Luttinger liquid with asymmetric dispersion

We present an extension of the Tomonaga-Luttinger model in which left and right-moving particles have different Fermi velocities. We derive expressions for one-particle Green's functions, momentum-distributions, density of states, charge compressibility and conductivity as functions of both the velocity difference ε and the strength of the interaction β. This allows us to identify a novel restricted region in the parameter space in which the system keeps the main features of a Luttinger liquid but with an unusual behavior of the density of states and the static charge compressibility κ. In particular κ diverges on the boundary of the restricted region, indicating the occurrence of a phase transition. Received 20 May 2002 / Received in final form 23 August 2002 Published online 19 November 2002     

Zero bias anomaly in the density of states of low-dimensional metals

We consider the effect of Coulomb interactions on the average density of states (DOS) of disordered low-dimensional metals for temperatures T and frequencies ω smaller than the inverse elastic life-time 1/τ. Using the fact that long-range Coulomb interactions in two dimensions (2d) generate ln²-singularities in the DOS ν(ω) but only ln-singularities in the conductivity σ(ω), we can re-sum the most singular contributions to the average DOS via a simple gauge-transformation. If σ(ω) > 0, then a metallic Coulomb gapν(ω) ∝ |ω|/e ⁴ appears in the DOS at T = 0 for frequencies below a certain crossover frequency Ω ₂ which depends on the value of the DC conductivity σ(0). Here, - e is the charge of the electron. Naively adopting the same procedure to calculate the DOS in quasi 1d metals, we find ν(ω) ∝ (|ω|/Ω ₁)^1/2exp(- Ω ₁/|ω|) at T = 0, where Ω ₁ is some interaction-dependent frequency scale. However, we argue that in quasi 1d the above gauge-transformation method is on less firm grounds than in 2d. We also discuss the behavior of the DOS at finite temperatures and give numerical results for the expected tunneling conductance that can be compared with experiments. Received 28 August 2001 / Received in final form 28 January 2002 Published online 9 July 2002     

壳模型对143Pm核跃迁几率的计算

原子核跃迁几率理论计算和实验对比是分析描述原子核内部结构的主要手段之一。目前采用重离子核反应观测到^143Pm核（Z=61，N=82）高自旋能级结构:激发态最大能级达x=8397．6keV，对应自旋J=47／2（h=1）。利用核壳模型在计算^143Pm核能级结构及对应的自旋宇称基础上，系统地对其γ级联跃迁链以及纯E2跃迁进行了计算，并与实验数据进行对比。采用OXBASH程序的单粒子跃迁公式计算了^143Pm的跃迁几率。At present, the high spin state of ^143 Pm（Z = 61, N = 82） have been investigated. The level scheme of ^143Pm has been extended up to an excitation energy Ex = 8 397.6 keV and spin J =47/2（ h = 1 ）. Based on the nuclear shell model （NSM）, we have calculated the sequences of γ-ray transition rates and the pure E2 reduced transition probabilities of ^143Pm, and compared with experimental data. The formula of single-particle transition probability in the OXBASH code was applied in this paper.     

Trapping neutral fermions with a PT-symmetric trigonometric potential in the presence of position-dependent mass

The relativistic problem of neutral fermions subject to PT-symmetric trigonometric potential (∼iαtanαx)$(\sim \mathrm{i}\alpha \tan \alpha x)$ in 1+1$1+1$ dimensions is investigated. By using the basic concepts of the supersymmetric quantum mechanics formalism and the functional analysis method, we solve exactly the position-dependent effective mass Dirac equation with the vector coupling scheme and obtain the bound state solutions in closed form. The behavior of the energy spectra is discussed in detail.     

Scattering matrix for Feshbach-Villars equation for spin 0 and 1/2: Woods-Saxon potential

The Feshbach-Villars equation for spin 0 and 1/2 in the presence of Woods-Saxon potential is solved using an unified approach. The good boundary conditions for jumping potential are found and Klein tunneling and Klein paradox are discussed. The scattering matrix is constructed and the phase shifts, the transmission and reflection coefficients are deduced.     

The WKB method for the Dirac equation with the vector and scalar potentials

The WKB approximation is developed for the Dirac equation with the spherically symmetrical vector and scalar potentials. The relativistic wavefunctions are constructed, new quantization rule containing the spin-orbital interaction is obtained. For spherically symmetrical model of the Stark effect the quasi-classical spectrum of relativistic hydrogen-like atom is calculated. Application of the WKB method to the mass spectrum of the hydrogen-like quark systems was done.     

The Bargmann-Wigner formalism for spin 2 fields

The Bargmann-Wigner formalism has been applied to describe the spin-2 field in terms of the symmetric fourth-rank multi-Dirac spinor Ψ_αβγδ. A serious problem of the standard anzatz is that the resulting equation of motion has the trivial solution with all field components being independently equal to zero. We here show that this problem is an artefact of the neglection of terms containing the matrix γ⁵ in the decomposition of ϕ into the Clifford algebra basis. We further emphasize importance of the gauge 4-vector field in that respect.     

Electronic structure of spin-chain compounds: common features

The incommensurate composite systems M₁₄Cu₂₄O₄₁ (M = Ca, Sr, La) are based on two fundamental structural units: CuO₂ chains and Cu₂O₃ ladders. We present electronic structure calculations within density functional theory in order to address the interrelations between chains and ladders. The calculations account for the details of the crystal structure by means of a unit cell comprising 10 chain and 7 ladder units. It turns out that chains and ladders can be treated independently, which allows us to introduce a model system based on a reduced unit cell. For the CuO₂ chains, we find two characteristic bands at the Fermi energy. Tight binding fits yield nearest and next-nearest neighbour interactions of the same order of magnitude.     

Semiconductor quantum dots in high magnetic fields

We review and extend the composite fermion theory for semiconductor quantum dots in high magnetic fields. The mean-field model of composite fermions is unsatisfactory for the qualitative physics at high angular momenta. Extensive numerical calculations demonstrate that the microscopic CF theory, which incorporates interactions between composite fermions, provides an excellent qualitative and quantitative account of the quantum dot ground state down to the largest angular momenta studied, and allows systematic improvements by inclusion of mixing between composite fermion Landau levels (called Λ levels).     

Scattering of a relativistic scalar particle by a cusp potential

We solve the Klein–Gordon equation in the presence of a spatially one-dimensional cusp potential. The scattering solutions are obtained in terms of Whittaker functions and the condition for the existence of transmission resonances is derived. We show the dependence of the zero-reflection condition on the shape of the potential. In the low-momentum limit, transmission resonances are associated with half-bound states. We express the condition for transmission resonances in terms of the phase shifts.