How is particle creation (or annihilation) in non-relativistic many body...
How is that, in many body physics, particle creation and annihilation is possible even though it is a non-relativistic theory?
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Help Understanding Correlations In Many Particle (Beam) Physics
I am having a lot of trouble looking at the statistical properties and having some sort of intuitive sense of correlations among different properties of many body systems (in particular charged ion...
View ArticleIndistinguishable particles and probability density
I am given the following (probably simple) exercise, but I think I misunderstand something: Let $psi_{a,b}(r_1,r_2)$ be a two-particle state, calculate the probability density for distinguishable and...
View ArticleWave function of N electrons in a superconductor
Assuming that the wave function consisting of $N$ electrons is $Psi_{N}(bf{r_1,r_2,cdots r_N)}$ then in the presence of a magnetic field ($bf{B}=nabla times A$), how do I show that the current can be...
View ArticleHamiltonian for electron hole
I found in lectures notes that the Hamiltonian containing the energy of a electron hole without any interaction is given by $$H = sum_k d_k^{dagger} d_k left( frac{hbar k^2}{2m_V} – E_{0,V} right)$$...
View ArticleHartree Fock equations
I don’t understand how the Hartree Fock equations define an iterative method! For this discussion, I am referring to the HF equations as described here: click me! Basically if you guess a bunch of...
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Tidal tails of galaxies after collision
When there is a collision of 2 disc shaped galaxies, there is a tail formation created from both the galaxies. I read here that this was due to tidal forces, but I couldn’t figure out how this happens....
View ArticleBCS-BEC crossover
It would be really helpful if somebody could describe what does one mean by a BEC-BCS Crossover. I was going through articles available on the topic, but I was unable to grasp the gist of the topic.
View ArticleUnitarity of Symmetrisation operators
How can i proove that the symmetrisation operators $S_{pm}$ are unitary? Defining $S_{pm}$ on the $N$ Particle Fock Space by it’s effect on $|Psi rangle=| Psi_1 rangle otimes… otimes| Psi_Nrangle $...
View ArticleGrand potential $leftrightarrow$ ground state energy of interacting electrons...
I want to calculate the ground state energy $E_0$ of interacting electrons in a solid at $T=0$ via pertubation theory and Feynman diagrams, i.e. I want to understand the connection between the...
View ArticleDifferentiating between Tensor Networks
I am trying to study tensor networks and their application to quantum phase transitions. However, I had a question concerning the connection between the projected entangled-pair states (PEPS) and the...
View ArticleGaussian integral on a Riemannian manifold
How do I estimate the Gaussian integral $int d^nx sqrt{g(x)}~e^{-x^2} $ on a Riemannian manifold $(M,g=det~g_{munu})$? I’ve tried to consider $sqrt{g(x)}$ as an analytic function and expanded it. My...
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Consider a particle of reduced mass $mu$ orbiting in a central force with...
Consider a particle of reduced mass $mu$ orbiting in a central force with $U=kr^n$ where $kn>0$. (a) Explain what the condition $kn>0$ tells us about the force. Sketch the effective potential...
View ArticleNumerical problem with Hartree-Fock equations for dilute Bose gas
I have to solve the following set of equations self-consistently: $$begin{align} n_c(mathbf{r}) & = frac{1}{g}left[mu - V_{rm ext}(mathbf{r}) - 2 g n_{T}(mathbf{r}) right] \[3mm]...
View ArticleProblem using spin-restricted form of the second-quantized nonrelativistic...
I have a problem that confuses me a lot. The two-electron part of the electronic nonrelativistic Hamiltonian can be written begin{equation} frac{1}{2}sum_{pqrs} (pq|rs)...
View ArticleWhat does a bucked honeycomb lattice mean?
I was going through some literature where they have mention about bucked honeycomb lattice, but I was unable to understand about the bucked honeycomb term.
View Articlehow to construct self-energie diagrams
I am working on self-energie and feynmann diagrams. they are not very easy to get but i think i am starting to understand how it works but of course i am not realy sure.and before going any further i...
View ArticlePerturbation method for Hubbard hamiltonian
I’ve got a hamiltonian to solve from perturbation methods: $$H=underbrace{-tsum_sigmasum_{i=1}^N(a^dagger_{isigma}a_{i+1sigma}+a^dagger_{i+1sigma}a_{isigma})}_{hat...
View Articlesecond quantization – time dependent basis
In the second quantization time-independent field operator can be expanded in the orthonormal basis: $$hat{Psi}(mathbf{x}) = sumlimits_{i}hat{a}_{i} phi_{i}(mathbf{x})$$ Time evolution of the field...
View ArticleNonequilibrium Green's functions weakly interacting two-component Bose gas
I am planing to describe time evolution of two-component BEC. I was thinking about non-equilibrium Green’s functions, but I don’t if the method can be applied to the problem describe below. I know...
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