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By T. Kaise
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Extra resources for Representations de Weil et GL2 Aigebres de division et GLn (Vers les corps de classes galolslens I, II)
Example text
At the moment of writing, there is no theoretical formula for predicting the value of critical temperature in a given compound. 1. 003 There is even no rule for predicting whether a certain substance will undergo the superconducting transition at low temperature or not. Actually, this is one of the main problems in the field of superconductivity—how to calculate the Tc value in different materials. If we could know how to estimate the Tc value for any specific material, there would be no need for this book.
The coherence length ξGL defines variations of the order parameter of the superconducting condensate, whilst the pair size ξ is related to the wavefunction of a Cooper pair (see Fig. 4). Thus, in general, the coherence length and the Cooper-pair size do not relate directly to one another. Secondly, the coherence length depends on temperature, ξGL (T ), while the Cooper-pair size is temperature-independent. The coherence length diverges at T → Tc . However, in conventional superconductors at zero temperature, ξGL (0) = ξ because in conventional superconductors, the phase coherence is mediated by the overlap of the Cooper-pair wavefunctions—the process which does not give 31 Basic properties of the superconducting state rise to a “new” order parameter.
Compact superconducting cables would replace unsightly power lines and revolutionize the electrical power industry. A world with room-temperature superconductivity would unquestionably be a cleaner world and a quieter world. Compact superconducting motors would replace many noisy, polluting engines. Advance transportation systems would lessen our demands on the automobile. Superconducting magnetic energy storage would become commonplace. Computers would be based on compact Josephson junctions. Thanks to the high-frequency, high-sensitivity operation of superconductive electronics, mobile phones would be so compact that could be made in the form of an earring.