JiXin Dai

Transition temperatures of Bose-Einstein condensation in traps

A careful study is made of the definitions of the transition temperature Tc of an ideal Bose system in traps. We review several physical quantities that are used to define the transition temperature, which corresponds to different kinds of Tc. The different definitions give different values for Tc and the differences are quite large for finite systems. This makes the comparisons of theoretical predictions of the transition temperature shift with experimental results quite difficult. We also find that the derivative of chemical potential with respect to temperature is nearly discontinuous. This implies that in the thermodynamic limit the system might undergo a first-order phase transition.

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.

Phonon spectrum of YBCO obtained by specific heat inversion method for real data

In this paper, the phonon spectrum of YBCO is obtained from experimental specific heat data by an exact inversion formula with a parameter for eliminating divergences. The results can be compared to those of neutron inelastic scattering, which can only be carried out in a few laboratories. Some key points of specific heat-phonon spectrum inversion (SPI) theory and a method of asymptotic behaviour control are discussed. An improved unique existence theorem is presented, and a universal function set for numerical calculation of SPI is calculated with high accuracy, which makes the inversion method applicable and convenient in practice. This is the first time specific heat-phonon SPI has been realized for a concrete system.

CRITICAL PROPERTIES AND DISTRIBUTIONS OF TWO-DIMENSIONAL BOSE–EINSTEIN CONDENSATION

By studying the critical properties of a 2D Bose–Einstein condensation (BEC) in traps, we obtain the accurate analytic expressions of transition temperature, condensed fraction, and specific heat. The analytic results fit in fairly well with numerical results. We find that an isotropical potential favors most for condensation to occur. With the aid of Bloch summation, we study the distributions of coordinates and momenta of the system. Some clear physical pictures are presented.

The spatial and momentum distribution of Bose–Einstein condensation in harmonic traps

In this paper some expressions of the distributions of coordinates and momenta of Bose system in external field with clear physical picture are presented with aid of Bloch summation. The process, signature and physical implication of Bose–Einstein condensation and phase transition in finite systems are discussed.

A theoretical model calculation of measurement of anisotropic resistivity for high Tc superconductor

Abstract This paper presents a unified theoretical model for the measurement of anisotropic resistivity. Firstly, a dual integral equation system is proposed for crystal or film of high Tc superconductor (HTS). Then the integral equation system is decoupled by a suitable integral transformation and the dimension is reduced by using the Schlomilch theorem of 1857, so that the 3D partial differential equation is transformed into a 1D integral–differential equation. It is shown that the singular part of the kernel can be separated analytically. The universality and scaling law are discussed and some useful universal correction curves are presented. It is expected that this work will be helpful in the analysis for the measurement of anisotropic resistivity.

A possible mechanism of superconductivity based on Wigner crystal and BEC

A new possible mechanism is suggested based on the Wigner crystal and Bose–Einstein condensation. Our previous studies on the singular states that Loudons singular ground state is rejected by the orthogonality criteria. It is shown that 2D Wigner crystal can exist and to be a possible mechanism for HTS.

A unified solution of the inverse black-body radiation problem and some exact solutions

The inverse black-body radiation problem is very interesting, especially in remote sensing, such as the remote detections of the surface temperature distributions of earth, sun, etc. In this field, Chens solution with modified Mobius inversion formula has received much attention and was highly appreciated by Maddox in Nature (Maddox 1990 Nature 344 377). Dais exact solution in a closed form has succeeded in obtaining a series of exact solutions. In this paper, it is shown that, by using a new representation of inverse Laplace transformations and a famous formula of the Riemann zeta-function, Chens solution can be derived from Dais formula, without using the modified Mobius inversion formula. The unique existence theorem and convergence of the series of Chens series solution are also proven firstly. Some exact solutions are obtained by this new solution formula, which will be useful to test purely numerical inversions.

ON THE MAXIMUM AND CHARACTERISTIC CURVATURE OF CURRENT DENSITY OF HIGH Tc SUPERCONDUCTOR YBCO IN FLUX RELAXATION

The flux relaxation is one of important topics in the studies of high Tc superconductivity, because it is related to the energy loss in practical applications. There are many mechanisms, theories and relaxation laws suggested in the literatures. It is very interesting to test them according to the characters and compare them with the experiments. Some people think that the characters of the famous theories are their negative curvature. According our inversion solution, the relaxation ArcG law and experimental data analysis, the relaxation law has both positive and negative signs. This prediction is hopeful to be checked by experiments in future. The current densities of many high Tc superconductors decrease very rapidly in the early time in the relaxation. People do not know what their maximums are. In this work, a theory to determine these maximums of the current densities is presented. The theory is concretely realized by inversion for some real data of the YBCO and their maximum current densities are obtained.

AN APPLICATION OF THIRD FORMALISM OF QUANTUM STATISTICS AND A DIAGONALIZATION THEOREM IN ASYMPTOTIC EXACT THEORY OF SUPERCONDUCTIVITY

Starting from an electron-phonon interacting model, by means of the third formalism of quantum statistics, and with the aid of a diagonalization theorem, the Tc of superconductors from weak coupling to strong coupling cases are studied in a unified way. Our results are comparable with those of McMillans theory, (which is valid up to the electron-phonon (e-ph) coupling parameter λ~1, a good agreement is shown for λ<1.3) and the Allen and Dyness theory. Especially our results are very close to those of Hg spectrum with λ~2.0 and some strong coupling compounds. The theory is exact in the thermodynamic limit, without introducing variation method, the compensation of the dangerous diagrams in finite order in perturbation theory, abnormal greens function etc.