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-3
votes
0answers
23 views

How does a levy walker work?

I have read that a levy walker is a random walker which changes it direction after times which have power law distribution. is there any range for exponent of this distribution?
4
votes
0answers
91 views

Two-point function of a free massless scalar field in Euclidean space-time

Let $\phi(x)$ be a free massless scalar field on $d$-dimesnional space-time with Euclidean metric. I am interested in the operator formalism, i.e. $\phi(x)$ is an operator satisfying $\Delta \phi=0$ ...
1
vote
0answers
33 views

What's the connection between the pole contours of propagators and their causality?

Wikipedia distinguishes between three kinds of propagators for a scalar field: The Retarded propagator's contours have $\mathrm{Im}(k^0)>0$ on both poles, so its limit is completely in the first ...
1
vote
0answers
41 views

Deriving the correlation function of a system interacting with a bath of harmonic oscillators

I'm working on the book Quantum Effects in Biology by Mohesni et all. My question is however not biology related, it is about a section on quantum master equations in the weak system-bath coupling ...
1
vote
0answers
14 views

Relating $C_j(t-t') = \left<\hat{B}_j(t)\hat{B}_j(t')\right>$ to $\left<\hat{B}_j(t)^2\right>$

I'm trying to relate a known quantum correlation function $C_j(t-t') = \left<\hat{B}_j(t)\hat{B}_j(t')\right>$ (which is not real!) of a (time dependent, but this is not super relevant) quantum ...
1
vote
2answers
631 views

Green function for simple harmonic oscillator

I'm interested in examples on how to use Green function (GF)for simple harmonic oscillator (SHO)? I am from undergrad physics, so I need a fundamental math and quantum mechanical application of GF ...
2
votes
1answer
94 views

S-matrix element

I'm confused with the relation between the fully resummed propagator in a given QFT and the corresponding S-matrix element. According to the LSZ reduction formula ($\phi^4$ theory for definiteness ...
16
votes
1answer
343 views

LSZ reduction vs adiabatic hypothesis in perburbative calculation of interacting fields

As far as I know, there are two ways of constructing the computational rules in perturbative field theory. The first one (in Mandl and Shaw's QFT book) is to pretend in and out states as free ...
5
votes
0answers
117 views

I find there are two methods to calculate the amplitude in QFT. Is it equivalent? [duplicate]

I find there are two methods to calculate the amplitude in QFT. First method: Use LSZ reduction formula $$\langle p_1\cdots p_m;out|k_1\cdots k_n;in\rangle=\big(\frac{i}{\sqrt{Z}}\big)^{n+m}\int ...
1
vote
0answers
14 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. ...
0
votes
0answers
13 views

How to get the vibratonal frequency of a bond using FFT of velocity autocorrelation function?

I guess there is some errors in the way I am calculating VAC since I ma ending up with a peak whose frequency is two times the actual frequency. I ran an MD simulation long enough with 60 molecules of ...
7
votes
1answer
473 views

Differential equation (Greens function) satisfied by the kernel using path integrals

I'm reading Feynman and Hibbs, Quantum Mechanics and Path Integrals. How do I show that the kernel $$\tag{2-25} K(x_2 t_2;x_1 t_1)=\int e^{\frac{i}{\hbar}S[2,1]}\mathcal{D}x$$ satisfies the ...
0
votes
0answers
13 views

Pearson correlation of neural responses with it's linear estimation

I am trying to anderstand the following fact: Suppose I have a linear estimation of a stimulus: $ \hat{s} = \mathbf{w}^T(\mathbf{r} - \mathbf{f}(s_0)) + s_0$ where $\mathbf{w}$ is a vector of ...
0
votes
0answers
36 views

Can anyone suggest any good texts on Green's functions in quantum mechanics?

I am currently learning about Green's functions and want to write an essay on their use in quantum mechanics as part of an assessment. I have seen that they can be used in describing the probability ...
0
votes
0answers
47 views

$i\epsilon$ in CFT correlation functions

M. Luescher in his talk on p.6 writes that the 2-point correlation function of a Hermitian local field $O_k$ of scaling dimension $d=3-k$ looks like $$ \langle 0| O_k(x) O_k(y) |0\rangle = A_k (x-y-i ...
0
votes
0answers
62 views

Interpretation of the density-density correlation function

I'm trying to get a physical interpretation of the density-density function $\mathrm{Cor}(r,r')=<\Psi^\dagger(r)\Psi(r)\Psi^\dagger(r')\Psi(r')>$ For example, when we have a optical lattice ...
1
vote
0answers
20 views

Why are isoprobabilty contours circles for uncorrelated functions and ellipse for correlated functions? Kindly explain.

I would like to know how to understand these and to learn how to go from a scatter plot to the isoprobabity contour plots. Thanks is advance!
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 ...
1
vote
0answers
41 views

Density-Density correlation function - Bose Hubbard in Bogoliubov theory

a Bose-Hubbard-Hamiltonian in the Bogoliubov theory can be written as (http://arxiv.org/pdf/cond-mat/0011108v1.pdf): $H=\sum_k \omega_k b_k^\dagger b_k$ I tried now to calculate the density-density ...
0
votes
0answers
23 views

Wavefunction overlap in graphene

In calculation of the response functions of graphene we need to calculate the 4-point correlation function of the form : $$ \langle T \rho(q,\tau)\rho(-q,0)\rangle $$ The article I'm reading states ...
5
votes
2answers
434 views

Time-ordered operator in Srednicki

On page 51 Srednicki states, "Note that the operators are in time order...we can insert $T$ without changing anything". This I agree with. But then on the next paragraph he states "The time order ...
38
votes
4answers
14k views

Why correlation functions?

While this concept is widely used in physics, it is really puzzling (at least for beginners) that you just have to multiply two functions (or the function by itself) at different values of the ...
0
votes
1answer
42 views

Relation of the cross product of the functions to the cross product of their Fourier spectra

I know that according to the Convolution theorem the Fourier transform of the convolution of two functions $f$ and $g$ is equal to the product of their Fourier spectra: $\mathcal{F}\{f*g\} = ...
1
vote
0answers
40 views

QFT: Limits in Time Ordered Correlation Function Derivation

Background In part of the derivation for the time ordered correlation function I have the following equation (This equation I am fine with - it is what follows that I am not), $$ ...
3
votes
1answer
100 views

What is meant by open-string tachyon scattering amplitude?

It was said here that Veneziano derived: open-string tachyon scattering amplitude from principles of Regge theory and S-matrix theory and used the Euler beta-function to make all the critical ...
1
vote
3answers
67 views

Correlation function $\langle s_1(x, t)s_2(x', t')\rangle$ vs $\langle s_1(x, t)s_2(x', t')\rangle-\langle s_1(x, t)\rangle\langle s_2(x', t')\rangle$

The correlation function in statistical mechanics is defined in either of two ways $$g(\mathbf{x}-\mathbf{x}', t-t') = \left\langle s_1(\mathbf{x}, t)s_2(\mathbf{x}', t') \right\rangle$$ ...
0
votes
1answer
33 views

Meaning of and relationship between pair distribution function/ coherence functions/ correlation function

This is what I understand so far (But I might already be wrong): The pair distribution function (PDF) $g^{(2)}(\textbf{x},\textbf{x}')$ is the probability of finding a particle at x if there is ...
2
votes
0answers
41 views

S-matrix element for forward scattering and amputed green function

I'm studying dispersion relations applied as alternative method to perturbation theory from Weinberg's book (Vol.1) Let's consider the forward scattering in the lab frame of a massless boson of any ...
3
votes
1answer
74 views

Why do the conserved charges in the case of SSB of a global symmetry not exist?

Reading "From Linear SUSY to Constrained Superfields" by Komargodski and Seiberg, I got a bit confused regarding the existence of the conserved charges in a theory with spontaneous symmetry breaking ...
1
vote
0answers
42 views

Generating functional for free and interacting theories [closed]

I'm asking probably a stupid question. We define the generating functional for free theories as $$ Z_0[J] = \int D \psi e^{i\int d^4x \left[ L_0(x) + J_l(x)\psi^l(x) \right]} $$ with $L_0$ the free ...
4
votes
1answer
215 views

Symmetry factor for Feynman diagrams in $\phi^4$-theory for $n$-points Green function

I'm working with two theories. Theory A: $H_{int} =\int d^3x \frac{Mg}{2}\phi\varphi^2$ Theory B: $\phi^4$-interaction: $H_{int} = \int d^3 x \frac{\lambda}{4!}\phi(x)^4$ Where $M$ is the mass ...
1
vote
2answers
154 views

Finite temperature correlation functions in QFT

Suppose that we want to calculate this imaginary time-ordered correlation function for an interacting system (in Heisenberg picture) : $$\langle \mathscr{T} A(\tau_A)B(\tau_B) \rangle =\frac{1}{Z} ...
1
vote
0answers
124 views

Proof of correlation function formula in quantum field theory

I am trying to prove the following formula used in QFT: $$\langle\Omega|T\{\Phi(x_1)\dots\Phi(x_n)\}|\Omega\rangle = \frac{\langle 0|T\{\Phi_I(x_1)\dots\Phi_I(x_n)S\}| 0 \rangle}{\langle 0|S| 0 ...
0
votes
1answer
205 views

Why four-point vertex function in $\phi^3$ theory?

So as I understand it the order of $\phi$ in a scalar Quantum field theory is indicative of the number of lines entering a given vertex. For example for $\phi^3$ this leads to vertices like the one ...
3
votes
2answers
62 views

How to measure transverse current-current correlation at arbitrary wave vector and frequency

Let $\hat J^{\mu}(t,\boldsymbol r) \equiv (c \hat \rho(t,\boldsymbol r), \hat{\boldsymbol J}(t,\boldsymbol r))$ be the density-current operator at spacetime coordinate $(t,\boldsymbol r)$, in the ...
1
vote
0answers
50 views

Difference between the propagators and vertex function [closed]

I am confused between Green's function and vertex function in field theory. Can someone please explain the difference between the two in context ${\lambda} {\phi}^4$ theory?
0
votes
0answers
77 views

Why does correlation length diverge at the critical point?

In thermodynamics, the correlation length diverges near the critical point on the phase diagram, I'd like to understand why this is the case. I've found a few different papers / books, but most only ...
3
votes
0answers
67 views

How should the path integral change under a dilation?

Let's say I have a two-point function of a scalar field in flat space: $$ \langle \phi(x)\phi(y)\rangle = \int \mathcal D \phi \, \phi(x)\phi(y)\,e^{iS[\phi]} $$ Then I dilate things: $$ \langle ...
0
votes
0answers
26 views

Two point correlator : Dispersion Relation

Does anybody has a reference or an advice on how to derive the following idendity? \begin{equation} \Pi(s) = \frac{1}{\pi} \int_0^\infty \frac{Im \Pi(s')}{s' - s} ds' \end{equation} where $\Pi(s)$ is ...
1
vote
0answers
43 views

Solution of Dirichlet problem for scalar field in Ads

I am reading "Anti de Sitter space and holography" by Witten. In this article he derives the two-point function for CFT from theADS/CFT correspondence for a massless scalar field living in the bulk. ...
2
votes
0answers
48 views

Pair correlation function of the QHE “plasma”

I am trying to teach myself the theory of quantum Hall effect, and realized that I can not reproduce a basic textbook result. Let me closely follow Girvin's Les Houches lectures ...
0
votes
0answers
61 views

Spatial correlation function and translation invariant

recently, i was puzzled by the spatial correlation function. in textbooks of statistical physics, they say that if the system is translational invariant, then the spatial correlation function ...
0
votes
0answers
20 views

Symmetry of retarded R-current correlator in $\mathcal{N}=4$ Super Yang-Mills

The retarded correlator of the R-current $J_\mu$ of $\mathcal{N}=4$ Super Yang-Mills theory is $$ C_{\mu\nu}(x-y)=-i\theta(x^0-y^0)\langle[J_\mu(x),J_\nu(y)]\rangle. $$ In this paper in eq. (2.4), I ...
0
votes
1answer
76 views

Two Point Correlator

I have a problem to reproduce the following identity: \begin{equation} \Pi_{\mu\nu}(q^2) = i \int d^Dx e^{iqx} \langle 0 | T \{j_\mu(x) j_\nu(0) \} | 0 \rangle = (q_\mu q_\nu - g_{\mu\nu} q^2 ) ...
1
vote
1answer
31 views

Energy corresponding to the peak of velocity power spectrum

I ran a MD simulation for a number of N molecular hydrogen. I used the velocity time history of system for each atom and subtract the velocity of center of mass of each molecule from the velocity of ...
0
votes
1answer
90 views

What are the 1PI correlations functions?

This question may be a little strange, but I'm currently going through my lecture notes and in the construction of the 1PI effective action there is a constant reference to 1PI correlation functions. ...
0
votes
0answers
36 views

Estimation of the autocorrelation for data on finite size interval

Let's consider we have a continuous random signal ${ t \in ] - \infty \,;\, + \infty [ \mapsto b (t)}$. We assume this signal to be stationary, so that when ensemble-averaged, one may introduce the ...
1
vote
0answers
38 views

What is the relation between scattering amplitudes, fluctuations, response functions and correlations in macroscopic equilibrium systems?

In Kardar's book Statistical Physics of Fields, he mentions that that correlations at different length scales can be measured by scattering. If its electric correlations, you would scatter light and ...
0
votes
1answer
87 views

Why is the correlation of an observable and its derivative zero?

Why is the correlation of an observable and it's derivative zero? And why does this not only hold for $\langle A(t) \dot A(t) \rangle $ but also for $\langle A(0) \dot A(t) \rangle $ ? These averages ...
3
votes
0answers
90 views

Why does decay of correlations imply absence of order?

In a few articles I have read, a two-point correlation function $\langle g(x)g(y) \rangle$ is shown to decay with increasing distance of $x$ and $y$, and this is then taken to imply an absence of the ...