VARIATIONAL CALCULATION OF THERMODYNAMIC PROPERTIES OF SUPERCOOLED LIQUID METALS

By means of Gibbs-Bogoliubov (GB) thermodynamic variational calculation,the thermodynamic properties of the supercooled liquid metals,such as the 3rd family elements Al,Ga and Tl and transition metal Ti were calculated using the hard-sphere (HS) system as reference.The values of mean atomic volume,Helmholtz free energy,internal energy and entropy as well as specific heat at constant volume,isothermal bulk modulus,thermal expan- sion coefficient and specfic heat under constant pressure were evaluated.The glass transition temperature,T_g,is easily obtained from the C_p-T plot.The glass forming ability for metal can be predicted from T_g/T_m,which is in agreement with the experimental results.

A note on localized transition in the spin-boson model by variational calculation

We present mathematical analyses of the evolution of solutions of the self-consistent equation derived from variational calculations based on the displaced-oscillator-state and the displaced-squeezed-state in spin-boson model at a zero temperature and a finite temperature. It is shown that, for a given spectral function defined as J（w） = π∑k Ck^2 = π/2αw^8w^1-s, there exists a universal sc for both kinds of variational schemes, the localized transition happens only for 2 s ≤ sc, moreover, the localized transition is discontinuous for s 〈 sc while a continuous transition always occurs when s = sc. At T = 0, we have sc = 1, while for T ≠ 0, sc = 2 which indicates that the localized transition in super-Ohmic case still exists, manifesting that the result is in discrepancy with the existing result.

Energy Positions of the ^1,3D^eRydberg Series of the He-Like Ions Up to the <i>N</i>= 9 Threshold

The doubly excited states of helium-like ions are investigated using a combination of the no-linear parameters of Hylleraas and the β-parameters of screening constant by unit nuclear charge. Calculations are performed for total energies of low-lying doubly excited states (N = 2 - 9) in He-like ions up to Z = 10. The results obtained from the novel method are in good agreement with the available theoretical calculations and experimental observations.

ORDERED ANALYTIC REPRESENTATION OF PDES BY HAMILTONIAN CANONICAL SYSTEM

Based on the method of symplectic geometry and variational calculation,the method for some PDEs to be ordered and analytically represented by Hamiltonian canonical system is discussed.Meanwhile some related necessary and sufficient conditions are obtained

Excitonic transitions in Be-doped GaAs/AlAs multiple quantum well

A series of GaAs/A1As multiple-quantum wells doped with Be is grown by molecular beam epitaxy. The photolu- minescence spectra are measured at 4, 20, 40, 80, 120, and 200 K, respectively. The recombination transition emission of heavy-hole and light-hole free excitons is clearly observed and the transition energies are measured with different quantum well widths. In addition, a theoretical model of excitonic states in the quantum wells is used, in which the symmetry of the component of the exciton wave function representing the relative motion is allowed to vary between the two- and three- dimensional limits. Then, within the effective mass and envelope function approximation, the recombination transition energies of the heavy- and light-hole excitons in GaAs/A1As multiple-quantum wells are calculated each as a function of quantum well width by the shooting method and variational principle with two variational parameters. The results show that the excitons are neither 2D nor 3D like, but are in between in character and that the theoretical calculation is in good agreement with the experimental results.

A new N* resonance as a hadronic molecular state

We report our recent work on a hadronic molecule state of the KKN system with I =1/2 and jR = 1/2＋. We assume that the A（1405） resonance and the scalar mesons, f0（980）, ao（980）, are reproduced as quasi-bound states of KN and KK, respectively. Performing non-relativistic three-body calculations with a variational method for this system, we find a quasibound state of the KIlN system around 1910 MeV below the three-body breakup threshold. This state corresponds to a new baryon resonance of N＊ with JP ： 1/2＋. We find also that this resonance has the cluster structure of the two-body bound states keeping their properties as in the isolated two-particle systems. We also briefly discuss another hadronic molecular state composed by two K and one N, which corresponds to a resonance.