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3
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1answer
65 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 ...
0
votes
1answer
36 views

Second quantization of the energy current operator

I am reading Mahan many-particle physics(3rd edition). On P25 he derive the energy current operator in second quantization like this: Equation of energy conservation: $$\frac{\partial ...
2
votes
1answer
62 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 ...
1
vote
0answers
42 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 ...
10
votes
6answers
633 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 ...
1
vote
0answers
46 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 ...
6
votes
1answer
167 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 ...
5
votes
4answers
683 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 ...
1
vote
0answers
63 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
vote
1answer
61 views

The Holstein-Primakoff Representation (approximation)

I have a question regarding the Holstein-Primakoff representation. In the HP-representation we define the spin operators in terms of bosonic creation and annihilation operators. $$ S_j^+ = \sqrt{2S ...
5
votes
1answer
211 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 ...
4
votes
0answers
88 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 ...
3
votes
1answer
99 views

Do holes have wavefunctions?

Do holes (as in the absence of an electron) have wavefunctions? In my understanding, when we talk about holes, we are implicitly invoking two multiparticle wavefunctions: $$\tag{1} \Psi(x_1,...,x_N)= ...
1
vote
0answers
74 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
1answer
121 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 ...
4
votes
1answer
129 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 ...
3
votes
1answer
254 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 ...
3
votes
2answers
157 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 ...
2
votes
0answers
70 views

Questions on the elementary excitations in the resonating-valence-bond(RVB) states?

It is known that the RVB states can support spin-charge separations and its elementary excitations are spinons and holons. But it seems that there are some different possibilities for the nature of ...
21
votes
3answers
2k 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 ...
4
votes
1answer
221 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 $$ ...
2
votes
3answers
119 views

Holes in a P-type semiconductor under external force E

Basically in almost every semiconductor texts, there will be all these concepts concerning electrons, holes, dopants, fermi-levels. However, I have been always confused about the picture of hole ...
0
votes
0answers
58 views

Wave function interaction

If you have two or more wave functions that represent electrons or other charged particles, how would the force on one be calculated based on the charge of the others.
1
vote
0answers
123 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? ...
3
votes
1answer
140 views

What does it mean for a Hamiltonian to be SU(2) invariant?

Can somebody explain what it means when one says a Hamiltonian is SU(2) invariant? I know Heisenberg Hamiltonian is SU(2) invariant but why?
1
vote
0answers
120 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 ...
4
votes
2answers
240 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 ...
2
votes
1answer
67 views

A change of sign in the electron-hole second quantization form

It is common to see people do a change of sign in the so called electron-hole representation, namely, $$ b^{\dagger}_{-k}=a_{v,k} $$ similar argument also seen in 1992 mattuck's book "guide to ...
2
votes
1answer
235 views

Hubbard-Stratonovich transformation and mean-field approximation

For an interacting quantum system, Hubbard-Stratonovich transformation and mean-field field approximation are methods often used to decouple interaction terms in the Hamiltonian. In the first method, ...
17
votes
2answers
664 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, ...
1
vote
0answers
82 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!
1
vote
1answer
150 views

superposition of two states with different number of particles

In an electron gas with no mechanism of production or destruction of electrons is it possible to prepare an state which is superposition of states with different number of electrons? ...
1
vote
2answers
209 views

Probabilities in statistical mechanics

I am reviewing some concepts in statistical mechanics and am becoming confused with how to calculate probabilities when a system has $N$ non-interacting particles. For instance, let's say we have ...
0
votes
0answers
27 views

Computing the Ideal Rotational Ratio of B(E2;2+ to 0)/[Q(2)]^2

Although the title is fairly specific, I was wondering how the following is computed by assuming ideal collective nuclear rotation: $$ \frac{B(E2;2^+_1 \to 0^+_1)}{[Q(2^+)]^2}\approx .244 $$ I'm, ...
0
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0answers
44 views

Significance of Landau's Roton concept

Is Roton a fundamental concept or there is more basic description of it in terms of other quasi particles?
0
votes
0answers
68 views

relative phase/sign in $\Psi$ after exchange of composite particles with angular momenta

I'm reading Quantum Liquids by A.J. Leggett and became confused by the following statement in the first chapter. Consider now a pair of such identical atoms. In the absence of appreciable coupling ...
1
vote
0answers
161 views

What is the origin of the many-body expansion?

I'm looking for the original introduction of the many-body expansion (MBE) in the scientific literature. More specifically, I'm interested in a theoretical justification of the rapid convergence of ...
1
vote
0answers
168 views

Are there any good reading materials for variational approach in many-body theory? [closed]

I need something like a summary of existing results, including the treatment of BCS Hamiltonian and Hubbard model. Auerbach's book is a good one but I still hope to get more comprehensive review. My ...
4
votes
1answer
189 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". ...
10
votes
1answer
449 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
157 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
224 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
121 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} ...
12
votes
1answer
4k 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
98 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
319 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
389 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
88 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
436 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
42 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 ...