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Boris V. Vasiliev Supercondustivity Superfluidity

Superconductivity and Superfluidity 20.0 log n e (T) Pb 19.5 In Sn Hg nn\2 19.0 18.5 Zn Ga Al Tl Cd log 2n 0 18.0 18.0 18.5 19.0 19.5 20.0 Figure 7.5 nn\1 The comparison of the number of superconducting carriers at T = 0 with the number of thermally activated electrons at T = T c . This comparison is shown in Table 7.4 and Figure 7.5. (Data has been taken from the tables [32], [22]). From the data described above, we can obtain the condition of destruction of superconductivity, after heating for superconductors of type-I, as written in the equation: n e (T c ) ≃ 2n 0 (7.28) 7.5 The Sound Velocity of the Zero-Point Oscillations Condensate The wavelength of zero-point oscillations Λ 0 in this model is an analogue of the Pippard coherence length in the BCS. As usually accepted [22], the coherence length ξ = v F 4∆ 0 . 88 Science Publishing Group

Chapter 7 The Condensate of Zero-Point Oscillations and Type-I Superconductors The ratio of these lengths, taking into account Eq.(6.20), is simply the constant: Λ 0 ξ ≈ 8π2 α 2 ≈ ·10 −3 . (7.29) The attractive forces arising between the dipoles located at a distance Λ0 2 other and vibrating in opposite phase, create pressure in the system: from each P ≃ d∆ 0 dV ≃ d2 Ω L 6 . (7.30) 0 In this regard, sound into this condensation should propagate with the velocity: √ 1 dP c s ≃ . (7.31) 2m e dn 0 After the appropriate substitutions, the speed of sound in the condensate can be expressed through the Fermi velocity of electron gas c s ≃ √ 2π 2 α 3 v F ≃ 10 −2 v F . (7.32) The condensate particles moving with velocity c S have the kinetic energy: 2m e c 2 s ≃ ∆ 0 . (7.33) Therefore, by either heating the condensate to the critical temperature when each of its volume obtains the energy E ≈ n 0 ∆ 0 , or initiating the current of its particles with a velocity exceeding c S , can achieve the destruction of the condensate. (Because the condensate of charged particles oscillations is considered, destroying its coherence can be also obtained at the application of a sufficiently strong magnetic field. See below.) 7.6 The Relationship ∆ 0 /kT c From Eq.(7.28) and taking into account Eqs.(7.3),(7.21) and (7.26), which were obtained for condensate, we have: ∆ 0 kT c ≃ 1.86. (7.34) Science Publishing Group 89

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