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2
votes
2answers
104 views

Describing a single photon with creation and annihilation operators

Since I am not fully aware of the creation and annihilation operator formalism for single photons, I want to ask, if the following is correct: I am considering a photon in the vacuum which travel ...
0
votes
2answers
113 views

What is the general theory that describes the interactions between strings?

What is the general theory that describes the interactions between strings? I mean the basic object in the theory is (closed) string and they have interactions among them. The string theory, as I ...
2
votes
1answer
94 views

Time reversal operator in tight-binding model with second quantization form

In the tight binding model, $H=\sum_{r,r'}ta^{\dagger}_{r}a_{r'}+h.c.$. When conducting a time reversal transformation, what form will this Hamiltonian take? Or how can I express time reversal ...
8
votes
0answers
406 views

Horrifying electron gas model

I am given the Hamiltonian, in an exercise called plasmons, and where $\langle, \rangle $ denotes the expectation value. $$ H = \sum_{k} \varepsilon_k a_k^{\dagger} a_k + \sum_{k_1,k_2,q} V_q ...
4
votes
0answers
267 views

Is non-relativistic quantum field theory equivalent with quantum mechanics?

Related post Can we "trivialize" the equivalence between canonical quantization of fields and second quantization of particles? Some books of many-body physics, e.g. A.L.Fetter and ...
3
votes
0answers
154 views

Fock Subspaces and Weight Vectors

This is my first time taking a physics course (I'm a mathematics major), so I'm encountering a lot of new things, which I'm kind of expected to know. In particular, how to work with Bosons. I've got ...
2
votes
0answers
47 views

How to formulate collapse in polarization subspace of a photon?

I am wondering how to describe the collapse of a photon state when it is measured in the polarization degree of freedom (say by a filter which let pass just one particular polarisation). Let the free ...
2
votes
0answers
140 views

Trace of the number operator in second quantization

I would like to find the helmholtz free energy of a system $F=-T ln(Tr[e^{\frac{-H}{T}}])$ namely a bcs superconductor (using Annett's notation) $H=\sum E_k (b_{k\uparrow}^\dagger ...
2
votes
0answers
62 views

generation / destruction of fermions by phonons

my Hamiltonian consists of 1D free fermions coupled to a bosonic bath. The interaction is dictated both by scattering terms $H^{scatt}=\sum_{kq}\alpha^S_{kq}c^\dagger_kc_{k+q}X_q+h.c.$ as well as ...
2
votes
0answers
100 views

Second quantization with qubits

Is "second quantization" means system wich can contain variable, unknown, superposed and otherwise uncertain number of qubits? Can "second quantized" system contain 0.5% of 1 qubit and 95% of 2 ...
1
vote
0answers
86 views

Derivation of Rashba spin-orbit coupling in tight-binding model

Rashba spin-orbit coupling Hamiltonian in free space can be written as: $H_{\text{so}}=\int d^3r \Psi^{\dagger}(\mathbf{r}) \gamma (p_{x}\sigma _{y}-p_{y}\sigma _{x})\Psi(\mathbf{r})$. I expand ...
1
vote
0answers
57 views

Why is this equation regarding boson coherent states true?

I'm reading the proof of the closure for boson coherent states and it involves the following step: $$ \int \prod_{\beta}\frac{\mathrm d \phi^*_{\beta} \mathrm d \phi_{\beta}}{2 \pi i} e^{-\sum_\beta ...
1
vote
0answers
81 views

Normal ordering

If I understood correctly there are two terms called normal ordering: $:c c^\dagger: = c^\dagger c \hspace{.5cm}$so shifting all creation operators to the left and all annihilation operators to the ...
1
vote
0answers
146 views

Second quantization Hamiltonian Matrix for an aggregate

I am working on the matrix form of the Hamiltonian in the second quantization. I haven't taken any course on second quantization and I'm learning it on my own. I'm a little bit confused about the ...
1
vote
0answers
142 views

Time ordering and Fermions

Having time ordering operator for fermions, should it reverse sign if it swaps operators with opposite spin variable? In other words should $T[c_{t_1,\uparrow}c_{t_2,\downarrow}^\dagger]$ return ...
0
votes
0answers
36 views

Hamiltonian for semiconductor

I was wondering which terms we need in a semiconductor Hamiltonian where no transition between the valence and conduction band occur? First we would have a term describing the energy of the full ...
0
votes
0answers
39 views

What is the missing step in this result regarding the creation operators in Fock space?

In the above extract from Simons and Altman: Condensed Matter Field Theory, I am having trouble getting from (2.3) to (2.4) in the case of Fermions (ζ=-1 and the n(subscript i) values are modulo 2). ...
0
votes
0answers
29 views

piezoelectric in quartz

Does any one know if it is possible to find the relation between the ac current frequency applied to a piezoelectric and the change in the crystal lattice due to this current BY USE OF HAMILTONIAN (in ...
0
votes
0answers
23 views

Linear Canonical Transformation in Berezin's book on Second Quantization

This question pertains to linear canonical transformations for bosons in chapter II of Berezin's book "The Method of Second Quantization". Berezin considers a linear transformation of creation and ...
0
votes
0answers
23 views

Two state Hubbard modell

I am given the two state Hamiltonian $$ H = U \sum_{j \in \{L,R\}} n_{j \uparrow}n_{j \downarrow} - t \sum_{\sigma \in \{\uparrow,\downarrow\}}(a_{L \sigma}^{\dagger}a_{R \sigma} +a_{R ...
0
votes
0answers
18 views

States in valence and conduction band

I often see a Hamiltonian in second quantization written for the valence and conduction band. Now, I was wondering: What are the single-electron states that form the prouct state they act on? So what ...