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.     

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.     

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     

A model for temperature-dependent collisional quenching of NO A2 Σ+

A model for the temperature-dependent electronic quenching of NO A ^{2 +} is presented. The model is appropriate for collision partners having stable negative ions, which are predicted to have large quenching cross-sections. Colliders with relatively large negative electron affinities are predicted to have cross-sections that are near-zero at room temperature and can increase dramatically at very high temperatures. A negligibly small electronic quenching cross-section is predicted for collision partners having negative ions that are unstable on a collisional timescale. Results of the model are compared to experimentally measured cross-sections for a number of species of interest in combustion and aerothermodynamic applications.     

The asymptotic behaviour of the exact and approximative ν = 1/2 Chern-Simons Green's functions

We consider the asymptotic behaviour of the Chern-Simons Green's function of the ν = 1/ system for an infinite area in position-time representation. We calculate explicitly the asymptotic form of the Green's function of the interaction free Chern-Simons system for small times. The calculated Green's function vanishes exponentially with the logarithm of the area. Furthermore, we discuss the form of the divergence for all τ and also for the Coulomb interacting Chern-Simons system. We compare the asymptotics of the exact Chern-Simons Green's function with the asymptotics of the Green's function in the Hartree-Fock as well as the random-phase approximation (RPA). The asymptotics of the Hartree-Fock Green's function correspondence well with the exact Green's function. In the case of the RPA Green's function we do not get the correct asymptotics. At last, we calculate the self consistent Hartree-Fock Green's function. Received 5 July 2001 and Received in final form 30 November 2001     

Particle resonance in the Dirac equation in the presence of a delta interaction and a perturbative hyperbolic potential

We show that the energy spectrum of the one-dimensional Dirac equation, in the presence of an attractive vectorial delta potential, exhibits a resonant behavior when one includes an asymptotically spatially vanishing weak electric field associated with a hyperbolic tangent potential. We solve the Dirac equation in terms of Gauss hyper-geometric functions and show explicitly how the resonant behavior depends on the strength of the electric field evaluated at the support of the point interaction. We derive an approximate expression for the value of the resonances and compare the results calculated for the hyperbolic potential with those obtained for a linear perturbative potential. Finally, we characterize the resonances with the help of the phase shift and the Wigner delay time.     

平行五波长高效液相色谱指纹图谱全息整合法定量鉴定杞菊地黄丸的整体质量

建立了杞菊地黄丸(Qijudihuang Pill, QJDHP)平行五波长(PFW)高效液相色谱(HPLC)指纹图谱,并依据系统指纹定量法结合全息整合法定量鉴定了杞菊地黄丸的整体质量。采用反相HPLC法,以丹皮酚(POL)为参照物峰,分别于203、228、265、280和326 nm下检测,分别确定了51、49、52、49和47个共有指纹峰,建立了QJDHP的PFW-HPLC指纹图谱。分别以权重法、均值法和投影参数法整合5个波长下各样品的定性定量全信息,结果基于5个波长综合信息用系统指纹定量法鉴定11批QJDHP样品,其中有8批质量为好,1批为较好,质量一般为2批。评价时以均值法最为简捷和准确。本实验结果表明,平行多波长指纹图谱整合法是基于从全信息角度整体定性和定量鉴定中药质量的有效可信方法,是对HPLC-二极管阵列检测（DAD）三维指纹图谱的简化定量处理,其整体综合定量鉴定结果具有可靠性。     

Synthetic Approach to 6-Benzoyl-2H-[1,2,4]triazine-3,5-dione and 6-Benzyl-5-thioxo-3,4-dihydro-2H-[1,2,4]triazin-3-one and Studies on Their Transformation to Fused[1,2,4]triazine Systems

Reaction of phenylpyruvic acid with semicarbazide afforded 6-benzyl-2H-[1,2,4]triazine-3,5-dione ( 1 ) which upon oxidation with potassium dichromate furnished 6-benzoyl-2H-[1,2,4]triazine-3,5-dione ( 2 ) in good yield. Constructing pyrazolo[3,4-e][1,2,4]triazine system ( 4 ) was achieved by reacting 2 with arylhydrazines in ethanolic solution. However treatment of 2 with the less reactive heteroarylhydrazines gave only the corresponding hydrazones ( 3 ). Attempt for constructing 1,2,4,5,10-pentaaza-dibenzo[a,d]cyclohept-3-one ( 7 ) from 2 was failed and (benzoimidazol-2-yl) [1,2,4] triazine derivative ( 6 ) was the only product. Reaction of 1 with phosphorus pentasulphide afforded compounds 8 and 9 . Compound 8 was transformed to the hydrazino compound 14 , which led to the construction of triazolo[4,3-d] [1,2,4]triazine system. Thus compounds 15 and 16 were obtained by reacting 14 with carbon disulfide or acetic anhydride respectively. Attempt to couple 8 with chloroacetic acid failed, while it's known isomer 10 led to the formation of thiazolo [2,3-c] [1,2,4]triazine derivative ( 13 ). Simple theoretical calculation using AM1 and PM3 semiempirical Hamitonian provided rational ways to correlate the reactivity with structure proposed.     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998