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Chapter 7 The Condensate of Zero-Point Oscillations and Type-I Superconductors
Two electron pairs at an in-phase oscillations have a high energy of interaction and
therefore cannot form the condensate. The condensate can be formed only by the particles
that make up the difference between the populations of levels N 0 −N 1 . In a dimensionless
form, this difference defines the order parameter:
Ψ =
N 0 N 1
− . (7.5)
N 0 + N 1 N 0 + N 1
In the theory of superconductivity, by definition, the order parameter is determined by
the value of the energy gap
Ψ = ∆ T /∆ 0 . (7.6)
When taking a counting of energy from the level ε 0 , we obtain
∆ T
∆ 0
= N 0 − N 1
N 0 + N 1
≃ e2∆ T /kT − 1
e 2∆ T /kT
+ 1 = th(2∆ T /kT ). (7.7)
Passing to dimensionless variables δ ≡ ∆ T
∆ 0
, t ≡ kT
kT c
and β ≡ 2∆0
kT c
we have
δ = eβδ/t − 1
= th(βδ/t). (7.8)
e βδ/t + 1
This equation describes the temperature dependence of the energy gap in the spectrum
of zero-point oscillations. It is similar to other equations describing other physical
phenomena, that are also characterized by the existence of the temperature dependence
of order parameters [43], [44]. For example, this dependence is similar to temperature
dependencies of the concentration of the superfluid component in liquid helium or the
spontaneous magnetization of ferromagnetic materials. This equation is the same for all
order-disorder transitions (the phase transitions of 2nd-type in the Landau classification).
The solution of this equation, obtained by the iteration method, is shown in Figure 7.2.
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