Correlation Definition and 370 Threads

Green functions are defined in mathematics as solutions of inhomogeneous differential equations with a dirac delta as the right hand side and are used for solving such equations with a generic right hand side. But in QFT, n-point correlation functions are also called Green functions. Why is...

Wick's theorem allows one to write a free theory time-ordered ##n##-point correlation function as a product of free theory time-ordered ##2##-point correlation function. The procedure involves the pairwise Wick contraction of fields such that external fields are not paired up each...

Consider the following time-ordered correlation function: $$\langle 0 | T \{ \phi(x_{1}) \phi(x_{2}) \phi(x) \partial^{\mu}\phi(x) \partial_{\mu}\phi(x) \phi(y) \partial^{\nu}\phi(y) \partial_{\nu}\phi(y) \} | 0 \rangle.$$ The derivatives can be taken out the correlation function to give...

I thought I understood the concept of a correlation function, but I having some doubts. What exactly does a correlation function quantify and furthermore, what is a correlation length. As far as I understand, a correlation between two variables ##X## and ##Y## quantifies how much the two...

The ##1##-point correlation function in any theory, free or interacting, can be made to vanish by a suitable rescaling of the field ##\phi##. I would like to understand this statement. With the above goal in mind, consider the following theory: $$\mathcal{L} =...

Given the theory $$\mathcal{L}=\frac{1}{2}(\partial_{\mu}\phi)^{2}-\frac{1}{2}m_{\phi}^{2}\phi^{2}+\partial_{\mu}\chi^{*}\partial^{\mu}\chi-m_{\chi}^{2}\chi^{*}\chi+\mathcal{L}_{\text{int}},\qquad \mathcal{L}_{\text{int}}=-g\phi\chi^{*}\chi,$$ the time-correlation function ##\langle \Omega |...

I'm reposting this piece of logic because my earlier attempts to get it across failed - nobody got what I was saying. This is about binary sequences like ##010110100111001001...##. All we need to know about a particular sequence is its length, ##N## and the number of 1's it contains. The logic...

What is the relation between the correlators ##\langle 0 | T\phi(x_{1})\phi(x_{2}) | 0 \rangle## and ##\langle 0 | T\phi(p)\phi(x=0) | 0 \rangle##? I can derive the momentum space Feynman rules for ##\langle 0 | T\phi(x_{1})\phi(x_{2}) | 0 \rangle##. Are the momentum space Feynman rules for...

First let me ask this: Consider a pair of entangled photons fired at a respective detector after passing respective polarisation filters. If a photon passes a polarisation filter, is it in a superposition of having passed and not having passed? Is the measuring device (that detects the...

Consider the 2-point correlator of a real scalar field ##\hat{\phi}(t,\mathbf{x})##, $$\langle\hat{\phi}(t,\mathbf{x})\hat{\phi}(t,\mathbf{y})\rangle$$ How does one interpret this quantity physically? Is it quantifying the probability amplitude for a particle to be created at space-time point...

Suppose we have a source of polarization-entangled photons, that fires pairs of photons in opposite directions at two detectors with orientation-adjustable polarizationfilters in front of them. Obviously, there is a correlation between the orientation of the respective filters and the joint...

I am trying to better understand the concept of second order coherence G2(τ) (in particular G2(0)) and a few questions have arisen. Note that I am trying to get a physical idea of what is happening so I would appreciate it if your responses can keep the math to the minimum possible. :) How do...

If we assume there is no counterfactual definiteness, would that mean that measurements on entangled particles needn't be correlated, for if you don't compare the results, you just don't know if they do?

Hello I have a set of data points, with errors (X1 , Y1 +- deltaY1) , (X2 , Y2 +-deltaY2) etc I have the covariance matrix for these bins I want to integrate this set of data points: SUM_i ( Y_i * X_binWidth_i ) How do I combine the errors, taking into consideretation the...

I have a question that seems to reflect my main concern with QM. Here it is: Consider a series of polarisation-entangled photon pairs that are sent in opposite direction to two measuring devices (e.g. at opposite ends of the universe). The measurement consists of detection of a photon after...

If I'm correct, a series of with respect to some property entangled particles exhibits a correlation between several measurements of that property by means of two measuring devices. My question is: is it possible that between measurements the physical constitutions of the measuring devices...

Just taking an advance in what I want to learn someday: I understand that decoherence and entanglement are more or less equivalent. So, I take it decoherence is in principle a process of entanglement. Consider two particles A and B who are entangled. if A decoheres by interacting with particle...

I was wondering. In this example I use polarized photons, but maybe it is applicable to electrons and spin also. We can prepare two completely unentangled polarized photons, and send them in opposite directions to two detectors preceded by a filter at particular angles. Both of them will show a...

I just need a little assistance on the last two questions. I place per capita and death in L1 and L2 but I am lost. Country Per Capita Cigarette Consumption 3900...

do the presence of macronutrients (N,P,K) increase the amount of radionuclides (U,Th,K) in the sediments. how are they related?

This has come up in a number of threads, so I made this thread to talk about it. I think that an interpretation of this in the Schrödinger picture should be possible at least in the style of Feynman. This would go something like this. ##\begin{eqnarray*} \langle A(s)A(t)\rangle_\psi &=&...

I've been looking at detector coincidences and tried to find what general limits apply to coincidences. I was surprised how simply the calculation works out. My question is whether it is correct and where can I find similar stuff ? Consider two binary sequences produced by random processes...

I have been reading about the physical meaning of exchange-correlation hole and this is what I have found so far: Exchange hole - attributed to the spin of the electrons. Electrons of same spin will not occupy the same orbital because of Pauli Exclusion Principle. This leads to the lowering of...

Hello guys, I am investing the effect of three parameters on a process and I need to come up with a correlation connecting these three correlations together. I have the experimental results for f(x,0,0), f(x,y,0) and f(x,y,z). I tried to do 3d interpolation with Matlab but since the change is...

Hi, I made some measurements in a vehicle and I have one output signal (i.e. force in a vehicle component) and many input signals which few are digital (discrete only 2 values are possible) and others are anolog (continuous variables).Here you can see the output signal and two of the many...

Hello I have to variables X and Y, 50,000 in each row (a time series of 2 years). I am curious how to calculate a linear correlation between the two, for example if X decreases does Y increase or decrease. Looking for formula or a MATLAB function :)

Hi all, On a vehicle I recorded an output signal that is positive and it's variability is lead to the 30 input signals, but not all together at the same insant. Just by checking the pairwise correlation between signals in a time periond, I'm able to detect which input signals lead to the...

[Mentor's note: Split off from https://www.physicsforums.com/threads/an-abstract-long-distance-correlation-experiment.852684/page-6 because this subthread was discussing possible mechanisms behind the phenomenon] My take on these: 1) - not weird at all - you send a photon in one direction...

Inspired by stevendaryl's description of an EPR-like setting that doesn't refer to a particle concept, I want to discuss in this thread a generalized form of his setting that features a class of long-distance correlation experiments but abstracts from all distracting elements of reality and from...

Everywhere I ready about HF or DFT the term exchange correlation functional comes up. I have a couple of fundamental questions about these: 1) Books say that the correlation energy is the difference between the exact energy (lets say we've found that somehow) and the hartree-fock energy and...

Hello everyone, I'm stuck at a elementary stochastic problem. I have to calculate means, variance and co-variance for two random variables. Homework Statement Let r,g,b∈ℕ. r red, g green and b black balls are placed in an urn. The balls are then drawn one at a time with replacement, until a...

Homework Statement I have been tasked with showing "how the mechanical energy of a planet determines the shape of its orbit", and I cannot for the life of me make sense of it. I've run into a formula, see below, but I'm not sure how to interpret it nor if it even applies in my case at all (as E...

Not sure if that's the technical name, but I refer the the number Excel give you between 0 and 1 when you use the "correl" command on two sets of numbers.

Homework Statement So I have two 1/2 spin systems A and B in a singlet state |\psi > = \frac{1}{\sqrt{2}} ( |+-> - |-+> ) . The question is: If I measured B and got S_{Bz} = 1/2 . What will I measure on state A on z axis? Homework EquationsThe Attempt at a Solution The answer I think is...

I am early in my career and trying to pursue a career in software engineering (I use that term broadly). Like any normal person, I eventually want to make good money, hopefully around 6 figures. I assumed that there would be a direct correlation between how sophisticated a software job is and...

As I understand it, the 2-point fnuction is for 1 particle incoming, 1 particle outgoing. The 4-point function is for 2 particles incoming, 2 particles outgoing. Is this correct? So an N-point function describes N/2 incoming particles and N/2 outgoing particles? Thanks!

Hi everyone, I've encountered a curious problem I just can't figure out, and any input would be much appriciated!This is a personal project I'm working on, and as far as I know, there is no one else working on exactly the same. However, the computational study of critical phenomena is quite...

I want to calculate the correlation length of a rough surface from the intensity profile of diffuse and specular reflectance from that rough surface. By fitting with the Gaussian curve, I calculated FWHM of the intensity profile.Generally it is considered thatcorrelation length = 2/FWHMI also...

Hi, it is known that second order correlation function (g2) is a constant( =1) for ideal laser or single frequency light sources. So, what is the second order correlation function for non ideal laser? Is it still a constant or something related to the coherence time of the laser?

How do you prove that the maximum value of 2*cov(x,y) can be is equal to var(x) + var(y). Moreover, how do you prove that the correlation coefficient, cov(x,y)/(sigma(x)*sigma(y), can only be between -1 and 1.

My main difficulty is finding E(XY), where if we find it by integrating, we get ∫xy f(x,y) dy dx where f(x,y) is the bivariate normal density function. This integral is a nightmare... are there any tricks to evaluating this integral, or finding E(XY) for that matter?

Hello, How can I calculate a triple correlation between 3 signals A,B,C (each has 2 million samples)? I know xcorr do it for 2 signals by FFT each signal, multiplication and iFFT back. Since xcorr cannot do it for three signals, I try to do it "manually" by the above algorithm. So, the "regular"...

Hi guys, i have been confused by one statement on the spatial correlation funciton in the statistical physics textbook. They say for a spatial correlation function f(x1,x2), where x1 and x2 are the coordinate of particle 1 and 2, if the system has translational symmetry, then f depends only...

how can I interpret the condition "if sum of (xi-x_bar)^2(yj-y_bar)^2=0 when i=/=j?" why does this make the line linear?

I have two signals (time series) shown in the plot below. Just by looking at the figure, we can see that the two main peaks of both signals are very closely aligned (correlated), however the red signal has additional features elsewhere which don't match the blue curve. I am looking for some...

Calculate the discrete period cross correlation function for the pair of m-sequences given by - G1(D) = 1 + D2 + D5 and G2(D) = 1 + D2 + D3 - D4+ D5 I started by drawing the shift register diagrams and calculating each state, but that is a long process and I don't know how would i show the...

I'm looking for experimental correlation curves in Violation of Bell inequalities. I found only one in http://arxiv.org/abs/quant-ph/9806043 Do you think as an amateur we could ask per mail this data to professionals having done this experiment ?

Hi all. I'm learning something about critical phenomena and I have one problem. I'm bad with Fourier transforms so I don't know how from 7.37 we have 7.38. I have tryed everything I knew, but fruitless. I have attached picture of my problem. Does anybody has any idea how I can solve this?

Suppose X and Y have the same distribution, and Corr(X,Y) = -0.5. Find V[X+Y]. I know that Corr(X,Y)*SD[X]SD[Y] = Cov(X,Y) and also V[X+Y] = V[X] + V[Y] + 2Cov(X,Y) So there must be a missing link, maybe an identity, that I'm not realizing. I think the fact that the 2 variables have the same...

We know that in the Fourier transform formula ,there are mainly two terms function f(t) and complex exponential term ( function). But I am confused that what should i call Fourier transform formula as a correlation or convolution formula? So can anybody help regarding it?