Dai Xianxi

On the functional integral approach in quantum statistics: I. Some approximations

The susceptibility of a Kondo system in a fairly wide temperature region is calculated in the first-harmonic approximation in a functional integral approach. The comparison with the value obtained by renormalization group theory shows that in this region the two results agree quite well. The expansion of the partition function with infinite independent harmonics for the Anderson model is studied. Some symmetry relations are generalized. It is a challenging problem to develop a functional integral approach including diagram analysis, mixed-mode effects and some exact relations in the Anderson system proved in a functional integral approach. These topics will be discussed in a subsequent paper.

A concrete realization of specific heat-phonon spectrum inversion for YBCO

Abstract In this Letter, a phonon spectrum of YBCO is obtained from its experimental specific heat data by an exact inversion formula with eliminating divergence parameter [Dai Xianxi, Xu Xinwen and Dai Jiqiong, Proceedings of Beijing International Conference on High T c Superconductivity, Sept. 4–8 Beijing, China, (1989) 521], [Dai Xianxi, Xu Xinwen and Dai Jiqiong, Phys. Lett. A 147 (1990) 445]. The results are comparable to that from neutron inelastic scattering. Some key points of specific heat-phonon spectrum inversion (SPI) theory as well as a method of asymptotic behavior control are discussed. An improved unique existence theorem is presented. A universal function set for the numerical calculation in SPI is obtained, which will make the inversion method applicable and convenient in practice. This is the first time to realize the specific heat-phonon spectrum inversion in a concrete system.

Soliton and Soliton-Pair as the Intrinsic Phonon Localized Modes in an Anharmonic Monoatomic Chain

With the use of coherent-state method, a quantum approach for the intrinsic phonon localized modes in an anharmonic monoatomic chain is given. It is shown that the envelope soliton with zero group velocity can exist in the lattice and that the frequency of carrier wave is above the top of the frequency band. A new type of the intrinsic phonon localized mode which we call the soliton-pair intrinsic localized mode in the chain is also reported.

Cylindrical envelope solitary waves

The method of multiple-scales is used to investigate the nonlinear modulation of capillary-gravity waves with cylindrical symmetry. We find that the evolution of wave-packets is described by a nonlinear Schrodinger-like equation i(U + U/2τ) + αUξξ + β|U|2U = 0. Some exact and explicit cylindrical envelope solitary wave solutions are also obtained by means of variable transformations.

A model equation and its exact two dimensional solitary wave solutions for water wave dynamics

Using the method of multiple scales and considering the nearly two-dimensional modulation of the waves when the dimensionless surface-tension coefficient τ of fluid is close to 1/3, we proposed a new model equation which we call the higher-order KP equation for water wave dynamics. The exact and explicit two dimensional solitary wave solutions are also given.

Functional Integral Approach to the Transition Temperature of Attractive Interacting Bose Gas in Traps

The functional integral approach (FIA) is introduced to study the transition temperature of an imperfect Bose gas in traps. An interacting model in quantum statistical mechanics is presented. With the model we study a Bose gas with attractive interaction trapped in an external potential. We obtain the result that the transition temperature of a trapped Bose gas will slightly shift upwards owing to the attractive interacting force. Successful application of the FIA to Bose systems is demonstrated.

A universal correction function in the measurement of anisotropic resistivity in high Tc superconductivity

A kind of dual integral equation set was suggested for measuring the anisotropic resistivity of high Tc superconductors. Its solution, the useful universal correction function, curve and their universality were obtained.

A Set of Exact Solutions for Singular Integral Equation and a Divergence Problem of 1D Hydrogen Atom in Moment Representation

The divergence problem in momentum representation of some singular potentials in Schrodinger equation is discussed. A set of exact solutions for a singular integral equation and the criteria determining the solutions in momentum space are obtained. The problems on Loudons symmetric solutions and counter example of nondegeneracy theorem are solved.

Commensurate enhancement of critical current density with periodic columnar pins

Abstract A phenomenological calculation of commensurate enhancement of critical current density J c with periodic columnar pins in a magnetic field parallel is presented. The strongly pinned vortex lattice through columnar defects can carry the greatly enhanced J c , showing a series of lobes in J c ( B ) when vortex lattice matches the lattice of columnar defects. The results agree with experiments of J c both in temperature dependence quantitatively and in induction dependence qualitatively.

Model Equations and Their Solitary Wave Solutions in Cylindrical Coordinate System

The method of multiple-scales is used to investigate the evolution of a weak nonlinear internal waves between two-layer fluids in cylindrical coordinate system. Two reduced model wave equations, which we call a modified cylindrical KdV equation for axially symmetric case and a modified cylindrical KP equation for non-axially symmetric case, are derived and their solitary wave solutions are also obtained by relating them to the modified KdV equation by means of an appropriate variable transformation.