Dynamics of quasicrystals

The (lattice) dynamics of quasicrystals differs in many aspects from that of lattice periodic systems. This they have in common with other aperiodic crystals. The dynamics of quasicrystals is discussed here in the context of these general aperiodic crystals, but the special features of quasicrystals are stressed. The lattice dynamics is now fairly well understood. Especially for aperiodic crystals, there are excitations related to the possibility to describe the systems in superspace. These ‘phasons’ are discussed in particular.     

Surfaces of quasicrystals

The remarkable surface properties of quasicrystals have motivated extensive investigations of their intrinsic atomic and electronic structures. In this article, we summarize some of the main conclusions obtained so far. We also describe adsorption experiments where quasiperiodic surfaces are used as templates to grow thin films with novel structures. Finally we discuss some of their useful properties of current interest.     

Ground state structures in ferrofluid monolayers

Computer and theoretical investigation of particle arrangements in a thin film of a magnetic fluid at low temperatures is presented. The approach developed by us combines the simplicity of simulations and accuracy of the analytical model and allows studying particle aggregates and their properties. The systems under investigation were: a monodisperse and a bidisperse model in the absence of an external magnetic field, and a monodisperse model under the influence of an external field. Careful analysis of the most probable microstructures in a ferrofluid thin layer has been carried out at 0 K. The analysis of the stability of structures under thermal fluctuations allows making a conclusion about the microstructure of investigated system at low temperatures.     

Ground states in two-dimensional boson quantum field-theory

We consider λ:P(?):₂ models of Euclidean quantum field theory, P(?) = Σ_k=1²ⁿa_k?^k and define for them translation-invariant ground states. It appears that the number of them is not more than two provided $\text{λ}\text{m}{}_0{}^2$ is large.     

Classical ground states in one dimension

We give conditions on an interaction sufficient to guarantee that in one dimension it yield a periodic ground state with one or two particles per unit cell.Research supported in part by NSF Grant MCS 81-01596-A01.     

Topological states in quasicrystals

With the rapid development of topological states in crystals, the study of topological states has been extended to quasicrystals in recent years. In this review, we summarize the recent progress of topological states in quasicrystals, particularly focusing on one-dimensional (1D) and 2D systems. We first give a brief introduction to quasicrystalline structures. Then, we discuss topological phases in 1D quasicrystals where the topological nature is attributed to the synthetic dimensions associated with the quasiperiodic order of quasicrystals. We further present the generalization of various types of crystalline topological states to 2D quasicrystals, where real-space expressions of corresponding topological invariants are introduced due to the lack of translational symmetry in quasicrystals. Finally, since quasicrystals possess forbidden symmetries in crystals such as five-fold and eight-fold rotation, we provide an overview of unique quasicrystalline symmetry-protected topological states without crystalline counterpart.     

Uniqueness of the Ground State in Weak Perturbations of Non-Interacting Gapped Quantum Lattice Systems

We consider a general weak perturbation of a non-interacting quantum lattice system with a non-degenerate gapped ground state. We prove that in a finite volume the dependence of the ground state on the boundary condition exponentially decays with the distance to the boundary, which implies in particular that the infinite-volume ground state is unique. Also, equivalent forms of boundary conditions for ground states of general finite quantum systems are discussed.On leave from Institute for Information Transmission Problems, Moscow, Russia.     

Elasticity and dislocations in quasicrystals with 18-fold symmetry

Elasticity problems of quasicrystals with 18-fold rotational symmetry are studied. Constitutive equations and governing equations are obtained. For static elasticity problems, the displacement vectors in two phason fields are expressed in terms of two pairs of associated harmonic functions or two analytic functions. For dynamic problems, the displacement vectors can be represented in terms of an auxiliary function satisfying a fourth-order partial differential equation. A general solution of phasons is given by the solution of two diffusion equations. Phason elastic fields induced by a dislocation in a quasicrystal with 18-fold symmetry are determined and exhibit an inverse singularity.     

Ground states and flux configurations of the two-dimensional Falicov-Kimball model

The Falicov-Kimball model is a lattice model of itinerant spinless fermions (electrons) interacting by an on-site potential with classical particles (ions). We continue the investigations of the crystalline ground states that appear for various filling of electrons and ions for large coupling. We investigate the model for square as well as triangular lattices. New ground states are found and the effects of a magnetic flux on the structure of the phase diagram are studied. The flux phase problem where one has to find the optimal flux configurations and the nuclei configurations is also solved in some cases. Finally we consider a model where the fermions are replaced by hard-core bosons. This model also has crystalline ground states. Therefore their existence does not require the Pauli principle, but only the on-site hard-core constraint for the itinerant particles.     

Ground and excited state dipole moments of coumarin 337 laser dye

This paper reports that the effects of spectral properties of coumarin 337 laser dye have been investigated in different solvents considering solvent parameters like dielectric constant (?) and refractive index (n) of different solvent polarities. The ground state (μ_g) and excited state (μ_e) dipole moments are calculated using Lippert's, Bakhshiev's, and Kawski-Chamma-Viallet's equations. In all these three equations the variation of Stokes shift was used to calculate the excited state (μ_e) dipole moment. It is observed that the Bakhshiev method is comparatively better than the other two methods for ground state and excited state dipole moment calculations. The angle between the excited state and ground state dipole moments is also calculated.     

Ground State Energy of Dilute Bose Gas in Small Negative Potential Case

It is well known that the ground state energy of a three dimensional dilute Bose gas in the thermodynamic limit is E=4π a ρ N when the particles interact via a non-negative, finite range, spherically symmetric, two-body potential. Here, N is the number of particles, ρ is the density of the gas, and a is the scattering length of the potential. In this paper, we prove the same result without the non-negativity condition on the potential, provided the negative part is small.     

Ground State Energy of the Low Density Hubbard Model

We derive a lower bound on the ground state energy of the Hubbard model for given value of the total spin. In combination with the upper bound derived previously by Giuliani (J. Math. Phys. 48:023302, [2007]), our result proves that in the low density limit the leading order correction compared to the ground state energy of a non-interacting lattice Fermi gas is given by 8π a ? _u ? _d , where ? _u(d) denotes the density of the spin-up (down) particles, and a is the scattering length of the contact interaction potential. This result extends previous work on the corresponding continuum model to the lattice case.     

Rashba效应对抛物量子阱中极化子基态能的影响

采用LLP变分法研究了抛物量子阱中极化子的Rashba效应,得到了极化子基态能量的表达式,并讨论了半阱宽及波矢与基态能量之间的关系.结果显示,基态能量是半阱宽和电子-声子耦合强度的减函数,而是波矢的增函数.由于Rashba效应基态能量零自旋轨道分裂成两支.     

Efficient generation of two-dimensional cluster states in a cavity QED

We propose a scheme to achieve a kind of nontrivial multipartite pair-wise controlled phase operation in a cavity QED setup. The operation implemented is of geometrical nature and is not sensitive to the thermal state of the cavity. In particular, we have managed to avoid the conventional dispersive coupling so that high speed gate operation is achieved which is very important in view of decoherence. We show that this multipartite pair-wise controlled phase operation makes the generation of two-dimensional cluster states very efficient.     

二维声子晶体中Zak相位诱导的界面态

界面态具有巨大的实际应用价值,因此寻找界面态是一个既有科学意义也有应用前景的课题.在本文中,我们通过把二维正方晶格声子晶体的结构单元进行倾斜,构造出具有线性狄拉克色散的斜方晶格体系.狄拉克色散引起体能带Zak相位的π跃变,使得位于狄拉克锥投影能带两边的带隙具有不同符号的表面阻抗,从而导致由正方晶体体系与由其“倾斜”的斜方晶格体系构成的界面处存在确定性的界面态.     

Analytical solutions for some defect problems in 1D hexagonal and 2D octagonal quasicrystals

We study some typical defect problems in one-dimensional (1D) hexagonal and two-dimensional (2D) octagonal quasicrystals. The first part of this investigation addresses in detail a uniformly moving screw dislocation in a 1D hexagonal piezoelectric quasicrystal with point group 6mm. A general solution is derived in terms of two functions φ ₁, φ ₂, which satisfy wave equations, and another harmonic function φ ₃. Elementary expressions for the phonon and phason displacements, strains, stresses, electric potential, electric fields and electric displacements induced by the moving screw dislocation are then arrived at by employing the obtained general solution. The derived solution is verified by comparison with existing solutions. Also obtained in this part of the investigation is the total energy of the moving screw dislocation. The second part of this investigation is devoted to the study of the interaction of a straight dislocation with a semi-infinite crack in an octagonal quasicrystal. Here the crack penetrates through the solid along the period direction and the dislocation line is parallel to the period direction. We first derive a general solution in terms of four analytic functions for plane strain problem in octagonal quasicrystals by means of differential operator theory and the complex variable method. All the phonon and phason displacements and stresses can be expressed in terms of the four analytic functions. Then we derive the exact solution for a straight dislocation near a semi-infinite crack in an octagonal quasicrystal, and also present the phonon and phason stress intensity factors induced by the straight dislocation and remote loads.      

二维周期性复合介质中声波带隙结构及其缺陷态

用平面波展开方法和超元胞方法,研究了钢柱体在水中按周期性排列时声波的能带结构.讨论了钢柱体的横截面形状(圆形和正方形)、柱体的体积填充率及缺陷等因素对声波带隙结构的影响. 关键词： 声波 带隙 缺陷态     

Ground state of an exciton in a three-dimensional parabolic quantum dot: Convergent perturbative calculation

Working in the effective-mass approximation, we apply a powerful convergent perturbative technique of Turbiner's to the calculation of the ground state energy and the wave function of an exciton confined to a three-dimensional parabolic quantum dot. Unlike the usual Rayleigh–Schrödinger perturbation theory, Turbiner's approach works well even in the regime of strong coupling and does not require the knowledge of the full solution to the undisturbed problem. The second-order convergent calculation presented below is in excellent agreement with the results of exact numerical simulations for a wide range of system's confinement parameters.     

New classes of quasicrystals and marginal critical states

One-dimensional quasilattices, namely, the geometrical objects that represent quasicrystals, are classified into mutual local-derivability (MLD) classes. Besides the familiar class, there exist an infinite number of new MLD classes, and different MLD classes are distinguished by the inflation rules of their representatives. It has been found that electronic properties of a new MLD class are characterized by the presence of marginal critical states, which are considered to be nearly localized states.