Some Frontier Problems In Theoretical Physics Research - Bose - Einstein Condensation Of Transformation Temperature And Dependent Function, The Anisotropy Of Resistivity Measurement Theory, Electroacoustic Superconducting Strict Asymptotically Exact Solut

There exists certain self-inconsistency in some common-sensed expression of tran-sition temperature (Tc) of Bose-Einstein condensation (BEC) in harmonic traps. The principle of assuming μ=0at Tc is reexamined and a possible solution is proposed for2D and3D cases considering the derivatives of chemical potential. An effective approx-imation tool, the Bose-Einstein function, is studied and then applied to the solving of Tc because of this function’s excellent convergency. The expansions of BE functions at low temperatures, including those with negative indexes, are developed. These expan-sions are useful not only for the field-free case, but also for BEC in harmonic traps. Analytic fitting expressions of Tc in2D and3D cases are obtained.A new expression of correlation function of BEC in harmonic traps is presented and calculated. A new Gaussian type expression with two coordinates for different dimensions is obtained for the main part of correlation function. It is simple, well convergent and can asymptotically represent quantum correlation when N→∞. We hope this expression may be useful in the study of correlation behavior near transition temperature for Bose system in traps.Superconductivity continuously receives intensive attention both in theoretical and experimental studies. Resistivity, especially that of anisotropic films, is an interesting property in the study of superconductors. A line current (LC) method is developed for solving the difficulty in measuring anisotropic resistivity’s c component in the vertical direction of films. The insensitivity difficulty is solved through the arrangement of probes on the crystal and the application of Ω-series’theory. The extraction of c component is based on three measurements of two films with different orientations. The theory can also be applied to bulk samples of high Tc superconductor or semiconductor.A forgoing solution for LC method is presented for measuring resistivity’s three components of films based one sample. The exact solutions of type I and type II, with the edge effects taken into account, are obtained for the theory. Some exact solutions of the related simultaneous equation systems are obtained and expressed by elementary functions analytically, which will be useful for calculation.The condition of variable separation is discussed since some common mistakes are related this method. The uniqueness of analytic continuation are emphasized for its application in such problems. For some work has applied incorrect boundary condition but obtained formally correct result, the reason is analyzed and the correct form of result is obtained through different method.Starting from an electron-phonon model Hamiltonian (BCS type), we try to obtain an asymptotically exact solution. This is done under thermodynamic limit, through Stratonovich identity and the diagonalization theorem. With saddle point method, the partition function and a new gap equation are obtained. The gap equation is similar to that of BCS, but has an additional term. It causes the energy gap to be non-zero near the defined critical temperature. It offers us a different viewpoint towards the basic theory of superconductivity.