• 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.


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


(propose a free ad)

Site Statistics

205 submissions , 163 unreviewed
5,079 questions , 2,229 unanswered
5,348 answers , 22,758 comments
1,470 users with positive rep
819 active unimported users
More ...

  Perturbatively inaccessible intermediate or large coupling phases of classical non-quantum theories

+ 3 like - 0 dislike

Are there classical (ie. non-quantum) theories with inaccessible coupling regions, which can be shown to exist from extrapolating their RG flows derived from weak coupling ranges? Since these intermediate coupling ranges can neither be studied through weakly perturbing exact theories nor through effective theories of bound states, how else are they studied?

Background: For quantum systems like quantum phase transitions, QCD etc, much has been written about inaccessible coupling ranges (especially the intermediate coupling regions in BCS->BEC, quark->hadron etc where neither small coupling perturbation nor large coupling effective theories apply). These regions are indirectly shown to exist through extrapolating RG flow equation derived for weak coupling ranges. I want to know if such phases have been known to exist in non-quantum systems.

PS: I had asked a similar question (which is still open/unaswered), but that was purely in the context of classical turbulence: Similarities between laminar-turbulence transition and others like BCS-BEC crossover, quark-hadron transition etc

asked Nov 9, 2014 in Theoretical Physics by crackjack (110 points) [ revision history ]
edited Nov 11, 2014 by crackjack

Clarifying what I meant by classical theories: I am using 'classical theory' in its traditional form ie. a non-quantum theory. 

Vladimir Kalitvianski wrote (which was deleted for some reason?!):

My first idea may be silly, but let us consider a case of two attracting particles. When the kinetic energy of their relative motion is everywhere higher than the local attractive potential, such particles can only scatter. We may consider it as a regime of weak coupling. We can solve the scattering problem by the perturbation theory and obtain some series in powers of effective coupling.

However, if the kinetic energy of their relative motion is lower than the local attractive potential, the particles get coupled in some sort of a limited relative motion (a bound state). We can consider it as a regime of strong coupling.

You want to know whether we can/cannot extract information about a bound state from a perturbative (or exact) solution of a scattering problem?

No, its not silly! This is the essence of what happens in the strongly coupled quantum systems. But the bound state limits (hadrons of partons->hadron, BEC of BCS->BEC etc) are impossible (as yet) to derive from their weak coupling limits, but can at least be studied in terms of an effective theory of bound states. But the intermediate coupling ranges can neither be studied by effective theories nor by weakly coupled exact theories.

Similarly, I am interested in the intermediate coupling ranges of classical theories. To be specific, I would like to know if there are well known classical systems where such intermediate couplings appear, and how are they handled.

PS: Perhaps I should not have mentioned 'intermediate and large', but in many (quantum) systems the intermediate coupling ranges over several orders of magnitude before a bound state transition can occur.

Dear crackjack, I can share my experience of successfully using perturbative series in the intermediate and strong coupling ranges, but not in the Q/A section. My experience may have a limited significance for you, because I do not know what exactly you are interested in.

I have cleared some off-topic meta comments between Vladimir and myself. @VladimirKalitvianski If you have anything else to say, please continue it on my wall or send me a private message.

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:
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