All Questions
Tagged with hamiltonian statistical-mechanics
83
questions
3
votes
2
answers
203
views
Form of the Hamiltonian at Half-filling
I am trying to understand why chemical potential $= U/2$ is considered to be at half-filling in the case of the Hubbard Model Hamiltonian. So when I substitute this in its Hamiltonian, this is the ...
- 53
0
votes
1
answer
72
views
Is there a name for a Heisenberg-like model, but instead of the ZZ operator, we have one that favor only spin-up-spin-up configurations?
I understand that the Quantum Heisenberg XXZ model in 1D has the form:
$$\hat H = \frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}...
- 700
6
votes
0
answers
72
views
Determining a gapped Hamiltonian from correlation function [closed]
Consider a spin Hamiltonian. I am interested in understanding how the spin-spin correlation function $C(r_{ij}) = \langle \boldsymbol{S}_i \cdot \boldsymbol{S}_j \rangle - \langle \boldsymbol{S}_i \...
- 73
0
votes
1
answer
117
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Partition function for a $SO(3, 1)$ invariant "Hamiltonian"
Suppose, I look at the $SO(3, 1)$ generalization of $H = \frac{p^2}{2m}$, i.e. $$H = \lambda P^{\mu}P_{\mu}$$ where $P^{\mu}P_{\mu}$ is a $SO(3, 1)$ invariant object and $\lambda$ is some dimensionful ...
- 1,200
1
vote
0
answers
49
views
Existence of the thermodynamic limit of the hamiltonian operator
Given a N-particle system, with Hamiltonian operator equal to ${H}_N$. I'm interested in studying the limit N to infinity of the average of the hamiltonian over a set of states $\psi_{N}$. Is it ...
- 159
0
votes
2
answers
107
views
Should I partial trace the hamiltonian or partition function for a reduced system?
Suppose I have a quantum spin model, let's say e.g. the quantum transverse field model with hamiltonian $H$, on some lattice of particles, with partition function $\text{Tr}(e^{- \beta H})$ and I do ...
- 313
1
vote
0
answers
65
views
System interacting with Fermi Gas
My question denoted by a reduced dynamic for a system interacting with a reservoir.
Before asking the question, for completeness I will write in detail the statement of the problem and notation.
...
- 33
-4
votes
1
answer
81
views
Hamiltonian as a quadratic function [closed]
I’m reading R.K Pathria’s Statistical Mechanics, third edition, and I'm having trouble understanding eq. (8) in section 3.7.
It goes like this:
In many physical situations the Hamiltonian of the ...
2
votes
2
answers
214
views
Gibbs state and creation and annihilation operators
Let's consider quantum Fermi or Bose gas. Let $a(\xi)$, $a^{\dagger}(\xi)$ are standard annihilation and annihilation operators. Hamiltonian of system is denoted as
$$
\hat{H} = \int_{R^3} \frac{p^2}{...
- 33
1
vote
1
answer
218
views
Diagonalize a many-body Hamiltonian
Assume we start with a generic many-body Hamiltonian:
$$
H=\sum_{ij} t_{ij} a_i^\dagger a_j+\sum_{mnlk}U_{mnkl}a_{m}^{\dagger}a_{n}^{\dagger}a_la_k.
$$
Now if there is only the one-body part, which ...
- 11
1
vote
0
answers
330
views
Statistical mechanics of a gas in a rotating cylinder
The theoretical premises that allow us to study the statistical mechanics of a substance in a rotating equilibrium are not completely clear to me. For example, consider a gas ($N$ non-interacting ...
3
votes
0
answers
145
views
What is the interpretation of the eigenvalues of $e^{-\beta (H-\mu N)}$?
In quantum statistical mechanics, the equilibrium state is characterized by a density matrix $\rho$. Let me focus on the grand canonical ensemble, although the question also holds for the canonical ...
- 1,131
1
vote
1
answer
182
views
$p$-state Potts Model and symmetry [closed]
Consider a lattice spin system where the spin variable is the $i$th site
can have $p$ values, 0, 1, . . . , p − 1, and the nearest-neighbor Hamiltonian describes the system
This is called a $p$-state ...
- 177
0
votes
0
answers
64
views
Simplifying the master equation of a system
For a system described by a Hamiltonian $H= p_{x}^{2}/2m + b x$ with $b$ being a constant, the master equation for the density matrix ($\rho$) reads
$$\partial_{t} \rho(t,x) = -i [H (c), \rho (t,x)].$$...
- 374
0
votes
1
answer
82
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Dimensional inconsistency in evaluating the canonical partition function
We know that canonical partition of an $N$-particle system is given as
$$Z=\!\!\!\!\!\!\!\!\!\!\!\!\sum_{\text{All possible microstates}}\!\!\!\!\!\!\!\!\!\!\!\!e^{-\beta E}=\sum_E\Omega(E)e^{-\beta E}...
- 436