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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 ...
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0answers
99 views

Feynman rules for coupled systems

I have the following system of two coupled real scalar fields $\sigma$ and $\phi$: ...
4
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0answers
82 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 $\Delta \phi=0$ ...
4
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0answers
90 views

Can the correlation for the Potts model be bounded?

I am studying a $d$-state Potts model. A configuration $\sigma$, which assigns for each $x\in \mathbb{Z}^2$ a value $\sigma(x)\in [1,2,\ldots,d]$, with the probability on a finite lattice defined as ...
3
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0answers
66 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 ...
3
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0answers
114 views

Polology in Functional Integration

Completeness of Hilbert space (on-shell states) is a very powerful concept in canonical quantization, for example, to study the nonperturbative characteristics of the S-matrix, like polology (pole and ...
3
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0answers
214 views

Two-point correlation function for Potts Model

Consider the Potts model with three states , $\sigma (x) \in \{ 1, e^{2 \pi i/3}, e^{4 \pi i/3} \}$. I wanted to make sure that the following definition for two-point correlation function is correct: ...
3
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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 ...
3
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0answers
97 views

Where does one find pair-correlation functions for various materials?

What is the canonical source for finding pair-correlation functions for atoms in various materials? I am interested in both numeric computations and experimental measurements (like might be obtained ...
3
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0answers
1k views

How to prove Wick's Theorem (Zee's eq. I.2 (16)) via Gaussian integration?

I'm working through Zee's QFT in a Nutshell but there's an integral [I.2 (16)] I couldn't quite derive. The problem is to find $$\langle x_i x_j ... x_k x_l\rangle=\frac{\int ... \int dx_1 ... dx_n ...
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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 ...
2
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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 ...
2
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0answers
116 views

Autocorrelation function corresponding to density of states with significant rotational motion

Most statistical physics textbooks (at least the ones I've found) state simply that the density of states of a system can be found as the temporal Fourier transform of the velocity autocorrelation ...
2
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0answers
53 views

Non translation invariant correlator in CFT

I'm doing an exercise on vertex operators in the CFT book by Di Francesco & al.; exercise 9.2 p.329 : Using mode expansion show that: $$\langle\tilde{\phi(z)}\tilde{\phi(w)}\rangle= - \text{ln} ...
2
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0answers
110 views

How to calculate the 2-point function of gravitons?

I'm curious about how to calculate the 2-point function of graviton, but there are no textbooks of general relativity covering this problem. So how to calculate it? In which book can I find the ...
2
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0answers
235 views

Constructing Ward identity associated with conserved currents

Consider constructing the Ward identity associated with Lorentz invariance. It is possible to find a 3rd rank tensor $B^{\rho \mu \nu}$ antisymmetric in the first two indices, then the stress-energy ...
2
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0answers
126 views

Is time ordering defined for a single operator depending of two time variables?

The time ordering for the purpose of quantum mechanics is e.g. given by $${\mathcal T} \left[A(x) B(y)\right] := \begin{matrix} A(x) B(y) & \textrm{ if } & x_0 > y_0 \\ \pm B(y)A(x) & ...
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0answers
239 views

How does one derive the 2 halo term in two-point correlation function

This question is in reference to the paper here. In Equation (86) on page 28, the authors have given the two point correlation function \begin{equation*} \xi(\mathbf{x}-\mathbf{x}^{\prime}) = ...
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0answers
32 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 ...
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0answers
39 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 ...
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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 ...
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0answers
12 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. ...
1
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0answers
19 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!
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0answers
39 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 ...
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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), $$ ...
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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 ...
1
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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. ...
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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 ...
1
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0answers
19 views

Are correlators constructed out of Wilson loops singular in pure Yang-Mills?

If I have some gauge invariant function of two Wilson loops (such as $\left<\text{Tr}W_1 \text{Tr}W_2\right>$) does the expectation value diverge when the loops coincide the same way ...
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0answers
70 views

Correlation time (non linear) in ising model (3D)

I am currently implementing the classical Ising model (3D) for a demonstration. I use the common implementation of metropolis,teller,teller ("Metropolis"-algorithm) and measure certain quantities. ...
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0answers
61 views

Physical meaning behind causal massless scalar propogator

I know that for a scalar massless field in $(3+1)$ spacetime that: $$ \langle 0 | \phi(x) \phi(y) | 0 \rangle \propto |x-y|^{-2} = (-(t_x-t_y)^2 + (\vec{x}-\vec{y})^2)^{-1}. $$ I also know that $$ ...
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0answers
44 views

Non Zero correlation function (for large separations) in one particle state?

So i computed the following equal time correlation function for a one particle state. The vacuum correlations give the function $$\langle \phi(\vec x)\phi(\vec y)\rangle_0=D(\vec x-\vec y)\\ ...
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0answers
120 views

Derivation of Higher-order correlation functions from definition

I'm trying to understand the definition of the n-th order correlation function. My aim is to translate the math into a numerical implementation in order to compute the correlation function $g^{(n)}$ ...
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0answers
203 views

Equal time displacement correlation functions and their physical interpretation?

Displacement correlation functions in question are within harmonic approximation and are derived for example in: A. Maradudin, Dynamical properties of solids 1, 1 (1974). Maradudin says about the ...
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0answers
11 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?
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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 ...
0
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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 ...
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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 ...
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0answers
46 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
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0answers
60 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 ...
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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 ...
0
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0answers
22 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 ...
0
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0answers
73 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 ...
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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 ...
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0answers
59 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 ...
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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 ...
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0answers
35 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 ...
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0answers
25 views

Correlation Function of Langevin Equation

Suppose $\phi(x,t)$ is a function whose dynamics are governed by a Langevin equation. We may Fourier transform to obtain a Langevin equation for $\phi(q,t)$. Is it true in general that $ \langle ...
0
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0answers
64 views

Measuring typical distance between patches using 2D Fourier Transform

I need to extract information about the typical distance between the black patches in an image like the one I attached here. I tried to perform 2D FFT on it (using OpenCF fdt function in Python), but ...
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0answers
51 views

pair correlation function for heterogeneous nuclei

I have a system with heterogeneous size of nuclei of two liquids within a mixed fluid phase of those two liquids. I was wondering what would be the interpretation of pair correlation function for a ...