Preparation and Formation Process of TlBa₂Ca_n-1Cu_nO_y

Abstract

In the second part of this paper on micro-canonical ensemble a new numerical approach for consideration of quantum dynamics and calculations of the average values of quantum operators and time correlation functions in the Wigner representation of quantum statistical mechanics has been developed. The time correlation functions have been presented in the form of the integral of the WeylÏs symbol of the considered operators and the Fourier transform of the product of matrix elements of the dynamic propagators. For the latter function the integral WignerÈ LiouvilleÏs type equation has been derived. The initial condition for this equation has been obtained in the form of the Fourier transform of the Wiener path integral representation of the matrix elements of the propagators at initial time. A numerical procedure for solving this equation combining both molecular dynamics and Monte Carlo methods has been developed.Numerical results have been obtained for series of average values of the quantum operators as well as for the time correlation function characterizing the energy level structure, the momentum Ñow of tunnelling particles at barrier crossing and the absorption spectra of electrons in a potential well. The developed quantum dynamics method was tested by comparison of numerical results with analytical estimations. Tunnelling transitions and the e †ect of the quasi stationary state have been considered as the reasons for the peculiarities in behaviour of the time correlation functions and position and momentum dispersions.The possibility of applying the developed approach to the theory of classical wave propagation in random media have also been considered. For classical waves some results have been obtained for Gaussian beam propagation in 2D and 3D waveguides.

Rapid synthesis of nanoparticles of hexagonal type In2O3 and spherical type Tl2O3 by microwave irradiation

“…Thallium is a very important ingredient of many high-temperature oxide superconductors 7 due to the wide range of stoichiometries over which superconductivity is observed in such thallium-doped materials. 8 Because of such promising applications of In 2 O 3 and Tl 2 O 3 , it is very important to be able to fabricate their nanoparticles in crystalline form using a very simple method.…”

Reproducible synthesis by metal-organic chemical vapour deposition and thallium vapour diffusion of oriented thin-films : intergrowth of and structures

“…Since the discovery of superconductivity in the TlBaCaCuO system [1], enormous efforts have been made to synthesize reproducibe and selective single phases both as bulk [2][3][4][5][6][7] and thin-film [8][9][10][11][12] materials.…”

Phase Transition in Superconducting Thin Films of Tl System Employing a One-Zone Furnace and Deposited by Spray Pyrolysis

“…Using the first method and how far we have consulted, the research does not show a phase transition route, only mention under what conditions it is possible to achieve the crystalline phase Tl-2212 [31] or Tl-2223 phase [32], most of these studies agree to use thallium diffusion temperatures between 750 and 800˚C and gas atmospheres such as Ar, O 2 or air. Using the second method, there have been several studies on crystalline phase growth superconducting thin films of Tl [33], these studies have shown that in this system there may be ireversible phase transition and Tl-2223 and Tl-2212 [34]. This research showed that the deposition technique ultrasonic spray pyrolysis can be a viable technique for the growth of superconducting thin films is also available from superconducting thin films phase Tl-2223, Tl-2212 and Tl-1223 stably by the two-step method, using a one zone furnace.…”