All Questions
35
questions
0
votes
1
answer
73
views
$2\pi$-rotation of fermionic states vs. fermionic operators
Given a fermionic state $|\Psi\rangle$, a $2\pi$ rotation should transform it as
\begin{equation}
|\Psi\rangle \quad\to\quad -|\Psi\rangle \,,
\end{equation}
On the other hand, given a fermionic ...
- 426
2
votes
0
answers
76
views
Different ways to understand fermions [closed]
I first learned about fermions in my atomic physics class, where the teacher said that electrons obey the Pauli exclusion principle. Later, in my quantum mechanics class, I learned about identical ...
- 368
-1
votes
1
answer
74
views
Mechanistic Explanations for Electron Degeneracy Pressure [closed]
Most explanations of electron (or any fermion) degeneracy pressure cite Pauli's exclusion principle for fermions. I believe such explanations tell us why we should believe such phenomena exist, but ...
- 1,073
1
vote
0
answers
34
views
Normalisation for a two fermion state
I'm trying to follow this paper (Fermion and boson beam-splitter statistics. Rodney Loudon. (1998). Phys. Rev. A 58, 4904)
However, I don't quite understand where some of his results come from.
...
- 33
2
votes
1
answer
271
views
Origins and understanding hamiltonians for free fermions
I am starting to do some work on free-fermionic models, but I am having some problems understanding some things. My professor led me know that the hamiltonian for free fermions without mass in a ...
- 601
4
votes
0
answers
116
views
Is it possible to express any quadratic fermionic system in terms of a quadratic majorana system and viceversa?
Can one always write, for some suitable matrix $M$
$$
H= \sum^N_{jk}(A_{jk}c^\dagger_jc_k+B_{jk}c_jc_k+h.c.)=i\sum^{2N}_{jk} M_{jk} \gamma_j\gamma_k,
$$
for any $A,B$? And viceversa, can one always ...
- 1,544
0
votes
0
answers
110
views
Technique for diagonalising this free spinless fermionic Hamiltonian?
How does one diagonalise the following Hamiltonian?
$$
H = \sum_n \epsilon_n c^\dagger_n c_n + g \sum_n (c^\dagger_n c^\dagger_{-n} + c_{-n}c_n),
$$
where $c_n$ is a spineless fermionic op. Clearly we ...
- 1,544
1
vote
1
answer
300
views
How to diagonalise this free fermionic Hamiltonian?
I have the following $1$D fermionic Hamiltonian $H$, given by
$$
H = H^A_0+H
_0^B+H_I^{AB}=\sum_{jk\in A} H_{jk}^Ac^\dagger_j c_k + \sum_{jk\in B} H_{jk}^Bc^\dagger_j c_k + \lambda \sum_{j\in A, \ k \...
- 1,544
0
votes
1
answer
207
views
Two-site fermion system
I've to study a two-site fermion system with hamiltonian
$$H=\sum_{\sigma=\uparrow,\downarrow}[\epsilon_1 c^+_{1\sigma}c_{1\sigma}+\epsilon_2 c^+_{2\sigma}c_{2\sigma}+w(c^+_{1\sigma}c_{2\sigma}+c^+_{2\...
- 13
2
votes
1
answer
186
views
Wigner functional for fermionic fields (QFT in phase space)
I'm curently studying the Wigner functional formulation of Quantum Field Theory, which is derived from the Schrödinger picture: the operators which act on the states of the Fock space are functions of ...
- 370
7
votes
3
answers
961
views
Does the Pauli exclusion principle apply to one fermion and one antifermion?
I understand that two fermions cannot simultaneously have the same <momentum, spin> state. I know this is also true of two anti-fermions. But is it possible for one fermion and one anti-fermion ...
- 167
1
vote
1
answer
150
views
Ground state of 3 identical fermions laying over a circumference
We are asked to show that the ground state in a system of 3 free identical fermions that are on a circle of length, 2$\pi$, is equivalent to $\sin(q_1-q_2)+\sin(q_2-q_3)+\sin(q_3-q_1)$ up to some ...
- 31
1
vote
0
answers
56
views
Quantum factorization approximation for first order Coulomb energy
I'm working through "Advanced Quantum Mechanics" by Franz Schwabl, and he uses this G-correlation function to estimate the first order correction to the ground state energy in a Coulomb ...
- 167
3
votes
1
answer
241
views
Expectation value of time-evolved number operator for ground state Coulomb system
I'm going through "Advanced Quantum Mechanics" by Franz Schwabl, and he calculates the electron energy levels from the Coulomb interaction in a perturbative way (section 2.2.3). In the ...
- 167
4
votes
1
answer
350
views
Time reversal symmetry implies that fermions are massless?
In TASI Lectures on Emergence of
Supersymmetry, Gauge Theory and String in
Condensed Matter Systems some continuous limit of lattice model with fermions considered. And on page 6 there is a statement:
...
- 5,707