Hello.
In the following(p.2):
https://michaelberryphysics.files.wordpress.com/2013/07/berry187.pdf
Berry uses parallel transport on a sphere to showcase the (an)holonomy angle of a vector when it is parallel transported over a closed loop on the sphere.
A clearer illustration of this can be...
Hello,
Is the Berry connection compatible with the metric(covariant derivative of metric vanishes) in the same way that the Levi-Civita connection is compatible with the metric(as in Riemannanian Geometry and General Relativity)?
Also, does it have torsion? It must either have torsion or not be...
Hello!
I have learned Riemannian Geometry, so the only connection I have ever worked with is the Levi-Civita connection(covariant derivative of metric tensor vanishes and the Chrystoffel symbols are symmetric).
When performing a parallel transport with the L-C connection, angles and lengths are...
Let ##P## be a ##U(1)## principal bundle over base space ##M##.
In physics there are phenomenons related to a loop integration in ##M##, such as the Berry's phase
##\gamma = \oint_C A ##
where ##C(t)## is a loop in ##M##, and ##A## is the gauge potential (pull back of connection one-form of...
Hi. I'm taking a look at some lectures by Charles Kane, and he uses this simple model of polyacetylene (1D chain of atoms with alternating bonds which give alternating hopping amplitudes) [view attached image].
There are two types of polyacetylene topologically inequivalent. They both give the...
1. Homework Statement
Suppose that an infinite square well has width L , 0<x<L. Nowthe right wall expands slowly to 2L. Calculate the geometric phase and the dynamic phase for the wave function at the end of this adiabatic expansion of the well. Note: the expansion of the well does not occur...
Although strictly quantum mechanics is defined in ##L_2## (square integrable function space)， non normalizable states exists in literature.
In this case, textbooks adopt an alternative normalization condition. for example, for ##\psi_p(x)=\frac{1}{2\pi\hbar}e^{ipx/\hbar}##
##...
Hello,
I recently went through Griffiths' Quantum Mechanics text and there is a chapter called the Adiabatic Theorem that includes Berry phase and the Aharonov-Bohm effect.
As I found them very interesting, I would appreciate if anyone could provide me with some good sources(books, internet...
Some books say that there is a gauge transform that we can put an extra phase e^{i \phi ( R(t))} to the wave function.
Since R(t=0) = R(t=T), difference in \phi = 2 pi n, where n is any integers.
As gauge transform would lead to 2 pi n difference, berry phase is determined up to 2pi n.
However...