All Questions
51
questions
3
votes
1
answer
125
views
Why can't bosonic systems have fermionic excitations?
When reading Abrikosov's book AGD, there is a statement that 'It is obvious only that a Bose system can not have excitations with half-integral spins' (page 5).
I don't understand why this is the case....
- 51
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
0
votes
0
answers
38
views
Calculation of conformal dimension for Ising model in two dimensional space
Recently I was reading Ph. Di Francesco's book, "Conformal Field Theory", and in section 7.4.2 where it discussed about Ising model, conformal dimensions $(h,\bar{h})$ are deduced from ...
2
votes
1
answer
121
views
Thermal ground state?
Consider a system of $N$ fermions in a periodic box $\Lambda \subset \mathbb{R}^{d}$, described by the Hamiltonian
$$H_{N} = \sum_{k=1}^{N}(-\Delta_{x_{k}}-\mu) + \lambda \sum_{i< j}V(x_{i}-x_{j}) \...
- 1,131
2
votes
2
answers
214
views
Gibbs state and creation and annihilation operators
Let's consider quantum Fermi or Bose gas. Let $a(\xi)$, $a^{\dagger}(\xi)$ are standard annihilation and annihilation operators. Hamiltonian of system is denoted as
$$
\hat{H} = \int_{R^3} \frac{p^2}{...
- 33
2
votes
1
answer
160
views
How to find the QM propagator for more general quadratic theories? (and why didn't my attempts work?)
The Problem
I'm working on a problem using the Path Integral approach to quantum mechanics. Actually, more accurately I'm interested in the Wick rotated version of the problem, so I suppose ...
- 21
2
votes
1
answer
111
views
How is differential momentum assigned in multiparticle system of QFT?
I've been following Schwartz's book on quantum field theory, and got stuck at page 59 on Section 5.1 'cross section' of the book which argues that the region of final state momenta is the product of ...
- 57
1
vote
1
answer
272
views
Average value of creation and annihilation operators - are these two expressions the same?
Suppose we want to study many-fermions quantum mechanics on a lattice, so we start with a finite-dimensional Hilbert space $\mathcal{H}$ and go to its Fock space $\mathcal{F}_{\text{fer}}(\mathcal{H})$...
- 1,131
4
votes
1
answer
609
views
Is there a notion of a "Majorana boson"?
In a similar manner to how we can define Majorana fermionic operators $\gamma_j$ via
$$
c_j \propto \gamma_{2j+1} + i \gamma_{2j}^\dagger,
$$
where the $c$'s are fermionic creation/annahilation ...
- 1,544
1
vote
1
answer
96
views
What is the relation between joint measurability and common refinement (pure state decomposition) of density operators?
Here page 13, the author states "...just as two quantum observables are often not jointly measurable, two
decompositions of mixed states often have no common refinement (Actually, in
the ...
- 51
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
0
answers
106
views
Thermal state of free fermions in contact with a reservoir at temperature $T$?
Without loss of generality and for simplicity, consider a two fermion Hamiltonian
$$
H = \lambda (c_1^\dagger c_2 + c_2^\dagger c_1),
$$
where $c_i$ are fermionic ops, i.e. a hopping Hamiltonian. We ...
- 1,544
2
votes
0
answers
80
views
Interacting fermionic models with exact analytical solution?
Is there any interacting fermionic model (i.e. with more than quadratic terms) which can be analytically diagonalised? Even the "simple looking" Hubbard model seems to lack an analytical ...
- 1,544
2
votes
0
answers
124
views
How to compute the standard deviation of a free fermionic random correlation matrix
I am reading this paper on free random fermions. That is, fermions governed by
$$
H = \sum_{ij} t_{ij}c^{\dagger}_ic_j\quad \longrightarrow \quad H = \sum_k E_k d^{\dagger}_kd_k,
$$
with $t_{ij}$ ...
- 1,544
0
votes
1
answer
411
views
Why does the free fermionic 2-point correlation matrix $C_{ij}=\langle c^{\dagger}_i c_j\rangle$ have eigenvalues equal to either $0$ or $1$?
Consider a system of free fermions with Hamiltonian
$$
H = \sum_{ij} t_{ij}c^{\dagger}_ic_j\quad \longrightarrow \quad H = \sum_k E_k d^{\dagger}_kd_k,
$$
with $t_{ij}$ hermitian. An eigenstate $|\...
- 1,544