All Questions
Tagged with hamiltonian second-quantization
54
questions
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Momentum space representaion of an electron-phonon coubling Hamiltonian
I am facing a problem transforming the following Hamiltonian into momentum space:
\begin{align}\hat{H} = -\gamma \sum_\alpha\sum_{i=1}^2 \hat{X}_{i,\alpha} \hat{c}_{i,\alpha}^+\hat{c}_{i,\alpha} +t\...
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43
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Math in Hamiltonian of the hyperquantization of EM field
1. Background: I encounter this when looking into the hyperquantization of EM field.
We have the secondly quantized field as below:
$$\hat{E}^{(+)}(t)=\mathscr{E} e^{-iwt+i\vec{k}\cdot\vec{r}}\hat{a}=\...
-2
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2
answers
108
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Second quantization of hamiltonian of the Klein-Gordon field [closed]
Good day everyone. When I try to do a second quantization on the hamiltonian, I end up with the following equation,
$$ H = \int \frac{d^3p}{(2\pi)^3} \omega_{\vec{p}} {a_{\vec{p}}}^{\dagger} {a_{\vec{...
- 171
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52
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Sign of momentum doesn't affect Bogoliubov coefficients in Bogoliubov transformation for BEC
I'm running into some issues with the deriving Bogoliubov transformation. Specifically, in order to diagonalize the Hamiltonian
$$\begin{align}H = \sum_p \frac{p^2}{2m} \hat a^\dagger_p \hat a_p + \...
- 319
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118
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Diagonalization of Hamiltonian involving two particle interactions
For a non-interacting Hamiltonian, $H = \sum_{\alpha\beta} H_{\alpha\beta} c_\alpha^\dagger c_\beta$, we can diagonalize the $H_{\alpha\beta}$ matrix to find the eigenstates, which allows us to write ...
- 843
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31
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What is the significance of these lines in the explicit Bose-Hubbard Hamiltonian?
I was doing some 2nd quantization computational physics and as my first system i decided to build up a Bose-Hubbard Hamiltonian
$$
H = \sum_{k} \left\{ \tau_k(a^\dagger_{k} a_{k+1} + a_{k} a^\dagger_{...
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1
answer
93
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How can i write the matrix representation of the following Hatano - Nelson model Hamiltonian?
I have a $1$D and one band lattice model with hopping constants $J_R $ (to the right) and $J_L$ (to the left) and under open boundary condition. It has the following Hamiltonian :
$$H = \sum_{n} (J_R ...
- 1
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55
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What is the ground state of a Hamiltonian in $k$-space after Bogoliubov transformation? [duplicate]
Consider the following Hamiltonian in $k$-space, quadratic in terms of the $\gamma$ operators:
\begin{equation}
\hat{H}_2=\frac{1}{2}\sum_k
\begin{pmatrix}
\gamma_k^\dagger & \gamma_{-...
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60
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Matrix elements in second quantisation formalism
In a system with two orbitals $c$ and $d$ (each with two spin degrees of freedom), consider the Hamiltonian $$H=V(d^{\dagger}_{\uparrow} c_{\uparrow} + c^{\dagger}_{\uparrow}d_{\uparrow}+d^{\dagger}_{\...
- 303
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238
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Commutation of kinetic energy operator with Hamiltonian
I am basically trying to calculate current energy operator $\hat{\mathbf{J}}_E(\mathbf{r})$ by using Heisenberg equation of motion as
$$
-\nabla\cdot \hat{\mathbf{J}}_E(\mathbf{r})=\frac{i}{\hbar}[H,\...
- 831
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0
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31
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Quasi-periodic motion of $N$-particle systems [closed]
My question is about the time evolution of multi-particle systems in QFT. There are such systems evolving a-periodically. I struggle with the treatment of them, always obtaining periodic or quasi-...
- 11
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0
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42
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Hamiltonian of the BEC in 2nd quantization [closed]
If I have $N$ non-interacting particle (bosons) forming a BEC that is trapped to
$x = 0 $ (assume the system to be 1D) by an applied harmonic potential $V=\frac{1}{2}m\omega^{2}x^{2}$
How can I write ...
- 11
1
vote
1
answer
638
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Half-Filling Hubbard Model
How do I calculate the matrix elements of a 4x4 matrix following the Hubbard model? I am assuming half filling. I have the following states $$\lvert 1 \rangle = \begin{bmatrix}1 \\ 0 \\ 0 \\ 0\end{...
- 11
2
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1
answer
270
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On diagonalizing a $6\times 6$ Hubbard mean-field hamiltonian
I am struggeling with how to tackle a specific Hamiltonian. I am working with a mean-field Hubbard model and after the introduction of a specific order parameter and transform to momentum space, it is ...
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2
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What is $\varepsilon_i$ in second quantization Hamitonian?
I'm studying a solid state physics course I have difficulties with hamiltonian defined $$\hat H = \sum_{i}\varepsilon_i \hat c^\dagger \hat c = \sum_{i} \varepsilon _i \hat n_i .$$
I thought ...
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