The correlation-function tag has no wiki summary.
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Can one compute the vibrational spectrum of a bond by the Fourier transform of the dipole moment vector autocorrelation function $C_{\mu\mu}(t)$?
Is it true that one can calculate the vibrational spectrum of a bond by the Fourier transform of the dipole moment vector autocorrelation function $C_{\mu \mu}(t)$?
For example, suppose that I have ...
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2answers
113 views
$\langle B|A \rangle$ expressed in terms of the Partition Function
Say you have an electron departing from point A and reaching poing B after a time t.
According to some helping friend, the Partition Function for that electron going from point A to B can be written ...
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0answers
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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 ...
4
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2answers
77 views
Mean of a measurement on periodic data: what is the use of the inverse of correlation length?
Correlation and autocorrelation is something that in my Bachelor's programme in physics has been somewhat overlooked, so I'm in trouble understanding their use in this paper (The prisoner’s dilemma on ...
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2answers
392 views
What does the sum of two qubits tell about their correlations?
How much can I learn about correlations between two quits by measuring
the sum of their values? What is the best way to formalize such a
question?
Below is my original, longer formulation of ...
5
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1answer
69 views
Significance of Poles of Correlation Function in QFT
In QFT, specifically in scattering processes, what is the physical significance of the poles / residues of the $N$-point correlation function? And why?
2
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2answers
250 views
Correlation functions in thermal field theory etc
Suppose I am studying a field theory at finite temperature or some black hole formation scenario from boundary theory perspective in the sense of AdS/CFT. How is it possible to gain information about ...
2
votes
1answer
110 views
Product of VEVs vs. VEV of product
How can we prove the following cluster decomposition formula
$$\langle \phi_1 \phi_2 \rangle ~=~ \langle \phi_1 \rangle \langle \phi_2 \rangle,$$
where brackets denote vacuum expectation value (VEV) ...
3
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1answer
82 views
Use and understanding of higher-order correlation functions
The correlation function g1 is pretty easy to understand and the relation to young's double slit experiment is also clear to me.
In every quantum optics book I read so far correlation functions ...
5
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2answers
217 views
Can scattering amplitudes be simplified with 1PI diagrams?
I have been teaching myself quantum field theory, and need a little help connecting different pieces together. Specifically, I'm rather unsure how to tie in renormalization, functional methods, and ...
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0answers
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Contact Term and Schwinger Term
In field theory, when 4-divergences of time-ordered Green's functions are computed, there are extra terms known as 'Schwinger terms'.
When deriving the quantum equations of motion for time-ordered ...
2
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1answer
70 views
Eigenvalues of a mean correlation matrix (integral over correlation matrices with arbitrary density)
Consider a stationary dynamic system with state $s(t)$ and correlation structure described by $C_{ij}(\tau)=\mathbb{E}[(s_i(t+\tau)-\bar{s_i})(s_j(t)-\bar{s_j})]$. Given an arbitrary density function ...
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2answers
157 views
Correlation, Time Ordering, and Observables
In general, the product of two Hermitian operators $\phi$ will not be Hermitian, unless the two operators commute.
Question: is $X = T \phi(t_1) \phi(t_2)$ Hermitian? It doesn't seem to be if
$T ...
13
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2answers
64 views
Calculating correlation functions of exponentials of fields
In their book Condensed Matter Field Theory, Altland and Simons often use the following formula for calculating thermal expectation values of exponentials of a real field $\theta$:
$$ \langle ...
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0answers
83 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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1answer
86 views
Hamilton operator in absence of causal order?
I hope, this question isn't too broad or vague.
In a recent paper, Ognyan Oreshkov et al. worked out a theory of quantum correlations in absence of any causal order, dropping the assumptions of a ...
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1answer
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Differentiating Propagator, Greens function, Correlation function, etc
For the following quantities respectively, could someone write down the common definitions, their meaning, the field of study in which one would typically find these under their actual name, and most ...
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vote
1answer
111 views
Why can we not reduce the size of a system below the correlation length without qualitatively changing its properties?
This question is posed in the context of thermodynamics/statistical mechanics. Suppose we define the correlation length as the $\xi$ in the exponential factor $e^{-r/\xi}$ that appears in the ...
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2answers
182 views
How do I define time-ordering for Wightman functions?
This is a follow-up question to What are Wightman fields/functions
Ok, so based on my reading, the field operators of a theory are understood to be operator-valued distributions, that is, to be ...
4
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1answer
203 views
What are Wightman fields/functions
Simple question: What are Wightman fields? What are Wightman functions?
What are their uses? For example can I use them in operator product expansions? How about in scattering theory?
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1answer
369 views
Correlation function which has branch cut in momentum space
When correlation function has branch cut in momentum space,
how to find correlation in coordinate space?
For example
$$ \tilde {G}(\omega) = \frac{2i}{\omega+(\omega^2-\nu^2)^{1/2}}$$
How to get the ...
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0answers
358 views
How to prove Wick's Theorem (Zee's eq. I.2 (16)) via Gaussian integration?
I'm working through Zee's QFT in a Nutshell but there's an integral [I.2 (16)] I couldn't quite derive.
The problem is to find
$$\langle x_i x_j ... x_k x_l\rangle=\frac{\int ... \int dx_1 ... dx_n ...
3
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1answer
164 views
What is the time correlation function in the Green-Kubo formulation of ionic current?
I am reading a paper, and I came across the Green-Kubo formulation, where the conductivity $\sigma$ of charged particles is related to the time correlation function of the $z$-component of the ...
4
votes
1answer
222 views
Have the correlation functions of the XY spin chain model been calculated using a functional partition function with source terms?
Have the correlation functions of the XY spin chain model,
\begin{equation}
H=-\sum_l (J_x \sigma_l^x \sigma_{l+1}^x+J_x \sigma_l^y \sigma_{l+1}^y)-B\sum_l \sigma_l^z
\end{equation}
been calculated ...
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1answer
594 views
Autocorrelation Functions <---> Pair Correlation Functions
Are there any ways to convert an autocorrelation function to a pair correlation function, and vice versa?
4
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1answer
276 views
How would Kohn-Sham orbitals differ from 'true' elecron wavefunctions?
How would the non-interacting electron orbitals from a perfect DFT solution for a given potential shape differ from the 'true' electron wavefunctions? Or can you only really talk about the total ...
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2answers
210 views
Correlation Functions, Symmetries and Measurements
Is there a book that goes deep into correlation functions? What I'm interested in a book/article that explains in the detail the relation of the correlation functions with symmetries and how one can ...
13
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3answers
3k 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 ...
