Talk:Geometric phase

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An earlier edit (Angela) of the page introduced the Berry phase with something that is also found on Eric Weisstein's World of Science - but that description is misleading, so I replaced it. I did try to put the reference to "rotation of a particle" in further below, because I liked it as an example of what one actually could do in experiment. But general rotations alone don't create Berry phases, even when they're slow.

As I said on your talk page, I'm not an expert! I'm glad you checked it. I was just aiming to get some sort of basic introduction to the page and that was the information I happened to come across first. Angela 04:20, Sep 21, 2003 (UTC)

I believe when you mention the AB effect as a manifestation of geometric phase you mistankingly assign the adiabatic parameter to be the magnetic field inside the solenoid -- which is taken to be constant and thus is not adiabatically varied. The true adiabatic parameters are the ones describing the rotation of the quantum mechanical system around the solenoid. Johnny 16:23, Apr 20, 2006 (UTC)

The link to the paper on Fine Structure Constant is not to be credited in my opinion.

Agreed. I removed the link and replaced it by a resource letter by an expert group (Anandan et al.)

Factual problems

Pancharatnam - Berry phase is an example for geometric phase.

Polarized light in an optical fiber is an example for Pancharatnam-Berry phase

The article is very confusing, cause it is mixing geometric phase, Pancharatnam-Berry phase, Aharonov -Bohm effect. All the above are not the same, there are differences between them.

it might be more accurate to write in different sections about each geometric Phase - the berry phase and bohm-aharonov effect, to give it conditions and differences and at the end to give examples that connected to each kind of the geometric phase. —Preceding unsigned comment added by 77.127.62.79 (talk) 10:21, 6 August 2009 (UTC)

It would be nice to have a part of the article about non-ablelian Pancharatnam-Berry phases which can arise for example in closed loop adiabtic evolution of quantum systems with a ground state degneraracy.

I agree that there seems to be a problem with confusing different variants of phase, but from a different perspective than 77.127.62.79. Here is my objection. In all cases, a phase difference arises from going around a closed loop. However, there are two ways this can arise, and they both appear in the articles in different places.

(1) In the introductory two paragraphs, phase differences are ascribed to "topology" or (going around) "a singularity". I figure this refers to a non-simply-connected state space.

(2) In some of the examples (Foucault pendulum, polarized light, at least), the phase difference comes from integrating curvature. This is holonomy (of loops that can be continuously deformed to zero). In this case the space might easily be simply-connected (for example, a disk or R^2) without singularities or topology.

All of these are (mathematically) called holonomy, but the difference is whether the loops go around the topology (or a singularity), or not. As shown by the examples in (2), this is not actually necessary. I deliberately sharpened this issue by including links to "simply connected" and to "holonomy". However, the article is still flawed, because as it written, the general definition in the introduction refers to topology/singularity, whereas the examples, which ought to fall under the rubric set forth in the introduction, actual spring outside of it.

Now 77.127.62.79 complains that the article mixes up several different kinds of phase discrepancy: geometric phase, Pancharatnam-Berry phase, Aharonov -Bohm effect. Is it possible that this mixup is related to the one I have described? 84.227.227.228 (talk) 08:46, 6 April 2014 (UTC)

Examples

I felt the article needed some simple examples to help the reader understand what it is about. I added two. --ShanRen 22:28, 25 February 2007 (UTC)

Here's a new one from Science. I might add it when I get return, if no one else beats me to it. (I'd be more than happy if they did.) Ben Hocking ^{(talk|contribs)} 20:58, 21 December 2007 (UTC)

I think the sentence "there are no inertial forces that could make the pendulum precess" is misleading, because precession in this context usually refers to the rotation of the oscillation plane of the pendulum, and this rotation can be explained in terms of inertial forces (coriolis). To my understanding, what the cited article (ref 7) says, is that what cannot be explained by inertial forces is the angle shift after the pendulum comes back to its original position, which is a different thing. GreyClock (talk) 12:07, 29 May 2020 (UTC)

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