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Boris V. Vasiliev Supercondustivity Superfluidity

Superconductivity and

Superconductivity and Superfluidity 1.2 1.0 0.8 0.6 0.4 0.2 Figure 7.2 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 The temperature dependence of the value of the gap in the energetic spectrum of zero-point oscillations calculated on Eq.(7.8). This decision is in a agreement with the known transcendental equation of the BCS, which was obtained by the integration of the phonon spectrum, and is in a satisfactory agreement with the measurement data. After numerical integrating we can obtain the averaging value of the gap: ∫ 1 〈∆〉 = ∆ 0 δdt = 0.852 ∆ 0 . (7.9) 0 To convert the condensate into the normal state, we must raise half of its particles into the excited state (according to Eq.(7.7), the gap collapses under this condition). To do this, taking into account Eq.(7.9), the unit volume of condensate should have the energy: E T ≃ 1 2 n 0〈∆ 0 〉 ≈ 0.85 ( me ) 3/2 5/2 ∆ 2 2π 2 α 2 0 , (7.10) On the other hand, we can obtain the normal state of an electrically charged condensate when applying a magnetic field of critical value H c with the density of energy: E H = H2 c 8π . (7.11) 80 Science Publishing Group

Chapter 7 The Condensate of Zero-Point Oscillations and Type-I Superconductors As a result, we acquire the condition: 1 2 n 0〈∆ 0 〉 = H2 c 8π . (7.12) This creates a relation of the critical temperature to the critical magnetic field of the zero-point oscillations condensate of the charged bosons. 5 log E H Pb 4 In Sn Hg 3 Tl 2 Zn Ga Al Cd Figure 7.3 log E T 1 1 2 3 4 5 The comparison of the critical energy densities E T (Eq.(7.10)) and E H (Eq.(7.11)) for the type-I superconductors. The comparison of the critical energy densities E T and E H for type-I superconductors are shown in Figure 7.3. As shown, the obtained agreement between the energies E T (Eq.(7.10)) and E H (Eq.(7.11)) is quite satisfactory for type-I superconductors [32], [22]. A similar comparison for type-II superconductors shows results that differ by a factor two approximately. The reason for this will be considered below. The correction of this calculation, has not apparently made sense here. The purpose of these calculations was to show that the description of superconductivity as the effect of the condensation of ordered zero-point oscillations is in accordance with the available experimental data. This goal is considered reached in the simple case of type-I superconductors. Science Publishing Group 81

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