Quantcast
  • Register
PhysicsOverflow is a next-generation academic platform for physicists and astronomers, including a community peer review system and a postgraduate-level discussion forum analogous to MathOverflow.

Welcome to PhysicsOverflow! PhysicsOverflow is an open platform for community peer review and graduate-level Physics discussion.

Please help promote PhysicsOverflow ads elsewhere if you like it.

News

PO is now at the Physics Department of Bielefeld University!

New printer friendly PO pages!

Migration to Bielefeld University was successful!

Please vote for this year's PhysicsOverflow ads!

Please do help out in categorising submissions. Submit a paper to PhysicsOverflow!

... see more

Tools for paper authors

Submit paper
Claim Paper Authorship

Tools for SE users

Search User
Reclaim SE Account
Request Account Merger
Nativise imported posts
Claim post (deleted users)
Import SE post

Users whose questions have been imported from Physics Stack Exchange, Theoretical Physics Stack Exchange, or any other Stack Exchange site are kindly requested to reclaim their account and not to register as a new user.

Public \(\beta\) tools

Report a bug with a feature
Request a new functionality
404 page design
Send feedback

Attributions

(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,082 questions , 2,232 unanswered
5,353 answers , 22,789 comments
1,470 users with positive rep
820 active unimported users
More ...

  Mathematical rigorous introduction to solid state physics

+ 7 like - 0 dislike
4532 views

I am looking for a good mathematical rigorous introduction to solid state physics. The style and level for this solid state physics book should be comparable to Abraham Marsdens Foundations of mechanics or Arnols mechanics book for classical mechanics or to Thirrings Physics course for quantum mechanics.

Any recommendations?

Edit: As a reaction to Peter Shor's comment, I try to narrow the scope of the question a bit and give some more specific subareas of solid state physics I am in particular interested in:

  • semiconductors and applications
  • the quantum hall effect
  • superconductivity


This post has been migrated from (A51.SE)

asked Feb 24, 2012 in Resources and References by student (85 points) [ revision history ]
recategorized Apr 24, 2014 by dimension10
Solid-state physics is an enormous field; do you have any specific subareas of solid-state physics that you'd like a mathematically rigorous introduction to?

This post has been migrated from (A51.SE)
As a non-mathematician I've never gotten around to reading this, but it might be of interest since you mentioned QHE -- arxiv.org/abs/cond-mat/9411052   

3 Answers

+ 2 like - 0 dislike

The following books discuss rigorous methods in solid state physics:

  • "Renormalization group" by G. Benfatto and G. Gallavotti, see this link.
  • "Renormalization: an introduction" by M. Salmhofer, see this link.
  • "Fermionic functional integrals and the renormalization group", J. Feldman, H. Knorrer and E. Trubowitz, see this link.
  • "Non-perturbative renormalization" by V. Mastropietro, see this link.

See also the course by Rivasseau given at the CIME school in Cetraro, September 2010.

This post has been migrated from (A51.SE)
answered Feb 27, 2012 by Abdelmalek Abdesselam (640 points) [ no revision ]
+ 2 like - 0 dislike

You can wonder about the stability of matter in quantum mechanics or get caught by disorder to learn the rigorous aspects of localization in disordered systems.

This post has been migrated from (A51.SE)
answered Mar 2, 2012 by Vijay Murthy (90 points) [ no revision ]
+ 1 like - 0 dislike

The problem with this kind of books is that there is no special mathematics in solid state physics. There are books with titles like "Quantum Field Theory in Solid State Physics" or similar: modern methods in solid state originate from QFT, quantum chemistry and alike. Thus, rigorous introduction may be found there and not in solid state itself.

If you could specify particular topic, probably it would be possible answer your question.

This post has been migrated from (A51.SE)
answered Feb 25, 2012 by Nestoklon (340 points) [ no revision ]
Agreed. Also, if @student is taking his first course in SSP, he should, perhaps, pick a standard text such as Ashcroft/Kittel, for it is hard to say what mathematics are more important. In quantum many-body theory your main tool may be QFT, linear algebra, group theory or category theory depending on the field.

This post has been migrated from (A51.SE)
@JuanBermejoVega No I am not taking my first course in SSP, however I am by far not an expert in this field. Coming from mathematical physics I just want to have a second introduction which is more rigorous (both mathematical and conceptual) than the standard ones.

This post has been migrated from (A51.SE)
Then, if the answers above don't suffice, you could maybe specify your favourite topics.

This post has been migrated from (A51.SE)

Your answer

Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
Please consult the FAQ for as to how to format your post.
This is the answer box; if you want to write a comment instead, please use the 'add comment' button.
Live preview (may slow down editor)   Preview
Your name to display (optional):
Privacy: Your email address will only be used for sending these notifications.
Anti-spam verification:
If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:
p$\hbar$y$\varnothing$icsOverflow
Then drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds).
Please complete the anti-spam verification




user contributions licensed under cc by-sa 3.0 with attribution required

Your rights
...