# Why don't Cooper electrons accelerate infinitely?

• I
Summary:
cooper pairs, composite boson particles (spin number = 0 or 1) from two coupled electrons. The movement of cooper pairs is forming a superconducting current. Superconducting current does not have a dissipation of energy from Resistance as it happens in normal current so Qubit (Quantum bit) circuit could be treated as a system of only conservative forces. Why are not cooper electrons infinitely accelerating?
Hello, I am trying to learn Quantum mechanics and have some questions I cannot answer. cooper pairs, composite boson particles (spin number = 0 or 1) from two coupled electrons. The movement of cooper pairs is forming a superconducting current. Superconducting current does not have a dissipation of energy from Resistance as it happens in normal current so Qubit (Quantum bit) circuit could be treated as a system of only conservative forces. What is a potential for cooper pairs to move into? Why are not cooper electrons infinitely accelerating?

Summary: cooper pairs, composite boson particles (spin number = 0 or 1) from two coupled electrons. The movement of cooper pairs is forming a superconducting current. Superconducting current does not have a dissipation of energy from Resistance as it happens in normal current so Qubit (Quantum bit) circuit could be treated as a system of only conservative forces. Why are not cooper electrons infinitely accelerating?

Hello, I am trying to learn Quantum mechanics and have some questions I cannot answer. cooper pairs, composite boson particles (spin number = 0 or 1) from two coupled electrons. The movement of cooper pairs is forming a superconducting current. Superconducting current does not have a dissipation of energy from Resistance as it happens in normal current so Qubit (Quantum bit) circuit could be treated as a system of only conservative forces. What is a potential for cooper pairs to move into? Why are not cooper electrons infinitely accelerating?
If you are learning QT then starting with super-conductivity is bold ( and probably unwise). It is an interesting feature of this phenomenon that the equations predict that with a constant voltage applied across the superconductor a constant current flows. We cannot say why - it just happens that way.

Jirnyak
PeterDonis
Mentor
2020 Award
Why are not cooper electrons infinitely accelerating?

Why do you think they would be?

Why do you think they would be?
Probably beacuse the electrical formula ##V=IR## suggests this with zero resistance.

PeterDonis
Mentor
2020 Award
the equations predict that with a constant voltage applied across the superconductor a constant current flows

No, they predict that with zero voltage applied a constant current flows.

Probably beacuse the electrical formula ##V=IR## suggests this with zero resistance.

No, it suggests that ##V = 0## with ##R = 0##. See above.

vanhees71
[]
Why are not cooper electrons infinitely accelerating?
Sorry if I mislead you. Just to make my point about how tricky 'infinite conductivity' is, look at this (great) paper
My mistake is not remembering that it is the time derivative of the Nambu-Goldstone field that must be zero and this is equal to -V ( equation 29 ).

vanhees71 and Jirnyak
To accelerate electrons beyond the total watt power of the source, an outside source of energy is needed. This is how colliders work - they employ ultra powerful electromagnets to do the job.

Dale
Mentor
2020 Award
Why are not cooper electrons infinitely accelerating?
I think that you could write down the wave-function for the Cooper pair and then apply the acceleration operator. That should give you 0. My understanding is that the wave function of a Cooper pair goes all around the superconducting loop and everywhere has a non-zero current density operator and a zero acceleration operator.

Perhaps one of my colleagues could describe that in more detail or tell me that I am wrong. In any case, superconducting electrons are not little microscopic horses racing around a track and accelerating as they go.

Jirnyak
ZapperZ
Staff Emeritus
Summary: cooper pairs, composite boson particles (spin number = 0 or 1) from two coupled electrons. The movement of cooper pairs is forming a superconducting current. Superconducting current does not have a dissipation of energy from Resistance as it happens in normal current so Qubit (Quantum bit) circuit could be treated as a system of only conservative forces. Why are not cooper electrons infinitely accelerating?

Hello, I am trying to learn Quantum mechanics and have some questions I cannot answer. cooper pairs, composite boson particles (spin number = 0 or 1) from two coupled electrons. The movement of cooper pairs is forming a superconducting current. Superconducting current does not have a dissipation of energy from Resistance as it happens in normal current so Qubit (Quantum bit) circuit could be treated as a system of only conservative forces. What is a potential for cooper pairs to move into? Why are not cooper electrons infinitely accelerating?

Apply the concept of plane wave solution that you learned in basic QM. What do you think is the "average position" of a particle having such a wavefunction.

The Cooper pair wavefunction is a combination of such plane waves, meaning that these pairs are not localized. They have what we call "long range coherence", which is why they form supercurrents. You will run into huge conceptual problems if you try to apply classical E&M and classical electric current motion to such a scenario.

Zz.

Jirnyak, vanhees71 and berkeman
Demystifier
Gold Member
Why are not cooper electrons infinitely accelerating?
Because the maximal speed of electrons is the speed of light.

But perhaps the right question is this. If we put a superconductor in a synchrotron which accelerates electrons by electric field which lasts for a long time, will the electrons approach the speed of light in the superconductor (as they do in the vacuum)? I don't know the answer, perhaps a superconductor looses its properties at very high electron speeds.

Jirnyak
Because the maximal speed of electrons is the speed of light.

But perhaps the right question is this. If we put a superconductor in a synchrotron which accelerates electrons by electric field which lasts for a long time, will the electrons approach the speed of light in the superconductor (as they do in the vacuum)? I don't know the answer, perhaps a superconductor looses its properties at very high electron speeds.

"Photons inside superconductors develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors."
per Wikipedia | Photon | Properties | Experimental checks on photon mass | reference #39 Frank Wilczek, (2010)

Jirnyak, vanhees71 and Demystifier
Demystifier
Gold Member
"Photons inside superconductors develop a nonzero effective rest mass; as a result, electromagnetic forces become short-range inside superconductors."
Interesting. Does it mean that the Meissner effect expels not only the magnetic field from the superconductor (which every textbook says), but the electric field as well? If so, why is it not mentioned in the textbooks?

Jirnyak
I don't know... I've seen the EM force law described as "exponentially damped"

Jirnyak
ZapperZ
Staff Emeritus
Interesting. Does it mean that the Meissner effect expels not only the magnetic field from the superconductor (which every textbook says), but the electric field as well? If so, why is it not mentioned in the textbooks?

But this is by default because you have a perfect conductor.

Zz.

Jirnyak
Demystifier
Gold Member
But this is by default because you have a perfect conductor.
But if the electric field is always zero, then what gives the electrons the initial velocity needed to have the electric current in the first place? It is only during the stationary current that the electric field is zero in a perfect conductor. When the current changes (which is what this thread is about), then the electric field in a perfect conductor is not zero.

Jirnyak
ZapperZ
Staff Emeritus
But if the electric field is always zero, then what gives the electrons the initial velocity needed to have the electric current in the first place? It is only during the stationary current that the electric field is zero in a perfect conductor. When the current changes (which is what this thread is about), then the electric field in a perfect conductor is not zero.

There is no initial velocity the same way that photons have no initial velocity. There are already current flow in all directions. It is just that when a voltage is applied, a particular direction is selected.

Zz.

Jirnyak
Demystifier
Gold Member
There is no initial velocity the same way that photons have no initial velocity. There are already current flow in all directions. It is just that when a voltage is applied, a particular direction is selected.
Are you saying that it is impossible to have an alternating current in a superconductor?

Jirnyak
ZapperZ
Staff Emeritus