Questions tagged [correlation-functions]

A correlation function is a statistical correlation between random variables at two different points in space, time, or other parameter space, usually as a function of the variable distance between these points. In QFT, field autocorrelation functions are propagators, so use the "propagator" tag, instead.

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Hartree-Fock factorization

I am studying c-field methods applied to Bose-Einstein condensates to understand how one gets to e.g. the dissipative GPE. To do so, one splits the field operator for the Bose gas into a low- and a ...
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Time dependence of Drude-like correlation function obtained from Matsubara formalism

I'm trying to calculate the real time dependence of the correlation function that I've obtained in my effective model (it is closely related to the electron density correlation function), given in ...
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Computing correlation function $\langle e^{i\beta \phi(x)}e^{-i\beta\phi(0)}\rangle$ for massless scalar field $\phi$

I am currently reading Shankar's "Bosonization: How to make it work for you in condensed matter" (http://inspirehep.net/record/408901/). In page 9, I am stuck with computing the correlation function ...
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Correlation function from Laplace transform of distribution function?

I have a time-dependent random process $x(t)$ which takes on two values $\Delta_1$ and $\Delta_2$. I know the Laplace transforms of the (time-dependent) probabilities $\hat{p}_{ij}(s)$ of these values ...
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Signal coherence/correlation vs quantum coherence

In general, I understand a signal $s(t) \in \mathbb{C}$ is called "coherent" when it has a large autocorrelation function. A pair of different signals $s(t)$, $r(t)$ can also be "coherent" if their ...
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Do Bell’s inequalities assume particles can only have one variable to consider?

I have asked the question “How do you know when pairs are entangled?” I have asked “What is the difference between entangled and correlated?” I have also asked several similar questions, but I keep ...
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How to deduce the formula of the Correlation Length on a periodic lattice?

Sometimes in Monte Carlo simulations we need to compute the correlation length, but this is a hard task without a formula. However, for instance, in an periodic cubic lattice of $L^3$ spins, some ...
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Scattering amplitudes vs correlators

What are the practical differences between correlators and scattering amplitudes in quantum field theory? On a very practical level: scattering amplitudes describe the evolution of an IN state into ...
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A question in imaginary time Green's function

I am learning many-body quantum field theory with Bruus and Flensberg's Introduction to Many-body Quantum Theory in Condensed Matter Physics, there is a derivation that confuses me a lot. To add ...
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Veneziano amplitude from 3-point constants

Consider an open bosonic string in the critical dimension at $g_s = 0$ (only the sphere contributes to the string amplitude). The scattering of 4 tachyons is given by the Veneziano amplitude. I'm ...
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Systematic way of calculating 3-point worldsheet amplitudes

I'm looking for a systematic way of deriving the 3-point functions $\left< V_1(z_1, \bar{z}_1) V_2(z_2, \bar{z}_2)V_3(z_3, \bar{z}_3)\right>$ of the worldsheet CFT of a closed bosonic string. ...
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Vanishing correlation function

Mirror Symmetry p. 206, Eq. 10.192. I have an operator $\mathcal{O}$ that commutes with my supercharge $\overline{Q}_+$, $\left[\overline{Q}_+, \mathcal{O} \right]=0$. Why does the correlation ...
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Relation between standard and Kubo-transformed quantum correlations

Via path integral molecular dynamics it is possible to measure the Kubo transformed correlation function between two operators $\hat A$ and $\hat B$ \begin{equation*} K_{\hat A\hat B} = \frac 1 {Z_\...
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How do I fit a resonance curve?

In an experiment, I collected data points $(ω,υ(ω))$ that are modeled by the equation: $$υ(ω)=\frac{ωC}{\sqrt{(ω^2-ω_0^2)^2+γ^2ω^2}} \,.$$ How can do I fit the data to the above correlation? And ...
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Linear response treatment of the magnetization of a system of noninteracting fermions

While trying to solve an exercise, I ran into what looks like a contradiction. I'm sure I'm making some kind of mistake, but I couldn't spot it. I'm not asking for help in solving the exercise, which ...
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Error in histogram measurements

I ran into the following statement here and here but I believe it's more general. Let's suppose we're running a simulation of a system and we are interested in the distribution of a quantity (say $M$...
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Assumptions behind Ornstein-Zernike correlation function

Let $S(\mathbf q)$ be come correlation function in Fourier space ($\mathbf q$ = wavevector). In the study of condensed matter systems, I have often encountered the statements that a reasonable form ...
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Four point function with complex momenta?

It is well known that the four-point function $$\int_{\mathbb{R}^{3,1}}\frac {d^4 q}{((q+p_1)^2-i\epsilon)((q+p_2)^2-i\epsilon)((q+p_3)^2-i\epsilon)((q+p_4)^2-i\epsilon)}$$ can be computed using the ...
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