# 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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### Non-zero Euclidean commutator in 2D CFT?

In a Euclidean QFT, commutators of operators vanish for any spacetime separation. This can be argued very simply by using the path integral representation of the correlator, wherein operators become ...
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### Validity of Linear Response Theory

Suppose the perturbation of the hamiltonian is some multiple of the free hamiltonian, that is $$H=H_0+H_1=H_0+\lambda H_0=(1+\lambda)H_0.$$ Here, certain operators apparently have no response due to ...
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### Trace class of the position autocorrelation function

Let us consider a quantum system of $N$ distinguishable particles, and let us tag the configuration $\hat q_j$ of one of those. I am interested in checking whether the position auto-correlation ...
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### Why traditional turbulence theory concerns so much about statistics such as correlations?

I have been wondering why the traditional turbulence theory, e.g., Kolmogorov's 1941 theory, concerns so much about things like two-point correlations, structure functions, their scalings, and so ...
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### Fourier Transform of Density Operator boosting momentum

I am currently reading Girvin and Yang's book on Condensed Matter Physics. I am reading up on the dynamical structure factor and in Section 4.3 where they talk about how $\rho_{+q}$, which is defined ...
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### Change sign for response function

There is a argument about response function: according to the Kramers-Kronig relation$$G(\omega)=\int_{-\infty}^{+\infty}d\omega' \frac{A(\omega')}{\omega+i0_+-\omega'}$$ response function will change ...
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### Will an entangled system give different measurement then just correlation? [duplicate]

I have read this question: Correlation vs. entanglement for composite quantum system Entangled states can produce nonclassical correlations, but this is not necessarily the case. So far so good. ...
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### Analytical Continuation of Correlated function

The real time linear response function is given by Kubo's formula $$\chi_{AB}(t-t')=-i\Theta(t-t')\langle [A,B]\rangle.$$ This can also be obtained by analytically continuing the imaginary time ...
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### How many-body density $n(\vec{r},t)$ can be viewed as a kind of correlation function?

I am reading Martin's book: interacting electrons. In chapter five about the definition of the correlation function, some points about density as correlation function confused me. The author adopted ...
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### Maximally uncorrelated observables as a consequence of unbiasedness relation

In the case of a fully correlated scenario of $A$ and $B$, which are descirbed in mutually unbiased bases, why do the other observables have to be maximally uncorrelated. How does this follow from the ...
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### Question about the Dyson-Schwinger equation for 4-point function of the SYK model

In studying the SYK model, I have no idea how to get the kernel $K(t_a,t_b,t_3,t_4)$ and $\Gamma_0(t_1,t_2,t_3,t_4)$ and also ladder diagrams in the Dyson-Schwinger equation for 4 point function of ...
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### Doubt about the derivation of the Callan-Symanzik equation

I was reading about the Callan Symanzik equation from Peskin and Schroeder. On page 411, they assume that since $G^{(n)}$, the connected Green's function is renormalized, the $\beta$ and $\gamma$ ...
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### Calculation of pafaffian matrix form from spin-spin correlation function in free fermions theory

I want to calculate the following correlation functions \begin{equation} \langle\sigma^{x}_{\ell}\sigma^{x}_{m} \rangle=\langle B_{\ell}A_{\ell+1}B_{\ell+1}\ldots A_{m-1}B_{m-1}A_{m}\rangle \end{...
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### Eigenfunctionals and their application in physics

Is there any sensible meaning of the term eigenfunctionals? The object I want to describe is a solution to the following equation $${\mathscr D}_x F[g] = f(x) F[g]$$ where ${\mathscr D}_x$ is an ...
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### Structure factor and pair distribution function relation in 2D

I am trying to drive the integral form relation between pair distribution function and structure factor in 2 dimensions. In 3D we get: Where What would be the answer for $g(r)$ in 2D, my answer is:...
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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 ...