Anomalously localised states at the Anderson transition

Non-multifractal critical wave functions at the Anderson transition are numerically investigated for the SU(2) model belonging to the two-dimensional symplectic class. These states can be regarded as anomalously localised states (ALS) at criticality. Giving a quantitative definition of ALS, it has been revealed that the probability to find ALS increases with the system size and remains at a finite value even in the thermodynamic limit. The most probable, namely typical, critical states have the multifractal nature, while its probability measure is zero. In order to understand how ALS affect critical properties in infinite systems, we studied the distribution of the correlation dimension D₂ and the nearest-neighbour level spacing distribution P(s) by paying attention to ALS. Results show that the influence of ALS to these distribution functions is limited. This is because the spatial distribution of amplitudes in tail regions of ALS exhibits multifractality as in the case of typical critical wave functions.     

A study of the (3He,n) reaction on isotopes of tin

The (³He, n) reaction has been studied on^{112,116,118,120,124}Sn at 25.4 MeV. Angular distributions were measured over the range 0°–25° and the results compared with predictions of zero-range DWBA calculations. In addition to the around-state transitions, L = 0 transitions were also observed to low-lying states in every case. Simple two component wave functions, as well as those obtained from a more sophisticated pairing model, are compared with the data in order to explain the appearance of the anomalously low-lying excited 0⁺ states observed. L = 2 transitions were observed to low-lying 2⁺ states, but the strength of these transitions was much less than expected from the systematics of (t, p) results for N = 50 nuclei.     

The structure of the excited states in84Rb

Conclusion On the basis of the simple shell-model the anomalously high admixture of the E4-radiation to the M3-transition deexciting the isomeric state^84mRb has been explained. The exact evaluation of the amount of this admixture would require, however, detailed theoretical calculations considerating the configuration mixing in the wave functions of the 3⁺ and 6⁺ states in⁸⁴Rb.     

The Analytical Wavefunctions of SU(3) Limit in the Interacting Boson Model

A projection method to calculate the physical states from intrinsic states is put forward. Using this projection method, the physical states of the ground state band in the interacting boson model (IBM) SU(3) limit are calculated. The wave functions are expressed in terms of the building blocks of the IBM wave functions.     

Localization and critical diffusion of quantum dipoles in two dimensions

We discuss quantum propagation of dipole excitations in two dimensions. This problem differs from the conventional Anderson localization due to the existence of long-range hops. We find that the critical wave functions of the dipoles always exist which manifest themselves by a scale independent diffusion constant. If the system is T invariant the states are critical for all values of the parameters. Otherwise, there can be a "metal-insulator" transition between this "ordinary" diffusion and the Levy flights (the diffusion constant logarithmically increasing with the scale). These results follow from the two-loop analysis of the modified nonlinear supermatrix σ model.     

两腿XXZ自旋梯子模型的量子相变与量子临界现象

对于无限大尺寸两腿自旋1/2的XXZ自旋梯子模型,通过运用基于随机行走的张量网络(TN)算法数值模拟出基态波函数,首次尝试研究自旋梯子模型的约化保真度、普适序参量、纠缠熵等物理观测量,并系统研究基态保真度的三维挤点与二维分叉、约化保真度的分叉、局域序参量、普适序参量、纠缠熵和量子相变之间存在的关联关系.基于张量网络表示的算法在任意随机选择初始状态时,可以得到两腿XXZ量子自旋梯子系统简并的对称破缺基态波函数,该基态波函数是由于Z2对称破缺引起的.本文期望所提供的方法可为进一步研究凝聚态物质中热力学极限下的强关联电子量子晶格自旋梯子系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

Pair Formation of Hard Core Bosons in Flat Band Systems

Hard core bosons in a large class of one or two dimensional flat band systems have an upper critical density, below which the ground states can be described completely. At the critical density, the ground states are Wigner crystals. If one adds a particle to the system at the critical density, the ground state and the low lying multi particle states of the system can be described as a Wigner crystal with an additional pair of particles. The energy band for the pair is separated from the rest of the multi-particle spectrum. The proofs use a Gerschgorin type of argument for block diagonally dominant matrices. In certain one-dimensional or tree-like structures one can show that the pair is localised, for example in the chequerboard chain. For this one-dimensional system with periodic boundary condition the energy band for the pair is flat, the pair is localised.     

Three-body force and the tetraquark interpretation of light scalar mesons

We study the possible tetraquark interpretation of light scalar meson states a0(980), f0(980), κ,σ within the framework of the non-relativistic potential model. The wave functions of tetraquark states are obtained in a space spanned by multiple Gaussian functions. We find that the mass spectra of the light scalar mesons can be well accommodated in the tetraquark picture if we introduce a three-body quark interaction in the quark model. Using the obtained multiple Gaussian wave functions, the decay constants of tetraquarks are also calculated within the "fall apart" mechanism.     

Heavy-light mesons in a relativistic model

We study the heavy-light mesons in a relativistic model, which is derived from the Bethe-Salpeter equation by applying the Foldy-Wouthuysen transformation to the heavy quark. The kernel we choose is based on scalar confinement and vector Coulomb potentials. The transverse interaction of the gluon exchange is also taken into account in this model. The spectra and wave functions of D, D_s, B, B_s meson states are obtained. The spectra are calculated up to the order of 1/m Q, and wave functions are treated to leading order.     

Gamow-Teller strengths in the A = 14 multiplet: a challenge to the shell model

A new experimental approach to the famous problem of the anomalously slow Gamow-Teller (GT) transitions in the beta decay of the A=14 multiplet is presented. The GT strength distributions to excited states in 14C and 14O were studied in high-resolution (d,2He) and (3He,t) charge-exchange reactions on 14N. No-core shell-model calculations capable of reproducing the suppression of the beta decays predict a selective excitation of Jpi=2+ states. The experimental confirmation represents a validation of the assumptions about the underlying structure of the 14N ground state wave function. However, the fragmentation of the GT strength over three 2+ final states remains a fundamental issue not explained by the present no-core shell model using a 6homega model space, suggesting possibly the need to include cluster structure in these light nuclei in a consistent way.     

Resonant states and their uses

The paper shows, for a simple model, how the wave functions belonging to complex energy eigenvalues (resonance states) can be regarded as part of a complete set of states, containing also bound states and a continuum of (generally complex) wave functions. This forms the basis of an expansion, which is used to describe inelastic scattering in the plane-wave Born approximation, taking the same simple model for the target.     

Correlation of eigenstates in the critical regime of quantum Hall systems

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, [Formula: see text], gives an almost complete characterization of the critical behaviour of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.     

sine-Gordon模型与高斯波泛函方法

应用高斯波泛函方法,研究了sine-Gordon模型的基态、单粒子态和两粒子态。在Cole-man临界点附近,sine-Gordon系统趋于零质量玻色子系统,从而具有共形对称性。本文同时证明,当重整化质量有限时,在两粒子态中存在束缚态。 关键词：     

Extracting excitations from model state entanglement

We extend the concept of an entanglement spectrum from the geometrical to the particle bipartite partition. We apply this to several fractional quantum Hall wave functions on both sphere and torus geometries to show that this new type of entanglement spectra completely reveals the physics of bulk quasihole excitations. While this is easily understood when a local Hamiltonian for the model state exists, we show that the quasihole wave functions are encoded within the model state even when such a Hamiltonian is not known. As a nontrivial example, we look at Jain's composite fermion states and obtain their quasiholes directly from the model state wave function. We reach similar conclusions for wave functions described by Jack polynomials.     

The optical potential for the elastic heavy ion scattering

For the elastic scattering of heavy ions a microscopic model is developed which uses shell model wave functions which are localised at a certain distance both in coordinate and momentum space. The antisymmetrization is treated exactly. Using oscillator functions and the Brink-Boeker force the energy dependent real part of the optical potential for O₁₆- O₁₆ scattering is numerically determined. The results are compared with the analysis of experiments.     

Spectral properties of quasiperiodic superlattices and study of wave functions

We report the study of the spectral properties of a quasiperiodic superlattice within a tight binding model. Numerical work is carried out using the transfer matrix method. An approximate analytical scheme is used to obtain expressions for the band gaps which explain all the features obtained numerically. Due to the fact that blocks of atoms are repeated quasiperiodically, the gaps are shown to vanish at specific energies. These states have much the same behaviour as the extended states but the amplitude is a quasiperiodic function of the site index. The total number of such extended states are estimated. Since it is known that other states in quasiperiodic systems are critical, these states are expected to exhibit a cross-over behaviour to the critical states as a function of the energy. Multifractal analysis of the quasiperiodic wave function show that it has the same signature as the extended wave function. We briefly comment on the cross-over behaviour.     

Cluster methods to study the electronic structure of condensed matter

Multiple scattering techniques have been used to study the electronic states (core and continuum states) of condensed matter. The electronic density of states, total energies, charge and spin densities are computed self consistently. The electronic and magnetic properties of the materials are evaluated from this results. The model material is a finite cluster of atoms immersed in the spherical average potential of the rest of the system. The electronic states are then either core states or continuum states. Examples in which the wave functions are given molecular boundary conditions far from the cluster of atoms are also presented.     

Extreme wave formation in unidirectional sea due to stochastic wave phase dynamics

The authors consider a stochastic model based on the interaction and phase coupling amongst wave components that are modified envelope soliton solutions to the nonlinear Schrödinger equation. A probabilistic study is carried out and the resulting findings are compared with ocean wave field observations and laboratory experimental results. The wave height probability distribution obtained from the model is found to match well with prior data in the large wave height region. From the eigenvalue spectrum obtained through the Inverse Scattering Transform, it is revealed that the deep-water wave groups move at a speed different from the linear group speed, which justifies the inclusion of phase correction to the envelope solitary wave components. It is determined that phase synchronization amongst elementary solitary wave components can be critical for the formation of extreme waves in unidirectional sea states.     

Theory of angle-resolved photoemission from localised orbitals at solid surfaces

The theory of angle resolved photoemission from localised orbitals is reviewed and is cast in a form requiring the calculation of the purely outgoing wave emanating from an emitting atom, that describes the final state of the photoelectron, rather than using the more usual approach based on time reversed scattering states. An explicit expression is written down for the superposition of partial waves that results from emission from an atomic orbital, and it is pointed out that emission from more complex initial states such as localised bonds or Bloch and surface states, can be described by coherently combining such sets of partial waves. The effect of the crystal surface environment in damping and scattering the waves is described briefly. Model calculations are performed to investigate the major influences on the angular distribution of the photoelectrons. The profound effect of varying the polarisation direction of the incident light relative to the surface is discussed, with examples from the literature, showing how it can be used to determine the type of initial orbital. Emission from directed orbitals is studied and it is shown that scattering by the emitter potential can be an important effect, so that the radial wave function of the outgoing electron, which determines the amplitudes and phases of the outgoing waves, must be calculated with care. Different choices of these quantities lead in the model calculations to very different angular profiles, that sometimes bear little relation to the shape of the initial orbital. The consideration of emission from localised bonds shows that provided that bonds are not too strongly polarised, interference between waves from different centres is always significant at higher energies, and can also be important at energies of a few eV relative to the vacuum. Scattering by the ion cores of the surface region can strongly distort the angular distribution, or may have little effect. But it is generally difficult to decide a priori which influences are dominant for a particular case, so that the interpretation of angular profiles must be based on careful calculations including all these effects. The optimum energy range for the interpretation of experimental data is that from about 30 to 100 eV.