Superconductor Theory

[Richard D. Saam]

Acknowledging the accepted BCS Reference:
John Bardeen, Leon Neil Cooper and John Robert Schrieffer, "Theory of
Superconductivity", Physical Review, Vol 28, Number 6, December 1, 1957,
pages 1175-1204.

Equation 2.8 addresses a conservation of momentum condition
in terms of wave vectors k:

k1 + k2 = k1' + k2' (conservation of momentum)

But surely superconductivity is an elastic condition
also requiring conservation of energy:

k1^2 + k2^2 = k1'^2 + k2'^2 (conservation of energy)

It is noted that the linear 'conservation of momentum'
does not generate the non linear 'conservation of energy',

This superconductor elastic requirement
can be mechanistically accomplished by assuming a hexagonal lattice
which has a real and reciprocal lattice identity.
and introducing a 'g' factor such that:

g(k1 + k2) = k1' + k2' (conservation of momentum)

k1^2 + k2^2 = g(k1'^2 + k2'^2) (conservation of energy)

This superconductor mechanistic reasoning is developed in:

Superconductivity, The Structure Scale Of The Universe
https://arxiv.org/abs/physics/9905007
and particularly equations 2.3.11 and 2.3.12

Richard D Saam

[Richard Livingston]

Post by Richard D. Saam
John Bardeen, Leon Neil Cooper and John Robert Schrieffer, "Theory of
Superconductivity", Physical Review, Vol 28, Number 6, December 1, 1957,
pages 1175-1204.
Equation 2.8 addresses a conservation of momentum condition
k1 + k2 = k1' + k2' (conservation of momentum)
But surely superconductivity is an elastic condition
k1^2 + k2^2 = k1'^2 + k2'^2 (conservation of energy)
It is noted that the linear 'conservation of momentum'
does not generate the non linear 'conservation of energy',
This superconductor elastic requirement
can be mechanistically accomplished by assuming a hexagonal lattice
which has a real and reciprocal lattice identity.
g(k1 + k2) = k1' + k2' (conservation of momentum)
k1^2 + k2^2 = g(k1'^2 + k2'^2) (conservation of energy)
Superconductivity, The Structure Scale Of The Universe
https://arxiv.org/abs/physics/9905007
and particularly equations 2.3.11 and 2.3.12
Richard D Saam

If you consider the simple 1-dimensional elastic collision of two masses,
it is easy to show that if you assume conservation of energy and also
a relativity principle (either Galilean or Einstein) that those two conditions
imply conservation of momentum. You an also show that conservation
of energy and conservation of momentum imply the relativity principle.
An argument based on quantum mechanics and special relativity gives
the same result and also shows that it is the energy-momentum 4-vector
that is the most fundamental conserved quantity.

I'm not very familiar with superconductivity theory, but I wonder if adding
a 'g' factor as you do is the correct way to account for conservation of
energy.

Rich L.

[Richard D. Saam]

Post by Richard Livingston

Post by Richard D. Saam
John Bardeen, Leon Neil Cooper and John Robert Schrieffer, "Theory of
Superconductivity", Physical Review, Vol 28, Number 6, December 1, 1957,
pages 1175-1204.
Equation 2.8 addresses a conservation of momentum condition
k1 + k2 = k1' + k2' (conservation of momentum)
But surely superconductivity is an elastic condition
k1^2 + k2^2 = k1'^2 + k2'^2 (conservation of energy)
It is noted that the linear 'conservation of momentum'
does not generate the non linear 'conservation of energy',
This superconductor elastic requirement
can be mechanistically accomplished by assuming a hexagonal lattice
which has a real and reciprocal lattice identity.
g(k1 + k2) = k1' + k2' (conservation of momentum)
k1^2 + k2^2 = g(k1'^2 + k2'^2) (conservation of energy)
Superconductivity, The Structure Scale Of The Universe
https://arxiv.org/abs/physics/9905007
and particularly equations 2.3.11 and 2.3.12
Richard D Saam

If you consider the simple 1-dimensional elastic collision of two masses,
it is easy to show that if you assume conservation of energy and also
a relativity principle (either Galilean or Einstein) that those two conditions
imply conservation of momentum. You an also show that conservation
of energy and conservation of momentum imply the relativity principle.
An argument based on quantum mechanics and special relativity gives
the same result and also shows that it is the energy-momentum 4-vector
that is the most fundamental conserved quantity.
I'm not very familiar with superconductivity theory, but I wonder if adding
a 'g' factor as you do is the correct way to account for conservation of
energy.
Rich L.

But in this BCS reference case, the conservation of momentum in itself
does not imply the conservation of energy. The BCS reference creates a
lattice(not geometrically defined) lowered in energy by a gap in which
Cooper electron pairs move without resistance (They are elastic) But I
do not see from the BCS reference the basic application of conservation
of energy and momentum to achieve the required elastic characteristic.

My approach is to actually define the lattice amenable to conservation
of energy and momentum. It is a hexagonal lattice with each cell having
base B and height A and volume(cavity) = 2*sqrt(3)*A*B^2 and wave
vectors

KB = pi/B
KC = 4pi/(3sqrt(3)A)
KDs = (8pi^3/cavity)^(1/3)
KDn = (6pi^2/cavity)^(1/3

The hexagonal lattice has a necessary space filling property wherein its
real and reciprocal are equal compatible with the following:

p = mv = hK and E = (1/2)mv^2 = h^2*K^2/(2m)
(near virtual)

The elastic(conservation of energy and momentum) conditions are as
follows:

gs(KB + KC) = KDs + KDn (conservation of momentum)

KB^2 + KC^2 = gs(KDs^2 + KDn'^2) (conservation of energy)

The elastic condition (conservation of energy and momentum) is met with
the following numbers.

B/A = 2.379146658937169267

gs = 1.0098049781877999262

by other means a mass(mT) is derived
m= 110.107178208 x electron mass

The hexagonal model can be scaled keeping B/A a constant.

And finally a critical superconductor temperature (Tc) is defined:

E = Boltzmann Constant * Tc = h^2*KB^2/(2m)
time = 2*B/vdx

This superconductor critical Tc model is in general agreement with over
100 experimentally observed superconductors, nuclear quark parameters,
and celestial observations including the rotation time(8.22 hr) of the
interstellar interloper Oumuamua indicating this superconductivity
concept permeates the entire universe.

As a final note, this superconducting model conforms to the Einstein
stress energy tensor that is an elastic criterion.

Richard D Saam