# berry phase

1. ### A Berry phase and parallel transport

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...
2. ### A Is the Berry connection compatible with the metric?

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...
3. ### A Is the Berry connection a Levi-Civita connection?

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...
4. ### I Berry phase, Bra-Ket and gradient

Could somebody show me how to derive this equation? How can I get right side from left. Step by step, thanks....
5. ### A Integration along a loop in the base space of U(1) bundles

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...
6. H

### A Why electrical polarization can be expressed as Berry phase?

Could we calculate (linear) electric polarizability from Berry phase?
7. ### A Question about Berry phase in 1D polyacetylene

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...
8. ### Adiabatic expansion of infinite square well

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...
9. ### Matrix elements of non-normalizable states

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 $\psi_p(x)=\frac{1}{2\pi\hbar}e^{ipx/\hbar}$ ##...