Recent content by lichen1983312

Thanks very much, the reference is this one : https://aip.scitation.org/doi/10.1063/1.4890585

I am trying to use the k.p method to study quantum well band structure. One example Hamiltonian look like this [J. Appl. Phys., 116, 033709(2014)] where ##{{\hat k}_ \pm } = {{\hat k}_x} \pm i{{\hat k}_y}## and the matrix elements are function of ##{{\hat k}_i}## and if quantum well is grown...

Thanks very much, I will look into it.

Thanks That is what is said in the graph, which is taken from a different article. But if I only look at the Hamitonian and the basis functions, how can I tell?

I am trying to do some calculation based on a k.p model of GaN proposed by S. Chuang [Phys. Rev. B, 54, 2491]. It is a 8 by 8 Kane model with basis functions: The 8 by 8 Hamiltonian contain first order of k is where ##{k_ \pm } = {k_x} \pm i{k_y}## the reciprocal space and high symmetry...

I am leaning the Haldane model : https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.61.2015 Haldane imaged threading magnetic flux though a graphene sheet, and the net flux of a unit cell is zero. He argued that since the loop integral ##\exp [ie/\hbar \oint {A \cdot dr} ]## along a path...

Maybe the question is not so clear, I will use an example. A physical system is represented by k-dependent Hamiltonian operators ##\hat H(k)##, where ##k## is a point in the torus. Each linear operator ##\hat H(k)## has a set of discrete eigen-functions such that ##\hat H(k)\left| {{u_n}(k,r)}...

Is this possible? let's say there are two principal bundles ##{P_1}## and ##{P_2}## over ##M##, and ##{A_1}## and ##{A_2}## are corresponding gauge fields. Is it possible to smoothly change ##{A_1}## into ##{A_2}##?

Thanks very much for the explanation.

I mean should the Chern class be a even dimensional form like 2-form, 4-form..., and the circle is one dimensional. or you mean the 0-form is well defined? May be I am confused about the definition of Chern number. Does the U(1) bundle on a cirlce have a Chern number?

I am encountering this kind of problem in physics. The problem is like this: Some quantity ##A## is identified as a potential field of a ##U(1)## bundle on a space ##M## (usually a torus), because it transforms like this ##{A_j}(p) = {A_i}(p) + id\Lambda (p)## in the intersection between...

I have to ask this again, should the Chern class be only defined on a bundle whose base space is even dimensional? And are the Chern classes defined on a ##U(1)## bundle on a circle?

Thanks very much, you said "it follows easily that an oriented ##U(1)## bundle over the cylinder is also trivial", I have two questions 1, what about other bundles such as ##U(N)##? The original text says for the second graph a vector bundle on patch A must be trivial, what is the reason for...

Thanks again, I got a new question https://www.physicsforums.com/threa...ector-field-on-the-patches-of-a-torus.927959/ please take a look, this topic is driving me crazy.

Hi Lavinia, Thanks very much, that is very helpful!