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4
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1answer
228 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
83 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
453 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
293 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
109 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
430 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
192 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
718 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
609 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
398 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
987 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
31 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
196 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
294 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
144 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
723 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
185 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
550 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 ...
11
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 ...