Many body covers questions about systems consisting of a great number of particles and techniques used to tackle them.

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13
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613 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 ...
10
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0answers
121 views

time-dependent Hartree-Fock for two-component bosons

How does the ansatz for the time-dependent Hartree-Fock wavefunction look like in the second quantization if we have two-component boson system and in one case the Hamiltonian commutes with number of ...
7
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0answers
1k views

Why do Fermi liquids have T^2 resistivity?

I have often read that metals that are Fermi liquids should have a resistivity that varies with temperature like $\rho(T) = \rho(0) + a T^2 $. I guess the $T^2$ part is the resistance due to ...
6
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0answers
153 views

What is the largest number of bosons placed in a BEC?

What is the record for the largest number of bosons placed in a Bose-Einstein condensate? What are the prospects for how high this might get in the future? EDIT: These guys reported 20 million ...
5
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0answers
67 views

Two interacting electrons in infinite square potential - is there a solution?

If one were to look at Schroedinger's equation for two interacting electrons in a one dimensional infinite square well, it would something like this: ...
5
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0answers
160 views

Confusion regarding field operators

Second quantisation of the scalar field leads to an algebra of quantum field operators $$ [\phi(x),\phi(y)] = 0, \ \ [\pi(x), \pi(y)] = 0, \ \ [\phi(x),\pi(y)] = i\hbar \delta(x-y). $$ Where the field ...
4
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0answers
44 views

Dynamics of pairwise distances in the $n$-body problem

Consider the $n$-body problem where we are interested in describing the time evolution of $n$ masses interacting through a potential $U$. Let $D$ be the matrix containing all pairwise distances ...
4
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0answers
200 views

What is Resonance Width? Why we use it to distinguish different Regimes of the Anderson Model

The single inpurity Anderson Hamiltonian is ...
3
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0answers
48 views

Spectral density and Green's function

this is a basic question but from what I can see it has not been asked before. I am reading Nolting's "Fundamentals of Many-Body Physics". He speaks about the spectral density in characterising the ...
3
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0answers
133 views

Are symmetries of a degenerate ground-state manifold always broken?

If a Hamiltonian has a global symmetry and a degenerate ground state, then in the thermodynamic limit, the ground states $| \psi \rangle$ that are eigenstates of the symmetry operator typically become ...
3
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0answers
69 views

How to write the second quantization form of spin-orbit coupling(Dzyaloshinskii-Moriya interaction)?

Spin orbit coupling is the single particle term, so the second quantization form can be written like:$\langle \alpha\sigma|s\cdot(\nabla V\times P)|\beta\sigma'\rangle ...
3
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0answers
42 views

how 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 ...
2
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0answers
35 views

Is electron phonon interaction important away from fermi surface?

In weak coupling superconductor, the effective electron phonon interaction can be written as $$ H_{eff}=\frac{1}{2}\sum_{q,k_1,k_2,\sigma_1,\sigma_2} V_{k_1,q}C^{\dagger}_{k_1+q,\sigma_1} ...
2
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0answers
60 views

Numerical 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] ...
2
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0answers
80 views

Second order pole in Feynman diagrams

Hi, I am calculating density-density correlation function for a homogeneous electron gas. The Green's function for one of three first order connected diagrams(see attached figure) is, $$ ...
2
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0answers
172 views

Isotope effect in BCS Theory

The BCS theory for supercondictivity says that the effect of variation of lattice ion mass (M) and its effect on transition temperature is given as $T_{c} \space\alpha\space M^{-\beta}$ . The ...
2
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0answers
113 views

Fermion 1D Hubbard Model ground state in the U = 0 limit

I am trying to determine the ground state of the 1D fermionic Hubbard model at half-filling of $2L$ sites with $L$ electrons with spin-$\uparrow$ and $L$ electrons with spin-$\downarrow$ in the $U=0$ ...
2
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0answers
242 views

How to compute matsubara frequency summation over computer?

Matsubara frequency sum usually takes the following form: $S_\eta = \frac{1}{\beta}\sum_{i\omega_n} g(i\omega_n).$ But in my problem, $g(i\omega_n)$ is a lengthy expression, which can not be ...
2
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0answers
87 views

Is that possible to derive Landau-Fermi liquid theory from microscopic equation?

The question arised from reading Wen's book "Quantum Field Theory of Many-body Systems (Oxford 2004)" p204 To appreciate the brilliance of Landau-Fermi liquid theory, let us look at the ...
2
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0answers
103 views

Lennard-Jones induced pseudo-molecules

It can be shown that the Lennard-Jones potential - which describes the interaction between particles in non-ideal gases - gives rise to pseudo-molecules: after a triple "collision" of three ...
2
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0answers
53 views

Why the peak of spectrum gets vague when the dimension is lower?

In a many-body system, we can know the spectrum function at a particular temperature from Green function. It means density of states. A peak of spectrum represents one mode. My question is that in the ...
1
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0answers
51 views

reconstruct the wave-function from one body reduced density matrix?

Given a many body wave-function for a Fermion system, we can calculate the one-body reduced density matrix straightforwardly. Now suppose we know the one-body reduced density matrix, is there a way to ...
1
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0answers
20 views

Is a phason a Goldstone mode?

Suppose we have a lattice system whose ground state is an incommensurate charge-density wave. Strictly speaking, this ground state does not have Goldstone modes because the only symmetry that is ...
1
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0answers
15 views

Magnetic susceptibility in the spin triplet channel

In the literature and articles I sometimes see the phrase magnetic/electric susceptibility(or other kinds of correlation functions) in the triplet channel. I don't know what does it exactly mean. ...
1
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0answers
54 views

Alternative derivation of Gross-Pitaevskii equation

I wanted to derive time-dependent Gross-Pitaevskii equation in an alternative way, but I don't know if something presented below is allowed. Hamiltonian is the following (I do not assume translational ...
1
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0answers
64 views

Green's functions and spectral function

I'm struggling to understand something in the book by Fetter & Walecka, p.295, relating to the causal ($G$), advanced ($G^A$) and retarded ($G^R$) Green's functions, and the spectral function ...
1
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0answers
43 views

What does a body visible to the human eye moving at constant speed look like in QFT?

In regular $QM$ A single particle is going to have a wave function that solves the free schrodinger equation of energy and momentum such that $$dE/dp = v$$. Obviously the sense of nearness of ...
1
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0answers
75 views

Derivation of open boundary conditions for Non-Equilibrium Green's Function (NEGF)

It is widely claimed that the Non-Equilibrium Green's Function (NEGF) equations for the study of quantum transport have been derived from the many-body perturbation theory (MBPT). Yet the bridge ...
1
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0answers
41 views

Fermi Golden Rule derivation of quasi-electron lifetime

I wonder if there is a detailed derivation of the quasi-electron lifetime: \begin{equation} \frac{1}{\tau_k}=\frac{2\pi}{\hbar}\frac{1}{V^2}\sum_{k', ...
1
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0answers
46 views

Question(s) Regarding the Lindhard Function

As a theoretical chemist, I'm slightly outside of my element on a project my advisor gave me, so I come to your for help and direction. Basically, he wants me to integrate the imaginary part of the ...
1
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0answers
53 views

Inuitive analogy for localization?

I'm looking for a plain English analogy for electron/wave localization. And in particular weak localization and Anderson/strong localization. Is it possible to describe these phenomena in simple terms ...
1
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0answers
68 views

Correspondence between variational method and Feynman diagrams

There are two ways to look at the Hartree or Hartree-Fock equations. One method relies on the variational method for a particular type of the probe function and the second one originates from ...
1
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0answers
37 views

Holography with wave functionals rather than partition functions

Roughly speaking Gubser-Klebanov-Polyakov Witten's (GKPW) prescription in the context of holography tells us partition function of CFT is "equal" to that of the gravity theory in one higher dimension ...
1
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0answers
32 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
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0answers
44 views

Intuition behind modeling quantum impurities as two-level systems

I've been trying to get a basic understanding of quantum impurity problems, starting with the Anderson model. The Wikipedia article (along with some review articles) seems to explain the simplest ...
1
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0answers
122 views

Anderson-Higgs mechanism for the (non-relativistic) $U(1)$ gauge theory under the unitarity gauge

On Page 138, Quantum Field Theory of Many-body Systems: From the Origin of Sound to an Origin of Light and Electrons by Xiaogang Wen, when he demonstrates the Anderson-Higgs mechanism for the $U(1)$ ...
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0answers
37 views

Estimation of polarization perturbative term

I'm studying a diagrammatic approach to degenerate electron gas. Now I need to prove that the energy contribution, with an arbitrary potential, of polarization at first perturbative order given by the ...
1
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0answers
256 views

Good introduction to many-body Green's function via path integral formulation?

Can anyone kindly provide any information on valuable references or books on this topic? It appears to be prevalent in 90s papers on High-Tc superconductivity or quantum Hall effect, especially in a ...
1
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0answers
106 views

about orthogonal catastrophe

I am reading Wen's book, QFT of many-body systems ( @Xiao-Gang Wen ). I am a little confused about the orthogonal catastrophe introduced in Chap.5. Below Eq.(5.1.6), it is stated that ``the influence ...
1
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0answers
357 views

Mean-field approximation of the disordered state of Heisenberg model

Consider a 1D ferromagnetic Heisenberg model with the Hamiltonian $$\mathcal H=-J\sum_i \vec S_i\cdot \vec S_{i+1}.$$ For $|\vec S|=\frac{1}{2}$, we have the usual fermionic representation $\vec ...
1
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0answers
154 views

What do 'first moment' and 'second moment' of a canonical operator mean?

Can anyone explain to me what the first and second moments of a canonical operator mean, in the context of 1D harmonic chain? Thank you!
0
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0answers
14 views

Creation operators that differ by a reciprocal lattice vector

In very general terms, if you have an infinite lattice of atoms you can describe the physics in terms of creation (and annihilation) operators $\hat{a}_{\mathbf{R}}$, that create (and annihilate) an ...
0
votes
0answers
37 views

Construction of Wannier function for optical lattice potential

Parameters of the Bose-Hubbard model require the knowledge of the Wannier functions from the lowets band of the optical lattice potential $V(x) = V_{0}\sin^{2}(kx)$ according to equations: $$J = \int ...
0
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0answers
23 views

Nonequilibrium 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 ...
0
votes
0answers
38 views

Perturbation method for Hubbard hamiltonian

I've got a hamiltonian to solve from perturbation methods: $$H=\underbrace{-t\sum_\sigma\sum_{i=1}^N(a^\dagger_{i\sigma}a_{i+1\sigma}+a^\dagger_{i+1\sigma}a_{i\sigma})}_{\hat ...
0
votes
0answers
14 views

Two-particle correlation function for Slater determinant

In a paper by Peschel, http://arxiv.org/abs/cond-mat/0212631, he writes: Consider first a system of free fermions hopping between lattice sites. The one-particle correlation function is ...
0
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0answers
55 views

Operator notation?

I'm starting out with many-body quantum theory, second quantization etc. by reading the book by Bruus and Flensberg. In the first chapter they write; "A given local one-particle operator $T_j$ ... ...
0
votes
0answers
22 views

Can you do an n-body simulation in terms of energy and momentum?

An N-body simulation typically works directly in terms of the gravitational forces and accelerations. If you can solve the equations exactly, this is fine, but there are many instances where this is ...
0
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0answers
26 views

Quasi-electron lifetime at Dirac (Weyl) point

I would like to know how one should calculate the electron lifetime with chemical potential at the Dirac point from Fermi Golden Rule: \begin{equation} ...
0
votes
0answers
68 views

Two axis twist spin squeezing Hamiltonian

According to Kitagawa-Ueda (http://journals.aps.org/pra/abstract/10.1103/PhysRevA.47.5138), two-axis counter-twist (TACT) spin squeezing achieves maximal noise reduction. I simulated the scenario ...