All Questions
Tagged with mean-field-theorysuperconductivity
9 questions
0votes
0answers
63views
Connection between superconductivity and breaking of $U(1)$ symmetry in superconductors
$\newcommand{\Ket}[1]{\left|#1\right>}$Suppose I have a total Hamiltonian $H = H_0 + V$ given by the usual kinetic term $$H_0 = \frac{\hbar^2}{2m} \sum_{\mathbf{k}, \sigma = \uparrow, \downarrow} \;...
3votes
0answers
46views
How to select a proper term to proceed a mean-field approximation?
Recently I read some literature about how people use the mean-field approximation to solve a particular physical problem. However, I saw people using it in a different way when they dealt with ...
- 263
1vote
0answers
176views
Superconducting gap function vs condensation energy
Within BCS mean-field theory, what is the relationship between the superconducting gap function (or the superconducting order parameter $\Delta(k)$) and the condensation energy (the energy gained by ...
- 749
8votes
1answer
508views
Excitation spectrum in BCS theory and mean field theory
I've recently been learning about the BCS theory of superconductivity. An extremely rough idea is as follows: given the interacting BCS Hamiltonian $$ H = \sum_{\vec{k}\sigma} \xi_{\vec{k}} c^{\dagger}...
- 3,126
3votes
1answer
2kviews
Bogoliubov transformation BCS Hamiltonian
I am reading on the BCS theory and the bogoliubov transformation to diagonilize the BCS Hamiltonian. And there is one step that I really can't seem to get. So the Hamiltonian looks like this: \begin{...
- 27
2votes
1answer
209views
The spin index in general form of BCS Hamiltonian
I want to derive the general form of BCS Hamiltonian, and the original form is:$$H_{\mathrm{BCS}}=\sum_{k, \sigma} \xi_{k} c_{k, \sigma}^{\dagger} c_{k, \sigma}+\frac{1}{2} \sum_{k, k^{\prime}} \sum_{\...
- 1,682
1vote
1answer
257views
Many body BCS theory related question
I am trying to find the mean number of particles in the BCS ground state $|\psi>$, but I am stuck on a step. $$|\psi> = \Pi_{k}(u_{k} + v_{k}c^{{\dagger}}_{{k}{\uparrow}}c^{\dagger}_{{-k}{\...
5votes
1answer
890views
Path integrals and mean-field theory
I am interested in mean-field theories in the path integral formalism. However, I have a technical problem by evaluating the stationary phase approximation (mean-field approximation). After the ...
user82905
17votes
4answers
4kviews
Validity of mean-field approximation
In mean-field approximation we replace the interaction term of the Hamiltonian by a term, which is quadratic in creation and annihilation operators. For example, in the case of the BCS theory, where $...
user82905
