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Quasiparticles of quantum mechanics 
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#1
Jun2805, 04:05 AM

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I dont have a great understanding of quantum mechanics but i have been learning about superconductors at school. We've learnt about cooper pairs and how they are attracted and about their bosonlike behaviour. But theres one question that i cant completely answer and whilst looking on the internet i got a couple of contrasting and undefined answers.
What exactly happens to the unpaired electrons in superconductors? i know a couple of things such as they are influenced by the electric field and have no resistance. I have also read they are to do with the boseeinstien fluids in superconductors which i dont quite understand. Also i read that they have their certain properties due to their interaction or relationship with positive holes created by cooper pairs (this i dont understand at all). Any information or help on this topic is much appreciated. Thanks 


#2
Jun2805, 07:18 AM

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However, when you do an AC field, you will notice that the resistance is NOT zero for a superconductor. In such a case, depending on the AC freq., the field causes both the cooper pairs and the normal electrons to oscillate back and forth. So now the resistance is a result of both the cooper paired electrons and the normal electrons. Thus, you detect AC resistivity. The rest of your question, I don't understand, since it appears that you associated these unpaired electrons with a list of behaviors attributed to superconductivity, which they don't participate in. Zz. 


#3
Jun2805, 11:42 AM

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I wonder if the OP is not talking about (Cooper) paired electrons after all ? The second paragraph seems to contradict some of the things in the first. Besides, there doesn't seem to be a specific question about quasiparticles, which is the thread title.



#4
Jun2805, 01:19 PM

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Quasiparticles of quantum mechanics
Zz. 


#5
Jun2905, 07:25 AM

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ZapperZ, your first post answered most of my question about the resistivity of the unpaired electrons. so, THANKS!
the second bit confuses even me. basically i read that the reason they have no resistance is an interactin between the positive holes left other electrons and the unpaired electrons (which really confused me). i guess what im trying to ask is exactly what are quasiparticles and why do the free electrons become quasiparticles. like i said before, i dont have a great understanding of quantum mechanics and dont quite get the boseeinstien fluids in superconductors so an easy explination would be helpful. thanks 


#6
Jun2905, 07:35 AM

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What Landau did was to show that, in the case where the interactions between electrons are "weak", one can "renormalize" such interactions and dump it into the electron's mass, turning it into an effective mass. When one does this, one gets back a "noninteracting" particle back, but with a different mass. So he has turned one manybody problem (difficult) to a many onebody problem (easy). So you can use all you know about a "free electron" case, except the mass of the electron is now different. This different electron is called a "quasiparticle". It is a particle arising out of a singleparticle excitation that has been renormalized to take into account the manybody interactions. Zz. 


#7
Jun2905, 10:28 AM

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To the OP : It would help us to know what your level of education/learning is, so we can address your questions at the appropriate level.
2. I can only guess that you (your text or your notes) are talking about the mechanism for Cooper pairing  through the interaction of an electron with a lattice phonon (mode of oscillation of the positive ions). http://www.ornl.gov/info/reports/m/ornlm3063r1/pt3.html 1. One talks of quasiparticles in strongly interacting systems (where the interaction between electrons can not be treated as a small perturbation to the energy) 2. A Quasiparticle is a mathematical trick that allows us to calculate the properties of such systems by making them look like noninteracting systems of different particles (these different particles are the quasiparticles). 


#8
Jun2905, 11:03 AM

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The Fermi Liquid picture is valid within the "weak coupling" regime. We know that from the model. The question is whether it works outside of this approximation. Now, in the "strongly interacting" regime, there are many evidence to indicate that the "quasiparticle" picture may no longer be valid. For example, the normal state of optimally doped, and underdoped cuprates, ARPES measurements show NO quasiparticle peak (which are observed in the superconducting state). What this means is that the normal state of these cuprates are not the normal Fermi Liquid metals. This is very different than the conventional superconductor case where the superconductivity arises out of the already present quasiparticles. The selfenergy dependence as a function of temperature and the Matsubara frequency are also different than the predicted Fermi liquid model. There is more of a linear dependence than a quadratic depends that Fermi liquid predicted. Chandra Varma came up with a phenomenological model to describe this, calling it a "marginal fermi liquid". So in the strongly interacting regime, there are many indications that the "quasiparticle" concept either does not exist, or not very welldefined. Zz. 


#9
Jun2905, 12:57 PM

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Here's a nice summary written by Varma on the underdoped Cuprates : http://physicsweb.org/articles/world/13/2/8



#10
Jun2905, 01:44 PM

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:) Zz. 


#11
Jun3005, 02:29 AM

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We've breifly done a topic about superconductivity at school but the majority of the explianations that i have read in textbooks from school try to use a classical theory to descirbe superconductivity ( and it just doesnt make sense). Like i said i dont have a great understand of QM but i have a reasonable understanding (ive still got a alot to learn). I am very interested in physics etc. so i wanted to learn about how superconductors "actually" work. 


#12
Jun3005, 02:41 AM

P: 47

Furthermore, I have another question to do with supercondeuctors etc.
If the classical model of ion lattices and electrons in fixed orbits etc is incorrect and infact electron waves and potential wells and what not is correct. Then why does the BSC theory use lattices to describe how to electrons are attracted to eaqch otehr with the phonon being created? Or is the distortion of the lattice similar to the distortion of the potenial well of the ions? 


#13
Jun3005, 06:14 AM

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So in a metal, one can still picture ions in rigid locations. Such a description is perfectly valid. Zz. 


#14
Jun3005, 02:24 PM

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#15
Jun3005, 02:46 PM

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This is getting to be quite interesting and I'm having a deja vu feeling. :) Zz. 


#16
Jun3005, 08:27 PM

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