Electron spectrum and infrared transitions in semiconductor superlattices with a unit cell allowing for quasi-localised carrier states

We studied theoretically the electron spectrum and infrared transitions in a superlattice with a unit cell allowing for quasi-localised carrier states. The dispersion relation and the band structure of such a system have been found. We calculated the dipole matrix element for inter-subband carrier infrared transitions. The wave functions and the electron spectrum in this superlattice show a peculiarity when the energy of a band state approaches the energy of the quasi-localised state in the single cell. The absorption strength peaks up at the respective frequencies.     

Solution of Spin and Pseudo-Spin Symmetric Dirac Equation in (1+1) Space-Time Using Tridiagonal Representation Approach

The aim of this work is to find exact solutions of the Dirac equation in(1+1) space-time beyond the already known class.We consider exact spin(and pseudo-spin) symmetric Dirac equations where the scalar potential is equal to plus(and minus) the vector potential.We also include pseudo-scalar potentials in the interaction.The spinor wavefunction is written as a bounded sum in a complete set of square integrable basis,which is chosen such that the matrix representation of the Dirac wave operator is tridiagonal and symmetric.This makes the matrix wave equation a symmetric three-term recursion relation for the expansion coefficients of the wavefunction.We solve the recursion relation exactly in terms of orthogonal polynomials and obtain the state functions and corresponding relativistic energy spectrum and phase shift.     

s波π-π散射

本文用链状近似从一个不可重正化的作用拉氏函数计算π-π的s波散射振幅。这个作用拉氏函数所给出的p波散射恰恰正是Frazer-Fulco由色散关系得出的解。我们的计算结果指出,s波散射振幅中含有两个新的参数,因为作用拉氏函数是不可重正化的,引进新的参数是无法避免的,我们所得到的s波截面是与实验一致的,最后还讨论了我们的方法和色散关系方法的联系。     

Time-Dependent Variational Approach to Ground-State Phase Transition and Phonon Dispersion Relation of the Quantum Double-Well Model

The ground-state phase transition and the phonon dispersion relation of the quantum double-well model are studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty relation, we obtain an effective classical Hamiltonian for the system and equations of motion for the particle＇s expectation values. It is shown that the effective substrate potential transits from a symmetric double-well potential to a symmetric single-well potential, and the ground state exhibits a transition from a broken symmetry phase to a restored symmetry phase as increasing the strength of quantum fluctuations. We also obtain the phonon dispersion relations and the phonon gaps at the two phases.     

Applications of the Collective Field Theory for the Calogero–Sutherland Model

We use the collective field theory known for the Calogero–Sutherland model to study a variety of low-energy properties. These include the ground state energy in a confining potential up to the two leading orders in the particle number, the dispersion relation of sound modes with a comparison to the two leading terms in the low temperature specific heat, large amplitude waves, and single solution solutions. The two-point correlation function derived from the dispersion relation of the sound mode only gives its nonoscillatory asymptotic behavior correctly, demonstrating that the theory is applicable only for the low-energy and long wavelength excitations of the system.     

Dipolar excitons, spontaneous phase coherence, and superfluid-insulator transition in bilayer quantum Hall systems at nu = 1

The spontaneous interlayer phase coherent (111) state of a bilayer quantum Hall system at filling factor nu = 1 may be viewed as a condensate of interlayer particle-hole pairs or excitons. We show that when the layers are biased in such a way that these excitons are very dilute, they may be viewed as pointlike bosons. We calculate the exciton dispersion relation and show that the exciton-exciton interaction is dominated by the dipole moment they carry. In addition to the phase coherent state, we also find a Wigner crystal/glass phase in the presence/absence of disorder which is an insulating state for the excitons. The position of the phase boundary is estimated and the transition between these two phases is discussed.     

Correlated states of interacting particles and problems of the Coulomb barrier transparency at low energies in nonstationary systems

Premises for the formation of a correlated coherent state of particles in nonstationary quantum systems are considered. The relation between the correlation factor of particles and the probability of their passage through the potential barrier (including that in nuclear reactions) is analyzed. The optimal regime for parametric excitation of a harmonic oscillator is found, in which the asymptotic formation of the correlated state of particles takes place, the dispersion of their coordinates increases manifold, and the barrier transparency becomes many orders of magnitude higher at a low energy of interacting particles.     

Momentum and energy dependence of the anomalous high-energy dispersion in the electronic structure of high temperature superconductors

Using high-resolution angle-resolved photoemission spectroscopy we have studied the momentum and photon energy dependence of the anomalous high-energy dispersion, termed waterfalls, between the Fermi level and 1 eV binding energy in several high-T_{c} superconductors. We observe strong changes of the dispersion between different Brillouin zones and a strong dependence on the photon energy around 75 eV, which we associate with the resonant photoemission at the Cu3p-->3d_{x;{2}-y;{2}} edge. We conclude that the high-energy "waterfall" dispersion results from a strong suppression of the photoemission intensity at the center of the Brillouin zone due to matrix element effects and is, therefore, not an intrinsic feature of the spectral function. This indicates that the new high-energy scale in the electronic structure of cuprates derived from the waterfall-like dispersion may be incorrect.     

Effective one-dimensional models from matrix product states

In this paper we present a method for deriving effective one-dimensional models based on the matrix product state formalism. It exploits translational invariance to work directly in the thermodynamic limit. We show, how a representation of the creation operator of single quasi-particles in both real and momentum space can be extracted from the dispersion calculation. The method is tested for the analytically solvable Ising model in a transverse magnetic field. Properties of the matrix product representation of the creation operator are discussed and validated by calculating the one-particle contribution to the spectral weight. Results are also given for the ground state energy and the dispersion.     

Collective excitations of a periodic Bose condensate in the Wannier representation

We study the dispersion relation of the excitations of a dilute Bose-Einstein condensate confined in a periodic optical potential and its Bloch oscillations in an accelerated frame. The problem is reduced to one-dimensionality through a renormalization of the s-wave scattering length and the solution of the Bogolubov-de Gennes equations is formulated in terms of the appropriate Wannier functions. Some exact properties of a periodic one-dimensional condensate are easily demonstrated: (i) the lowest band at positive energy refers to phase modulations of the condensate and has a linear dispersion relation near the Brillouin zone centre; (ii) the higher bands arise from the superposition of localized excitations with definite phase relationships; and (iii) the wavenumber-dependent current under a constant force in the semiclassical transport regime vanishes at the zone boundaries. Early results by Slater [Phys. Rev. 87, 807 (1952)] on a soluble problem in electron energy bands are used to specify the conditions under which the Wannier functions may be approximated by on-site tight-binding orbitals of harmonic-oscillator form. In this approximation the connections between the low-lying excitations in a lattice and those in a harmonic well are easily visualized. Analytic results are obtained in the tight-binding scheme and are illustrated with simple numerical calculations for the dispersion relation and semiclassical transport in the lowest energy band, at values of the system parameters which are relevant to experiment. Received 3 December 1999 and Received in final form 22 March 2000     

A structural mechanics approach for the phonon dispersion analysis of graphene

A molecular structural mechanics model for the numerical simulation of phonon dispersion relations of graphene is developed by relating the C-C bond molecular potential energy to the strain energy of the equivalent beam-truss space frame. With the stiffness matrix known and further based on the periodic structure characteristics, the Bloch theorem is introduced to develop the dispersion relation of graphene sheet. Being different from the existing structural mechanics model, interactions between the fourth-nearest neighbor atoms are further simulated with beam elements to compensate the reduced stretching stiffness, where as a result not only the dispersion relations in the low frequency field are accurately achieved, but results in the high frequency field are also reasonably obtained. This work is expected to provide new opportunities for the dynamic properties analysis of graphene and future application in the engineering sector.     

Time-Dependent Variational Approach to the Phonon Dispersion Relation of the Commensurate Quantum Frenkel-Kontorova Model

The phonon dispersion relation of the commensurate quantum Frenkel-Kontorova model is studied by means of the time-dependent variational approach combined with a Hartree-type many-body trial wavefunction for the particles. The single-particle state is taken to be a frozen Jackiw-Kerman wavefunction. Under the condition of minimum uncertainty, equations of motion for the particle expectation values are derived to obtain the phonon dispersion relation. It is shown that the strength of the substrate potential and the phonon excitation gap are reduced due to the quantum fluctuations in comparison with those of the classical model. We also compare our results with those previously obtained by using the path-integral molecular dynamics.     

Cauchy matrix structure of the Mel'nikov model of long-short wave interaction

We propose a systematic method to construct the Mel'nikov model of long-short wave interactions, which is a special case of the Kadomtsev-Petviashvili (KP) equation with self-consistent sources (KPSCS). We show details how the Cauchy matrix approach applies to Mel'nikov's model which is derived as a complex reduction of the KPSCS. As a new result we find that in the dispersion relation of a 1-soliton there is an arbitrary time-dependent function that has previously not reported in the literature about the Mel'nikov model. This function brings time variant velocity for the long wave and also governs the short-wave packet. The variety of interactions of waves resulting from the time-freedom in the dispersion relation is illustrated.     

Splitting between quadrupole modes of dilute quantum gas in a two-dimensional anisotropic trap

We consider quadrupole excitations of quasi-two-dimensional interacting quantum gas in an anisotropic harmonic oscillator potential at zero temperature. Using the time-dependent variational approach, we calculate a few low-lying collective excitation frequencies of a two-dimensional anisotropic Bose gas. Within the energy weighted sum-rule approach, we derive a general dispersion relation of two quadrupole excitations of a two-dimensional deformed trapped quantum gas. This dispersion relation is valid for both statistics. We show that the quadrupole excitation frequencies obtained from both methods are exactly the same. Using this general dispersion relation, we also calculate the quadrupole frequencies of a two-dimensional unpolarized Fermi gas in an anisotropic trap. For both cases, we obtain analytic expressions for the quadrupole frequencies and the splitting between them for arbitrary value of trap deformation. This splitting decreases with increasing interaction strength for both statistics. For a two-dimensional anisotropic Fermi gas, the two quadrupole frequencies and the splitting between them become independent of the particle number within the Thomas-Fermi approach. Received 21 September 2001 and Received in final form 9 December 2001     

Theory of damping and fluctuations of the polariton due to its interaction with lattice vibrations

We present a model which describes the influence of lattice vibrations on the excitonpolariton. We solve the density matrix equation for the coupled photon-exciton-phonon system where the model of Haken and Strobl is used to describe the exciton phonon coupling which is responsible for the incoherent part of the motion. Our model allows us to calculate the dispersion relation of the damped polariton. Furthermore we may understand the optical absorption of crystals in the polariton picture. Our solution also exhibits the phenomenon of nonclassical light absorption.     

On shell,subtracted dispersion relations and low energy theorems from current algebra

A method discussed in an earlier paper is applied to the case of ππ and πN scattering and to electroproduction. As an example we derive for the ππ scattering amplitude a subtracted, covariant on-shell dispersion relation in which the subtraction polynomial is determined by the corresponding low energy theorem plus possibly small corrections. We also show how this same method may be applied to the derivation of low energy theorems.     

A dispersion relation for the density of states with application to the Casimir effect

The trace of a function of a Schrödinger operator minus the same for the Laplacian can be expressed in terms of the determinant of its scattering matrix. The naive formula for this determinant is divergent. Using a dispersion relation, we find another expression for it which is convergent, but needs one piece of information beyond the scattering matrix: the spatial integral of the potential. Except for this ‘anomaly’, we can express the Casimir energy of a compact body in terms of its optical scattering matrix, without assuming any rotational symmetry for its shape.     

Confinement of electrons in layered metals

We analyze the out of plane hopping in models of layered systems where the in-plane properties deviate from Landau's theory of a Fermi liquid. We show that the hopping term acquires a nontrivial energy dependence, due to the coupling to in-plane excitations, and the resulting state, at low temperatures, can be either conducting or insulating in the third direction. The latter is always the case if the Fermi level lies close to a saddle point in the dispersion relation.     

石墨烯纳米带电子结构的紧束缚法研究

在推导出的一般复式格子的π电子紧束缚能量色散关系的基础上,通过假定石墨烯纳米带的电子横向限制势为无穷大硬壁势,导出石墨烯纳米带的能量色散关系及石墨烯纳米带或为金属或为半导体的条件.结果表明：石墨烯纳米带的电子结构与其几何构型（对称性及宽度）密切相关,所以通过控制几何构型,可将其调制成金属或不同带隙的半导体.这意味着石墨烯纳米带对于发展新型纳米器件具有重要意义. 关键词： 石墨烯纳米带 复式格子 紧束缚模型 电子结构