Absorption lines of HLi2 by operator-ket expansion

The aim of this paper is twofold. We wish to explain and test an analytical method for calculating the matrix elements of linear operators, that simplifies the numerical calculation to mere bookkeeping. The method has been described in Huber, D., 1985, Int. J. quant. Chem., 27, 245 [1] and applied there to the general Watson-rotation-vibration hamiltonian for non-linear molecules. In this paper we want to show that the method can also be used in more complex cases. As an example we present an application to the calculation of the first electronic transition in Li₂H. The second aim is to report a calculation of the absorption spectrum of Li₂H and the discussion of its rotation-vibration states.     

线性塞曼劈裂对自旋-轨道耦合玻色-爱因斯坦凝聚体中亮孤子动力学的影响

利用变分近似及基于Gross-Pitaevskii方程的直接数值模拟方法,研究了自旋-轨道耦合玻色-爱因斯坦凝聚体中线性塞曼劈裂对亮孤子动力学的影响,发现线性塞曼劈裂将导致体系具有两个携带有限动量的静态孤子,以及它们在微扰下存在一个零能的Goldstone激发模和一个频率与线性塞曼劈裂有关的谐振激发模.同时给出了描述孤子运动的质心坐标表达式,发现线性塞曼劈裂明显影响孤子的运动速度和振荡周期.     

Polaron formalism applied to donor-acceptor pairs in semiconductors

The effective hamiltonian for the electronic states of a donor-acceptor pair in a polar semiconductor is formulated as a Fröhlich hamiltonian generalized to an electron and a positive hole interacting in the field of the positive donor and negative acceptor cores. The polarization of the lattice by the ion cores is simplified by a Platzman transformation; that by the electron and positive hole, by a further unitary transformation in the adiabatic approximation. The total effective hamiltonian including the lattice polarization energy is then considered for application of the variational principle to determine the parameters of the electron and positive hole effective mass functions. The Inglis-Williams analysis of the zero-phonon luminescent spactra of pairs is reconciled with the present theory by determining what single effective hamiltonian for the excited electronic state is consistent with their theoretical spactra. Within the approximations of their analysis, which are clarified, it is found to be the total effective hamiltonian. Finally, a more general and rigorously-derived effective hamiltonian is presented for the direct theoretical determination of the zero-phonon radiative transition energies of donor-acceptor pairs in compound semiconductors.     

Giant anisotropy of Zeeman splitting of quantum confined acceptors in Si/Ge

Shallow acceptor levels in Si/Ge/Si quantum well heterostructures are characterized by resonant-tunneling spectroscopy in the presence of high magnetic fields. In a perpendicular magnetic field we observe a linear Zeeman splitting of the acceptor levels. In an in-plane field, on the other hand, the Zeeman splitting is strongly suppressed. This anisotropic Zeeman splitting is shown to be a consequence of the huge light-hole--heavy-hole splitting caused by a large biaxial strain and a strong quantum confinement in the Ge quantum well.     

Classical periodic solutions of the equal-mass 2n-body problem, 2n-ion problem and the n-electron atom problem

We present a new family of classical periodic orbits for physically interesting hamiltonian systems, such as the Zeeman effect hamiltonian for the n-electron atom.     

Do we understand IBM parameters?

A microscopic calculation of interacting-boson model (IBM) parameters is performed for Xe isotopes within the framework of the broken-pair model. We employ a shell-model hamiltonian which reproduces the spectra of near-magic and semi-magic nuclei. As a first approximation we adopt the idea of Otsuka, Arima and Iachello, that IBM states represent fermion states built from collective S- and D-pairs — the SD space. We show that at least two effects are needed to explain the empirical values of IBM parameters. Firstly there is a reduction in collectivity of S- and D-pairs in states with several broken pairs, due to the Pauli-blocking effect of the latter. Secondly the shell-model hamiltonian mixes the SD space with other fermion states which are not explicitly represented in the IBM. Among the latter, states with a collective G-pair (J = 4) are the most important, but they contribute less than half of the total renormalization of the parameters. The calculated IBM parameters χ of the E2 transition operators exhibit similar trends to those which occur in the IBM hamiltonian.We explain the IBM Majorana force as a renormalization effect on states with even J; not as a repulsion in states with odd J. The latter emerge as rather pure states which mix little with the non-collective fermion space. This indicates that they may be experimentally observable.With our calculated parameters the IBM spectra and E2 transitions are of comparable quality to those obtained in IBM fits of the data.     

Rotational states and interacting bosons

Rotational states are investigated in terms of the interacting boson model. A ground-state rotational band is built from a shell-model many-nucleon system. It is shown that the S and D collective nucleon pairs play dominant roles in low-spin states of the band and that this S-D dominance is broken in high-spin states. The intrinsic hamiltonian is constructed from the effective nucleon-nucleon interaction used in the shell model calculation and the intrinsic state of the rotational band is shown to be comprised primarily of S and D pairs. We introduce a λ boson which is a linear combination of s, d and higher angular momentum bosons, and the boson intrinsic state is given by the λ boson condensate state. The s and d bosons constitute approximately 90 % of the λ boson, and the boson intrinsic state reproduces very well the energy and the intrinsic quadrupole moment of the nucleon intrinsic state. The s-d boson hamiltonian is constructed from the S and D pairs, while effects of non S-D pairs are also included by renormalization of the boson hamiltonian. The renormalization is made by using the λ boson. The s-d boson quadrupole operator is derived similarly. The boson hamiltonian and quadrupole operator thus derived reproduce well the exactly calculated values for low-spin states of the rotational band, although the accuracy decreases in high-spin states. It is shown that the IBM possesses the same physical picture of the rotational states as the Nilsson scheme with pairing correlations. It is therefore concluded that the IBM is capable of describing low-lying rotational states.     

Composite fermion hofstadter problem: partially polarized density wave states in the nu = 2/5 fractional quantum hall effect

It is well known that the nu = 2/5 state is unpolarized at zero Zeeman energy, while it is fully polarized at large Zeeman energies. A novel state with a charge/spin density wave order for composite fermions is proposed to exist at intermediate values of the Zeeman coupling for nu = 2/5. This state has half the maximum possible polarization, and can be extended to other incompressible fractions. A Hartree-Fock calculation based on the new approach for all fractional quantum Hall states developed by R. Shankar and the author is used to demonstrate the stability of this state to single-particle excitations and to compute gaps. A very recent experiment shows direct evidence for this state.     

Nonperturbative quantum geometries

Using the self-dual representation of quantum general relativity, based on Ashtekar's new phase space variables, we present an infinite dimensional family of quantum states of the gravitational field which are exactly annihilated by the hamiltonian constraint. These states are constructed from Wilson loops for Ashtekar's connection (which is the spatial part of the left handed spin connection). We propose a new regularization procedure which allows us to evaluate the action of the hamiltonian constraint on these states.Infinite linear combinations of these states which are formally annihilated by the diffeomorphism constraints as well are also described. These are explicit examples of physical states of the gravitational field — and for the compact case are exact zero eigenstates of the hamiltonian of quantum general relativity. Several different approaches to constructing diffeomorphism invariant states in the self dual representation are also described.The physical interpretation of the states described here is discussed. However, as we do not yet know the physical inner product, any interpretation is at this stage speculative. Nevertheless, this work suggests that quantum geometry at Planck scales might be much simpler when explored in terms of the parallel transport of left-handed spinors than when explored in terms of the three metric.     

Spin and Majorana polarization in topological superconducting wires

We study a one-dimensional wire with strong Rashba and Dresselhaus spin-orbit coupling (SOC), which supports Majorana fermions when subject to a Zeeman magnetic field and in the proximity of a superconductor. Using both analytical and numerical techniques we calculate the electronic spin texture of the Majorana end states. We find that the spin polarization of these states depends on the relative magnitude of the Rashba and Dresselhaus SOC components. Moreover, we define and calculate a local "Majorana polarization" and "Majorana density" and argue that they can be used as order parameters to characterize the topological transition between the trivial system and the system exhibiting Majorana bound modes. We find that the local Majorana polarization is correlated to the transverse spin polarization, and we propose to test the presence of Majorana fermions in a 1D system by a spin-polarized density of states measurement.     

Period doubling in quasi-one-dimensional systems : A nonadiabatic approach

In this article we propose a new approach to the electron-phonon problem in partially filled bands. With the help of the ‘rotating wave approximation’ we derive a reduced hamiltonian that can partially be diagonalized analytically in a many-particle basis. Structurally different many-particle states show up. While in the conventional adiabatic treatment of quasi-one-dimensional systems already an arbitrary small electron-phonon coupling can lead to a Peierls-type distortion, within the here proposed formalism we may conclude that a critical coupling strength has to be overcome for an energy gap above the highest occupied state to occur.     

Far-infrared magneto-absorption of donor-bound excitons in germanium: Pseudo-acceptor model

The magneto-oscillatory absorption spectrum of the arsenic-bound excitons in germanium observed at 118.6 μm reveals a series of absorption lines similar to the Zeeman spectrum of the acceptor impurity. This fact indicates that the bound excitons have the excited states associated with the light-hole Landau ladders and these excited states can be described by the model of a hole bound to the D^- state, i.e. the pseudo-acceptor model. The hole binding energy of the ground state of the bound excitons has been obtained to be 4.7 meV, which is smaller compared with the binding energy of the acceptor impurity.     

流动变量线性分布的MUSCL格式

本文提出一种线性函数斜率的确定方法并证明用其近似代替网格内流动变量的初始分布,MUSCL格式具有二阶精度。引入单调性限制条件和一定的耗散机制后,该方法适合于Euler坐标系下的计算。本文在处理间断时,用激波关系式代替特征线方程,解决了特征线法在全流场计算中的应用问题。最后,本文给出Emery问题和一个火箭喷流问题的计算结果。     

Spin order in paired quantum Hall states

We consider quantum Hall states at even-denominator filling fractions, especially nu=5/2, in the limit of small Zeeman energy. Assuming that a paired quantum Hall state forms, we study spin ordering and its interplay with pairing. We give numerical evidence that at nu=5/2 an incompressible ground state will exhibit spontaneous ferromagnetism. The Ginzburg-Landau (GL) theory for the spin degrees of freedom of paired Hall states is a perturbed CP2 model. We compute the coefficients in the GL theory by a BCS Stoner mean-field theory for coexisting order parameters, and show that even if repulsion is smaller than that required for a Stoner instability, ferromagnetic fluctuations can induce a partially or fully polarized superconducting state.     

Chemical shift of Zeeman masses in polar semiconductors

We discuss the problem of determining effective masses from the Zeeman splitting of 2p-levels in shallow impurities. In polar semiconductors we find the Zeeman mass to depend upon the chemical nature of the impurity (chemical shift), which can usually be described by a central-cell potential. In spite of its short range, it can influence even 2p-levels, if, due to electron-phonon interaction, 1s-one-phonon states are admixed to 2_p-zero-phonon states.     

Spin wave impurity states in linear chain ferromagnets and antiferromagnets

A simple linear chain model is used to find the perturbed states in Heisenberg ferromagnets and antiferromagnets with a magnetic impurity. The defect is characterized by a different nearest neighbor exchange coupling, spin, anisotropy field and gyromagnetic ratio from the corresponding parameters for the host lattice. A semiclassical calculation demonstrates that for some values of the defect parameters, resonant states in the spin wave band can arise near the bottom of the band, while for other values, localized states will occur. The various physical conditions for the occurrence of those states are given. When an applied magnetic field is included in the model calculation, a gap mode instability can occur for some values of the gyromagnetic ratio of the impurity spin. For some combinations of defect parameters, a local mode can be transformed into a resonant mode and vice versa by the magnetic field. The impurity-induced absorption is also calculated.     

Transport induced dimer state from topological corner states

Recently, a new type of second-order topological insulator has been theoretically proposed by introducing an in-plane Zeeman field into the Kane-Mele model in the two-dimensional honeycomb lattice. A pair of topological corner states arise at the corners with obtuse angles of an isolated diamond-shaped flake. To probe the corner states, we study their transport properties by attaching two leads to the system. Dressed by incoming electrons, the dynamic corner state is very different from its static counterpart.Resonant tunneling through the dressed corner state can occur by tuning the in-plane Zeeman field. At the resonance, the pair of spatially well separated and highly localized corner states can form a dimer state, whose wavefunction extends almost the entire bulk of the diamond-shaped flake. By varying the Zeeman field strength, multiple resonant tunneling events are mediated by the same dimer state. This re-entrance effect can be understood by a simple model. These findings extend our understanding of dynamic aspects of the second-order topological corner states.     

Entangling atoms in photonic crystals

We propose a method for entangling a system of two-level atoms in photonic crystals. The atoms are assumed to move in void regions of a photonic crystal. The interaction between the atoms is mediated either via a defect mode or via a resonant dipole-dipole interaction. We show that these interactions can produce pure entangled atomic states. We analyze the problem with parameters typical for currently existing photonic crystals and Rydberg atoms and we show that the atoms can emerge from photonic crystals in entangled states. Depending on the linear dimensions of the crystal we estimate that a pair of atoms entangled in a photonic crystal can be separated by tens of centimeters. Receive 11 June 1999 and Received in final form 4 October 1999     

两体相互作用费米系统在自旋轨道耦合和塞曼场中的基态转变

在超冷费米系统中实现人造规范势的突破,吸引了许多新问题的研究,展现了许多新奇的物理现象.本文研究了在环阱中,具有自旋轨道耦合和塞曼作用的两体相互作用费米模型.通过平面波展开的方法,解析求解了两体费米系统的本征能态.系统的总动量为守恒量,可以在不同总动量空间中研究能谱.研究发现:随着塞曼相互作用增大,在不同总动量空间,两体费米系统的本征能量均逐渐降低,系统基态从总动量为零空间转变到有限值空间.从吸引到排斥相互作用,无塞曼相互作用时,基态总动量始终为零,有塞曼相互作用时,基态总动量从零转变为有限值.通过单粒子和基态动量分布研究,本文直观地揭示了由塞曼能级劈裂引起的基态转变.