QED in condensed matter systems

[mgb2]

Hi to everibody,

 

I'm a researcher working on mgb2 superconducting tape fabrication with a great passion for theoretical physics.

Recently I was reading a textbook about a new way to threat condensed matter systems (with N=10²³) in terms of QED who can be useful for my research field but very difficult (for me) to understand.

The basic lacuna that this book wish to fill in the analysis of condensed matter systems is the generalized neglect of the electro-dynamical interaction of the elementary systems with the electro-magnetic radiation field A(x,t).

Please, excuse me if I don't give you the book title and the author name but I would like to discuss in a situation without any prejudice.

The ideas expressed in this book may seems sometimes difficult to accept from the scientific community and my QFT understanding is not so high (maybe too low) to distinguish if whether or not these ideas are just "difficult to be accepted" or simply wrong.

 

So, I would ask you all if is possible to begin here a sort of "theory testing" in which, step by step, the theory will be shown and you shall find all of its possibly weaknesses.

 

Thanks in advance.

mgb2

[ajb]

So, I would ask you all if is possible to begin here a sort of "theory testing" in which, step by step, the theory will be shown and you shall find all of its possibly weaknesses.

 

Feel free to post and ask whatever questions you have. However, as it is very specialised I cannot guarantee the answers you will get will be of much help.

 

Generally, I do not think that many people are using QED (proper) for calculations in condensed matter physics or optoelectronics. I am not sure who to ask for help with this.

[mgb2]

Thanks ajb,

 

I'll start by uploading the first chapter of the book and let you the time to read before discussing all together.

 

When you all will be ready please start with questions and let me know if there is something wrong.

 

I don't think there is violation to copyright if only a part of the book is publicized.

Anyway, if I am wrong I will delete them immediately and we will find another way to discuss about it

 

 

Thanks

mgb2

 

 

 

Edited April 27, 2011 by mgb2

[swansont]

Generally, I do not think that many people are using QED (proper) for calculations in condensed matter physics or optoelectronics. I am not sure who to ask for help with this.

I'm not sure how much QED is being used either, but I know that using Bose-Einstein Condensates/Fermi gases/optical lattices to simulate condensed matter systems has been a big topic in atomic physics the past several years. Not my subfield, though.

 

Review article from 2007

http://arxiv.org/abs/0704.3011

[mgb2]

Dear swanson,

you are absolutely true, but the condensed matter systems I' talking about is ordinary matter with high density and temperature far from absolute zero.

This shall imply a profound difference in the behavior and in theoretical approximations.

 

 

mgb2

[mgb2]

Ok,

I think this first chapter add no particular new notions about the ones that are already known.

 

It is just to begin to handle with the language of QFT and the major points are related to describe both the matter and the e.m. wave-field as a collection of harmonic oscillators in the respective Hamiltonians on a proper Fock space.

 

Now the operators are the fields, which can be expanded as in 1.61 and the vectors of the Fock space can be written in form of coherent states, which can be expressed as an infinite superposition of the eigenvectors of the number operator.

 

Now, when we talk about annihilation and creation operators acting upon some state, we don't have to think to destroy or create a particle as in high energy physics but to the creation or destruction of a quasi-particle (excitation) in a particular mode of the field.

Basically this means that the number operator is conserved.

 

Another aspect is related to the difference in between coherence and long-range order.

If you consider the Bose gas of a fixed number N of non interacting elementary systems the correlation function is not zero but the order parameter expectation value is zero instead, because a₀|N>₀=c|N-1>₀ and ₀<N|N-1>₀=0 in 1.80.

 

The important notion to remind here is that of the Perturbative Ground State (PGS), well explained at pag 19 and the Coherent Ground State (CGS) 1.93 arising from the simple introduction of a two-body short-range interaction as in 1.81 and stemming from the fact that coherence over long distances demands an interacting theory that cannot be treated perturbatively.

 

Now let's go ahead with the second chapter to see what happen, in QFT, to the wave-particle duality with the well know problem of trajectory in QM and the effect of simply rescaling the theory let the particle number to appear in the transition amplitude 2.39.

 

Thanks for your attention

mgb2

Edited April 29, 2011 by mgb2

[mgb2]

Dear ajb,

 

what's wrong ?

why nobody is replying ?

 

Thanks

mgb2