Why don't Cooper electrons accelerate infinitely?

  • I
  • Thread starter Jirnyak
  • Start date
  • #1
19
8
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?
 

Answers and Replies

  • #2
5,432
292
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.
 
  • #3
PeterDonis
Mentor
Insights Author
2020 Award
35,931
13,996
Why are not cooper electrons infinitely accelerating?

Why do you think they would be?
 
  • #4
5,432
292
Why do you think they would be?
Probably beacuse the electrical formula ##V=IR## suggests this with zero resistance.
 
  • #5
PeterDonis
Mentor
Insights Author
2020 Award
35,931
13,996
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.
 
  • #7
EPR
440
103
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.
 
  • #8
Dale
Mentor
Insights Author
2020 Award
32,146
9,071
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.
 
  • #9
ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
Insights Author
35,977
4,683
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.
 
  • Like
Likes Jirnyak, vanhees71 and berkeman
  • #10
Demystifier
Science Advisor
Insights Author
Gold Member
12,364
4,690
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.
 
  • #11
993
48
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)
 
  • Like
Likes Jirnyak, vanhees71 and Demystifier
  • #12
Demystifier
Science Advisor
Insights Author
Gold Member
12,364
4,690
"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?
 
  • #13
993
48
I don't know... I've seen the EM force law described as "exponentially damped"
 
  • #14
ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
Insights Author
35,977
4,683
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.
 
  • #15
Demystifier
Science Advisor
Insights Author
Gold Member
12,364
4,690
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.
 
  • #16
ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
Insights Author
35,977
4,683
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.
 
  • #17
Demystifier
Science Advisor
Insights Author
Gold Member
12,364
4,690
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?
 
  • #18
ZapperZ
Staff Emeritus
Science Advisor
Education Advisor
Insights Author
35,977
4,683
Are you saying that it is impossible to have an alternating current in a superconductor?

Where did I say that, or even implied that?

AC in superconductivity isn't as simple as DC, because now, the AC resistivity is no longer zero. The electrons that do not participate in becoming a supercurrent may start to influence the electrical properties of the superconductor.

Zz.
 
  • Like
Likes Jirnyak, vanhees71, Mentz114 and 1 other person

Related Threads on Why don't Cooper electrons accelerate infinitely?

Replies
6
Views
791
Replies
2
Views
2K
Replies
102
Views
18K
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
15
Views
8K
Replies
3
Views
4K
  • Last Post
Replies
3
Views
907
Replies
6
Views
5K
Replies
16
Views
6K
Top