Chiral dynamics and antikaon-nuclear quasibound states

Recent developments are summarised concerning low-energy interactions as they relate to the possible existence of antikaon-nuclear quasibound states. An exploratory study of antikaons bound to finite nuclei is performed, with emphasis on the evolution of such states from light to heavy nuclei (A = 16–208). The energy dependent, driving attractive interactions are constructed using the s-wave coupled-channel amplitudes involving the Λ(1405) and resulting from chiral SU(3) dynamics, plus p-wave amplitudes dominated by the Σ(1385). Effects of Pauli and short-range correlations are discussed. The decay width induced by K⁻NN two-body absorption is estimated and found to be substantial. It is concluded that -nuclear quasibound states can possibly exist with binding energies ranging from 60 to 100 MeV, but with short life times corresponding to decay widths of similar magnitudes.     

Calculation of the parameters of resonance states using stabilization with non-Coulomb potentials

The possibility of replacing the Coulomb-type stabilization potential by stabilization potentials with non-Coulomb asymptotics is demonstrated for a model problem with one open channel, as an example. The influence of the form of the stabilization potential on the accuracy of calculation the phase shift function and the resonance parameters is discussed.     

Matrix Variational Pade Approximants and multi-step square-well potentials

It is shown that, contrary to earlier expectations, Matrix Variational Pade Approximants cannot give results in finite order, for general multi-step square-well potentials. It is proposed, then, that the set of test vectors, leading to MVPA, when a solution of the Schwinger variational principle is sought among them, be enriched in some non-trivial way. A resulting modification of the MVPA method should give exact phase shifts in finite order for any multi-step square-well potentials.     

Comment on RbHe bound and quasibound states

A theoretical study of the RbHe system leading support for recent evidence for a l =1 quasibound state.     

Lifetime analysis of quasibound states in coupled quantum wells

A simple time-dependent model is presented to investigate lifetimes of the quasibound states in coupled quantum wells (CQWs). The transfer matrix approach is employed to discretize the conduction-band profile of the heterostructure and form a dispersion equation whose zeros correspond to the complex eigenenergies. Both the bound and quasibound states are extracted numerically in the complex plane by Newton's method. The lower and higher well subbands are found to have negative and positive energy shift, respectively, as following the no level crossing theorem. Besides, the decay rate of the quasibound state is approximately proportional to the absolute energy shift. The quasibound states, which have larger energy shift, have shorter lifetime and decay more quickly. Furthermore, the differences in lifetime between the quasibound states in CQWs can be easily realized as all the wave functions are specially adjusted to form the relative probability density distributions.     

Quantum-to-classical crossover of quasibound states in open quantum systems

In the semiclassical limit of open ballistic quantum systems, we demonstrate the emergence of instantaneous decay modes guided by classical escape faster than the Ehrenfest time. The decay time of the associated quasibound states is smaller than the classical time of flight. The remaining long-lived quasibound states obey random-matrix statistics, renormalized in compliance with the recently proposed fractal Weyl law for open systems [W.T. Lu, S. Sridhar, and M. Zworski, Phys. Rev. Lett. 91, 154101 (2003)]. We validate our theory numerically for a model system, the open kicked rotator.     

Calculation of the optical absorption between surface states of silicon

A detailed calculation of the optical absorption between surface states on silicon is reported and the results compared with the observed absorption. Actually the observations relate to the (111) surface whereas the calculations involved the better understood (110) surface, but arguments are advanced to suggest that similar results should be obtained for both and a simulated (111) calculation presented. A model, which accurately reproduces the results of complete theoretical calculations, is used to obtain the surface state energies throughout the two-dimensional Brillouin zone, and to obtain the momentum matrix elements at each k point by utilising the effective mass sum rule. The formation of a band gap between the surface state bands, arising from surface rearrangement, is incorporated into the model in a physically sensible manner. There is very good agreement in both shape and absolute magnitude between the calculated and observed absorption clearly indicating that the measured absorption does arise from surface states. The (1, 1, 0) calculations show large polarisation effects which should be observable on reconstructed (1, 1, 0) silicon surfaces or on the III–V compounds.     

Defects, quasibound states, and quantum conductance in metallic carbon nanotubes

The effects of impurities and local structural defects on the conductance of metallic carbon nanotubes are calculated using an ab initio pseudopotential method within the Landauer formalism. Substitutionally doped boron or nitrogen produces quasibound impurity states of a definite parity and reduces the conductance by a quantum unit (2e(2)/h) via resonant backscattering. These resonant states show strong similarity to acceptor or donor states in semiconductors. The Stone-Wales defect also produces quasibound states and exhibits quantized conductance reduction. In the case of a vacancy, the conductance shows a much more complex behavior than the prediction from the widely used pi-electron tight-binding model.     

Filling of quasibound states by electrons in a schwarzchild field

Quasistationary states with energies < exist in the vicinity of a Schwarzchild black hole. The process of filling of these states by massive spinor particles is examined. The analysis is conducted in the Pauli approximation for small black holes M 1. In this case, it turns out that the distribution is a thermal distribution.Translated from Izvestiya Vysshikh Uchebnykh Zabedenii, Fizika, No. 8, pp. 75–77, August, 1983.     

Spectroscopy of quasibound states formed by molecular collisions in the presence of a laser

A theory is reported which describes spectroscopic transitions between quasibound states formed during molecular collisions in a laser field. A preliminary calculation suggests that the shapes of absorption lines are sensitive to the shapes of the potentials; hence a method for determining the latter. The calculation also shows that respectable cross-sections for scattering can be obtained at low laser powers.     

Quantum reflection pole method for determination of quasibound states in semiconductor heterostructures

The quantum reflection pole method (QRPM) is introduced for determining quasibound state eigenenergies and their lifetimes in symmetric, asymmetric, biased, and unbiased quantum heterostructures. In the QRPM the single-band effective-mass Schrödinger equation is solved without using complex arithmetic. Calculations are much simpler to perform than with previous methods. Further, results are found to be in excellent agreement with other rigorous techniques.     

Calculation of the structure and vibrational states for anionic forms of Co-, Ni-, and Cu-porphines

The structure and vibrations of neutral porphine metal complexes (Me-P, Me = Co, Ni, Cu) and their d-anionic forms with an additional electron localized in vacant d_x² -_y² - d_x^2 -_y^2 - and d_z² d_z^2 -orbitals are compared based on calculations by a DFT method. It is shown that such electron population causes a significant increase of the electronic charge on the macrocycle rather than on the Me atom and is accompanied by a considerable redistribution of π- and σ-electron densities (ρ_π ρ_σ). A predominant gain of ρ_π (0.49e) is found for the monoanion of Co-P (Co-P^–, d_z² d_z^2 -monoanion); of ρ_σ (0.6e), for Ni-P^–( d_x² -_y² - d_x^2 -_y^2 - monoanion). These features are reflected in both the structure of the anions and the behavior of their vibrational frequencies. The greatest frequency shifts among IR active modes when populating the d_z² d_z^2 - and d_x² -_y² - d_x^2 -_y^2 - orbitals occur for out-of-plane vibrations (>30 cm^–1) and in-plane modes (34–46 cm^–1) involving MeN- and C_αC_m-bonds, respectively. Abnormally large frequency lowering is found for B_1g-type modes (active in the resonance Raman spectrum) involving mainly C_αC_m-, C_βC_β-, C_αC_β-, and MeN-bonds. This is related to a change in the d_π-e_g interaction strength during such vibrations that contributes to a decrease in the corresponding force constants.     

Cut-off potentials and forms extensions

For operators bounded from below we show that the resolvents of the operators formed from cut-off potentials converge strongly to the operator defined by means of bilinear forms. Under further conditions we show that the resolvents converge in norm.     

Heavy-quark bound states in potentials with the Bethe-Salpeter equation

The spinless Bethe—Salpeter equation is solved for three attractive static quark-antiquark potentials of the form V(r)=–ar^–+br+c, 01, and the effective non-Coulombic power-law potential of the formV(r)=ar ^0.1+c to obtain the spin-averaged energy levels in bottomonium (b ) and charmonium (c ) families. The shifted 1/N expansion technique is used. Calculations of the energy eigenvalues are carried out up to third order and parameters of each potential are adjusted to obtain the best agreement with the experimental spin-averaged data (SAD). Flavor-dependent and flavor-independent cases are considered in this work.     

Landau Hamiltonians with random potentials: Localization and the density of states

We prove the existence of localized states at the edges of the bands for the two-dimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding eigenfunctions decay exponentially with the magnetic field and distance. We also prove that the integrated density of states is Lipschitz continuous away from the Landau energies. The proof relies on a Wegner estimate for the finite-area magnetic Hamiltonians with random potentials and exponential decay estimates for the finitearea Green's functions. The proof of the decay estimates for the Green's functions uses fundamental results from two-dimensional bond percolation theory.Supported in part by CNRS.Supported in part by NSF grants INT 90-15895 and DMS 93-07438.Unité Propre de Recherche 7061.     

Calculation of deformation potentials

The electronic contributions to the shear elastic stiffness constants are calculated for a d-band and bcc lattice First and second order deformation potentials are obtained. These, and not a high density of states, are mainly responsible for strong electronic effects (softening).     

一维Morse势的Dirac方程的束缚态

在标量型和矢量型Morse势相等的条件下,给出了Dirac方程束缚态的一维二分量波函数和一维四分量波函数的精确解.并且在求精确解时,运用一种新的自变量变换方法,使方程求解变得比较简单.