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3
votes
1answer
59 views

Where can I find a detailed derivation of the form of two body operators in the second quantization?

I've been looking around online for a couple hours now and I can't find a very informative derivation of the form for two body operators in the second quantization. Is there a resource online ...
0
votes
1answer
32 views

What is the form of the kinetic energy operator on a one dimensional (real space) lattice? (In second quantization)

I'm trying to figure out how one would write down the hamiltonian of a free fermion system (eventually in second quantization) on a one dimensional lattice and I'm having trouble both coming up with ...
0
votes
1answer
63 views

Fourier transform of random variables

My question is concerning Fourier transforms of random variables. So if the question itself is too heavy a task but you know of any good resources to learn this topic that would also be very much ...
8
votes
0answers
453 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
305 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
157 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
49 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
155 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
106 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
23 views

Creation and annihilation form of hamiltonian to derive a relation between the ac current applied to the crystal and the oscillations of the crystal

in the book "many-particle physics" by G.Mahan in piezoelectric subsection, it uses the second quantization formalism to derive the relation for hamiltonian of the electron-phonon interaction. so ...
1
vote
0answers
137 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
60 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
159 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
157 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
45 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
42 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
48 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
33 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
28 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 ...