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

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25
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4answers
5k views

Good reading on the Keldysh formalism

I'd like some suggestions for good reading materials on the Keldysh formalism in a condensed matter context. I'm familiar with the imaginary time, coherent state, and path integral formalisms, but ...
19
votes
2answers
6k 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 ...
18
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2answers
2k views

What is the difference between the Balmer series of hydrogen and deuterium?

In my quantum mechanics textbook, it claims that the Balmer series between hydrogen and deuterium is different. However, I was under the impression that the Balmer series $$H_\alpha, H_\beta, ...
14
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1answer
1k 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 ...
13
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0answers
615 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 ...
12
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5answers
3k 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 ...
11
votes
2answers
317 views

Combining two finite number fock spaces into one

Say I have two separate systems of identical Bosons, one with N Bosons the other with M. System one is described by a state $|\psi_1\rangle$ the other with $|\psi_2 \rangle$ which are expressed in a ...
10
votes
6answers
818 views

Tsunami dampening mechanisms

Encouraged by the zeitgeist let me ask the following: Is it feasible (now or in the future) to build systems a certain distance of a vulnerable coastline which can serve to dampen a tsunami before it ...
10
votes
2answers
2k 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 ...
10
votes
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 ...
9
votes
1answer
655 views

What is many body localization?

Is there any good definition of many body localization? It is the property of one state or it is the property of a Hamiltonian? Why does disorder play an important role in many body localization? ...
9
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1answer
1k 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. ...
8
votes
7answers
1k 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 & ...
8
votes
4answers
488 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
1answer
293 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] = ...
7
votes
6answers
461 views

Origins of many-particle interactions

The internal potential energy of an $N$ particle system is a general function of the coordinates of the particles: $U(r_1,...,r_N)$. In some approximations and expansions - e.g. virial expansion - it ...
7
votes
3answers
103 views

Validity of mean-field approximation

In mean-field approximation we replace the interaction term of the Hamiltonian by a term, which is quadratic in creation and annihilation operators. For example, in the case of the BCS theory, where ...
7
votes
2answers
1k 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
1answer
329 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 ...
7
votes
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
votes
2answers
226 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 ...
6
votes
1answer
258 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)?
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
votes
4answers
599 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 ...
5
votes
2answers
995 views

Subtleties in the exact solution to the 1D quantum XY model, in particular the Bogoliubov transformation

I am writing programs to construct the spectra of models with known exact solutions, and soon noticed some subtleties that are not often mentioned in most references. These subtleties are not ...
5
votes
1answer
695 views

Velocity distribution in Plummer's models and others mass distributions

The Plummer's sphere is an model for the mass density in a globular cluster of stars. For an $N$-body simulation I have initialized the position of $N$ masses with a Monte-Carlo technique but cannot ...
5
votes
1answer
66 views

Methods for handling close approaches in $N$-body simulations

In direct gravitational $N$-body simulations, what are the preferred methods for handling close approaches between bodies in order to preserve the accuracy of the evolution of the system?
5
votes
2answers
657 views

Where do mass polarization terms come from in many-body Hamiltonian? Why are they sometimes omitted?

This question is about the Hamiltonian for more than one particle (non-relativistic). Griffiths (Introduction to Quantum Mechanics, 2e) seems to imply that it is $\displaystyle ...
5
votes
1answer
76 views

Why are periodic boundary conditions used for the derivation of phonons? [duplicate]

I am currently reading "Quantum Field Theory for the Gifted Amateur". In chapter 2 Phonons are introduced as solutions (in k-space) of a coupled harmonic oscillator. In real space the oscillator is ...
5
votes
1answer
296 views

Which component shows spin squeezing under twisting Hamiltonian?

Given a many body spin system, a collection of N spin-1/2 particles, under the interaction of the twisting Hamiltonian: $$H_{int} = \sum_{i,j=1}^Na_{i,j}\sigma_{z,i}\sigma_{z,j}= A J_{z}^{2}$$ assume ...
5
votes
1answer
1k 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 ...
5
votes
1answer
383 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". ...
5
votes
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
votes
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 ...
5
votes
4answers
1k views

A quantitative explanation of EM coherence domains in liquid with DNA

I've been looking with interest at a recent biology paper claiming that DNA molecules give off electromagnetic signals which can cause the same types of molecules to be reconstructed at a remote ...
4
votes
4answers
292 views

How can I add dark matter to my $N$-body simulation?

I've written a simple non-scientific N-body simulation for fun: http://magwo.github.io/fullofstars/ I expected to create something looking like spinning galaxies (there are two invisible very heavy ...
4
votes
1answer
608 views

Proof that eigenvalues of Fermionic creation/annihilation operators are Grassman numbers

It's stated probably in all textbooks on many-body functional integrals that operators that satisfy $$ \hat{a}^\dagger \hat{a} + \hat{a} \hat{a}^\dagger = 1 $$ must have eigenvalues that satisfy $$ ...
4
votes
1answer
130 views

For $N$ particles acting under gravity, how long until they settle into a virial equilibrium?

As the title says, if I have a system of particles interacting only due to gravity, over what timescale do we expect them to fall into a virial equilibrium? By virial equilibrium I mean a system that ...
4
votes
1answer
331 views

How is Green function in many-body theory introduced?

Normally, for a (linear) operator $L$ and a DE $$ Lu(x) = f(x) $$ the Green function is defined as $$ LG(x,s) = \delta(x-s) $$ and it is found that $$ u(x) = \int G(x,s) f(s) ds $$ is the ...
4
votes
1answer
320 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 ...
4
votes
1answer
67 views

A seemingly paradox for Eigenstate Thermalization Hypothesis (ETH)

ETH states that for a system, all of its eigenstates thermalize. To be more specific, consider an energy eigenstate of the full system $H|n\rangle=E_n|n\rangle$. If the full system is in this ...
4
votes
1answer
69 views

Density of states in a system of interacting electrons

When we are introduced to the density of states in typical band-theory problems we neglect interaction between electrons, and thus we define the density of states of a sigle particle as: ...
4
votes
2answers
346 views

The momentum of a hole

I'm currently working through "A Guide to Feynman Diagrams in the Many-Body Problem" by R.D. Mattuck (self study, not a homework problem) and am stumped by the following problem: "In a system of free ...
4
votes
1answer
156 views

How to find positions of $n$ masses in Newton mechanics?

I ran into a problem while doing research. The problem can be described as: consider the original $n$-body problem, and if we fix the position of them(unknowns), no interaction among them, they don't ...
4
votes
1answer
542 views

Quantum Field Theory and the Hartree-Fock approximation

I'm currently reviewing some of my notes on Quantum Field Theory (the version of Greiner) and I was wondering if QFT always works in the Hartree-Fock approximation ? Or at least that's what it seems ...
4
votes
1answer
923 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 ...
4
votes
1answer
247 views

Feshbach resonance in simple terms

I was reading up Feshbach resonances in cold atoms and I was unable to grasp the concept. I will tell you what I have understood. We consider two body scattering processes elastic as well as ...
4
votes
1answer
586 views

Confused by Many-Body Formalism: Creation/Annihilation to Field Operators

I'm going through an introduction to many-body theory and I am getting tripped up on the formalism. I understand quantities such as $\hat {N} = ...
4
votes
2answers
480 views

Second Quantization - Texts

I am trying to familiarize myself with the ideas of Second Quantization. However, the literature that I can find online seems only to outline the tools of this formalism of quantum mechanics. There ...
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 ...