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

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4
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1answer
230 views

Why is the Wick contraction in HFB or BCS equal to a single-particle density?

I'm trying to understand how in Hartree-Fock-Bogoliubov (HFB) or BCS theory we can write a product of creation/annihilation operators as single-particle densities under the guise of "Wick's theorem". ...
11
votes
1answer
651 views

What're the relations and differences between slave-fermion and slave-boson formalism?

As we know, in condensed matter theory, especially in dealing with strongly correlated systems, physicists have constructed various "peculiar" slave-fermion and slave-boson theories. For example, For ...
2
votes
1answer
190 views

The matrix element of a normal-ordered operator

Eq (1.137) in Negele and Orland gives the following identity for a normal-ordered operator $A(a_i^\dagger,a_i)$: $$\langle \phi|A(a_i^\dagger,a_i)|\phi'\rangle=A(\phi_i^*,\phi'_i)e^{\sum ...
7
votes
1answer
245 views

Correlated three-particle Green Function

I know the relationship between normal and correlated two-particle Green Functions for fermions: $$G_c(1,2,3,4)=\Gamma(1,2,3,4)=G(1,2,3,4)+G(1,3)G(2,4)-G(1,4)G(2,3)$$ Also known as irreducible ...
1
vote
1answer
138 views

Coulomb interaction and conservation laws

In many-body solid-state physics, the Coulomb interaction term in the Hamiltonian usually implies the momentum conservation law in indicies: $$H_c=\frac{1}{2} \sum_{\mathbf{k},\mathbf{k}',\mathbf{q} ...
14
votes
1answer
5k views

Kubo Formula for Quantum Hall Effect

I'm trying to understand the Kubo Formula for the electrical conductivity in the context of the Quantum Hall Effect. My problem is that several papers, for instance the famous TKNN (1982) paper, or ...
1
vote
1answer
109 views

Notational techniques for dealing with creation operators on Fock space

This question is trying to see if anyone has some simple notation (or tricks) for dealing with operators acting on coherent states in a Fock space. I use bosons for concreteness; what I'm interested ...
4
votes
0answers
437 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 ...
5
votes
4answers
434 views

Examples of exact many-body ground state wavefunction

Is there any non-trivial many-body system for which the exact solution to Schrödinger's equation is known? (By non-trivial, I mean a system with particle-particle interactions.) Perhaps something like ...
2
votes
3answers
97 views

Can two distinct spatially separated many-body systems in the ground state contain entangled particles?

In particular, I am asking if two distinct many-body systems (e.g. system A and system B) separated at some arbitrary distance will necessarily be found to contain entangled particles (such that ...
5
votes
1answer
547 views

How to evaluate spin operators in second quantization for spin symmetry-broken Slater determinants?

Suppose we have the following Slater determinant: \begin{equation} | \Psi \rangle = \prod \limits_{i,i'} a^+_{i\alpha} a^+_{i'\beta} | \rangle \end{equation} where $a^+_{i\alpha}$ creates an electron ...
2
votes
0answers
43 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 ...
4
votes
1answer
258 views

Quantum $n$-body problem

Is the quantum $n$-body problem as difficult as the classical $n$-body problem? Or quantum mechanics allows to get a simpler exact solution? Suppose there are 3 particles with uniform potential ...
2
votes
1answer
99 views

Creating/Downloading a large Galaxy Dataset

I was wondering where I can get a more or less complete set of a galaxy to test an n-body simulation (preferably two colliding galaxies with approx 300k to 1M elements). Is it possible to extract ...
2
votes
1answer
583 views

What is different between resolvent and green function

I bumped into a book, where Resolvent $R^{\pm}(E)$ is defined as $e^{\mp iHt/\hbar}=\pm\frac{i}{2\pi}\int_{-\infty}^{\infty}dER^{\pm}(E)e^{\mp iEt/\hbar}$ and $R^{\pm}(E)=\frac{1}{\pm ...
2
votes
2answers
387 views

Time evolution of a reduced density matrix

For a bipartite quantum system evolving under some master equation, is the time derivative of the reduced density matrix equal to the partial trace of the time derivative of the matrix? In other ...
2
votes
1answer
120 views

Mutual Interaction of $N$-Particles in a Cartesian Plane

I am making a simulation of $N$-Particles in a cartesian plane and need help with understanding the basics. At anytime, in my particle system, I will have $N$ number of particles. I am treating the ...
3
votes
1answer
510 views

Feynman diagrams and Hartree-Fock

I am puzzled by some lines I read in Mattuck's book on Feynman diagrams in many-body problems ( http://www.amazon.com/Feynman-Diagrams-Many-Body-Problem-Physics/dp/0486670473 ) Page 21 (1.14) for ...
5
votes
1answer
219 views

Is it possible to make statements about bosonic/fermionic systems by taking the limit $\theta\to \pi$ or $\theta\to 0$, of an anyonic system?

One might naïvely write the (anti-)commutation relations for bosonic/fermionic ladder operators as limits $$ \delta_{k,\ell} = \bigl[ \hat{b}_{k}, \hat{b}_{\ell}^\dagger \bigr] = ...
6
votes
2answers
806 views

Equation of motion for the reduced density matrix

The equation of motion for the density matrix of a many body isolated quantum system is the von Neumann's equation: $\dot{\rho }(t)=i[\rho (t),H]$. How about the equation of motion for the reduced ...
7
votes
7answers
700 views

Is it wrong to talk about wave functions of macroscopic bodies?

Does a real macroscopic body, like table, human or a cup permits description as a wave function? When is it possible and when not? For example in the "Statistical Physics, Part I" by Landau & ...
7
votes
3answers
421 views

Question on the stability of the solar system

One of the pertinent questions about many body systems that causes me much wonder is why the solar system is so stable for billions of years. I came across the idea of "resonance" and albeit an useful ...
7
votes
2answers
1k views

How to get an imaginary self energy?

The Lehman representation of the frequency-dependent single particle Green's function is $$G(k,\omega) = \sum_n \frac{|c_k|^2}{\omega - E_n + i\eta}$$ where $n$ enumerates all the eigenstates of the ...
0
votes
0answers
35 views

Two particles interacting by a inverse-square-law force, find their positions in function of time [duplicate]

Possible Duplicate: Two particles are interacting through gravitational forces. How to find their positions in function of time? Given the initial positions and velocities $r_1(0), r_2(0), ...
5
votes
1answer
213 views

The Born-Oppenheimer approximation and muonic molecules

Does the Born-Oppenheimer approximation fail for muonic molecules (i.e. molecules where one or more electrons are replaced with muons)?
2
votes
1answer
336 views

significance of maxima and minima of time varying kinetic energy of a system

Consider a system of particles where the kinetic energy of the system is varying with time. I'd like to know the significance (or meaning) of the time derivative of the kinetic energy being zero at a ...
1
vote
2answers
148 views

A question on a system of particles governed by laws of gravity and electromagnetic field

Consider a system of many point particles each having a certain mass and electric charge and certain initial velocity. This system is completely governed by the laws of gravitation and electromagnetic ...
8
votes
1answer
799 views

Questions about the Dyson equation

I'm studying finite temperature many-body perturbation theory, and am trying to understand The Dyson equation. In particular, I'm using Mattuck - A guide to Feynman diagrams in the many body problem. ...
6
votes
2answers
198 views

How to understand order emerging from many-body system?

Like the order behavior shown in the image, is it due to the universality of some fundamental mathematic theory? Is there some general physics explanation for it? - edit: This question comes after ...
1
vote
5answers
610 views

Conserved quantities in generalized n-body problem

Given a collection of point-particles, interacting through an attractive force $\sim \frac{1}{r^2}$. Knowing only $m_1a=\sum_i \frac{Gm_1m_i}{r^2}$ and initial conditions we can deduce the motion of ...
12
votes
5answers
1k views

The Many Body problem

(This is a simple question, with likely a rather involved answer.) What are the primary obstacles to solve the many-body problem in quantum mechanics? Specifically, if we have a Hamiltonian for a ...