Xian-Xi 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.

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.

PHENOMENOLOGICAL IMPLICATIONS OF HIGH-Tc SUPERCONDUCTIVITY

We develop a phenomenological model for high-Tc superconductors. Some main features are emerging in copper oxides: characteristic quasi two-dimensional Cu-O planes, strong correlation of antiferromagnetism, existence of a vortex lattice structure, and observation of a small coherence length and a large penetration depth. These features indicate that the superconductive pair is reasonably constrained to a small volume in real space and may be conceived of as a string-carrying vortex, and therefore can be well simulated by the dual phenomenological local boson fields and Φ. The various mean-field ground states of the system are discussed. The field equations of motion are originally solved to get approximate analytical soliton solutions. The effective Hamiltonian is formulated by a variational method for finite temperatures. The model parameter behaviour described by the relationship of the variational parameters is investigated. We discuss the critical temperature Tc, the specific heat cV and its jump Δc at Tc, and the critical magnetic fields Hc1 and Hc2. These results are in agreement with experimental observations, especially the critical behaviours and the zero temperature values. The model also allows interpretation of the variation of Tc with oxygen vacancy x and that with doping fraction δ in Cu-O planes, as well as the dependence of γ (defined as the specific heat coefficient of the T-linear term) on δ.

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 UNIFIED THEORY OF MEASUREMENT OF ANISOTROPIC RESISTIVITY BASED ON A SINGLE SURFACE OF ONE (FROM THIN TO THICK) FILM

A unified method and theory for measuring anisotropic resistivity based on a single surface of a film with rapidly converging exact solutions is presented here for solutions appropriate to thin films (Type I solutions) and to thick samples (Type II solutions). Some of the exact solutions of the related simultaneous equation systems can be expressed in terms of elementary functions. The theory proposed here for measuring resistivity of anisotropic crystals is expected to be useful in many applications.

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.