial distribution that is absolutely continuous with respect to the Lebesgue measure. Recently, the SRB measures were found to be related to the nonequilibrium stationary state distribution functions for thermostated or open systems. Inspite of the importance of these SRB measures, it is difficult to handle them analytically because they are often singular functions. In this article, for three kinds of Baker-type maps, the SRB measures are analytically constructed with the aid of a functional equation, which was proposed by de Rham in order to deal with a class of singular functions. We first briefly review the properties of singular functions including those of de Rham. Then, the Baker-type maps are described, one of which is nonconservative but time reversible, the second has a Cantor-like invariant set, and the third is a model of a simple chemical reaction R<-->I<-->P. For the second example, the cases with and without escape are considered. For the last example, we consider the reaction processes in a closed system and in an open system under a flux boundary condition. In all cases, we show that the evolution equation of the distribution functions partially integrated over the unstable direction is very similar to de Rham's functional equation and, employing this analogy, we explicitly construct the SRB measures. (c) 1998 American Institute of Physics.     

Arithmetic properties of mirror map and quantum coupling

We study some arithmetic properties of the mirror maps and the quantum Yukawa couplings for some 1-parameter deformations of Calabi-Yau manifolds. First we use the Schwarzian differential equation, which we derived previously, to characterize the mirror map in each case. For algebraic K3 surfaces, we solve the equation in terms of theJ-function. By deriving explicit modular relations we prove that some K3 mirror maps are algebraic over the genus zero function fieldQ(J). This leads to a uniform proof that those mirror maps have integral Fourier coefficients. Regarding the maps as Riemann mappings, we prove that they are genus zero functions. By virtue of the Conway-Norton conjecture (proved by Borcherds using Frenkel-Lepowsky-Meurman's Moonshine module), we find that these maps are actually the reciprocals of the Thompson series for certain conjugacy classes in the Griess-Fischer group. This also gives, as an immediate consequence, a second proof that those mirror maps are integral. We thus conjecture a surprising connection between K3 mirror maps and the Thompson series. For threefolds, we construct a formal nonlinear ODE for the quantum coupling reduced modp. Under the mirror hypothesis and an integrality assumption, we derive modp congurences for the Fourier coefficients. For the quintics, we deduce, (at least for 5×d) that the degreed instanton numbersn _d are divisible by 5³ — a fact first conjectured by Clemens.Research supported by grant DE-FG02-88-ER-25065     

Universal properties of maps on an interval

We consider itcrates of maps of an interval to itself and their stable periodic orbits. When these maps depend on a parameter, one can observe period doubling bifurcations as the parameter is varied. We investigate rigorously those aspects of these bifurcations which are universal, i.e. independent of the choice of a particular one-parameter family. We point out that this universality extends to many other situations such as certain chaotic regimes. We describe the ergodic properties of the maps for which the parameter value equals the limit of the bifurcation points.     

A smoothing technique for discrete delta functions with application to immersed boundary method in moving boundary simulations

The effects of complex boundary conditions on flows are represented by a volume force in the immersed boundary methods. The problem with this representation is that the volume force exhibits non-physical oscillations in moving boundary simulations. A smoothing technique for discrete delta functions has been developed in this paper to suppress the non-physical oscillations in the volume forces. We have found that the non-physical oscillations are mainly due to the fact that the derivatives of the regular discrete delta functions do not satisfy certain moment conditions. It has been shown that the smoothed discrete delta functions constructed in this paper have one-order higher derivative than the regular ones. Moreover, not only the smoothed discrete delta functions satisfy the first two discrete moment conditions, but also their derivatives satisfy one-order higher moment condition than the regular ones. The smoothed discrete delta functions are tested by three test cases: a one-dimensional heat equation with a moving singular force, a two-dimensional flow past an oscillating cylinder, and the vortex-induced vibration of a cylinder. The numerical examples in these cases demonstrate that the smoothed discrete delta functions can effectively suppress the non-physical oscillations in the volume forces and improve the accuracy of the immersed boundary method with direct forcing in moving boundary simulations.     

Magnetic elements for switching magnetization magnetic force microscopy tips

Using combination of micromagnetic calculations and magnetic force microscopy (MFM) imaging we find optimal parameters for novel magnetic tips suitable for switching magnetization MFM. Switching magnetization MFM is based on two-pass scanning atomic force microscopy with reversed tip magnetization between the scans. Within the technique the sum of the scanned data with reversed tip magnetization depicts local atomic forces, while their difference maps the local magnetic forces. Here we propose the design and calculate the magnetic properties of tips suitable for this scanning probe technique. We find that for best performance the spin-polarized tips must exhibit low magnetic moment, low switching fields, and single-domain state at remanence. The switching field of such tips is calculated and optimum shape of the Permalloy elements for the tips is found. We show excellent correspondence between calculated and experimental results for Py elements.