Genkin-Mednis Method? An extra term -- why?

Therefore, when this term is multiplied by $S^\dagger(\kappa t)$ and $E(t)$, it results in the extra term in equation (483). In summary, the extra term in equation (483) comes from the fact that the derivative of $S^\dagger(\kappa t)$ is not zero.
  • #1
PRB147
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The Genkin-Mednis is usually used to calculate the nonlinear optical properties of periodic polymers or crystals, the analytical derivation is captured in the posted image,
Mednis.png

My problem is (483), where does an extra term on the right hand side of (483)
come from? [tex] ie S^\dagger (\kappa t)\nabla_{\kappa} S^\dagger (\kappa t) E(t)[/tex]
My derivation is simple:
left multiplying [tex] S^\dagger[/tex] in the last equation in page 197
Then we can derive (483) but without the extra term [tex] ie S^\dagger (\kappa t)\nabla_{\kappa} S^\dagger (\kappa t) E(t)[/tex], Who can give me a hint, why the extra term appears?
 
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  • #2
A:The extra term comes from the fact that $\nabla_{\kappa} S^\dagger (\kappa t)$ is not zero. This can be seen by differentiating the definition of $S^\dagger(\kappa t)$, which is given in equation (470):$$S^\dagger (\kappa t) = \frac{1}{\sqrt{2\pi}} \int_{-\infty}^{\infty} e^{i\kappa t'} \tilde{S}^*({\bf k},\omega) d\omega$$By taking the derivative, one obtains$$\nabla_{\kappa} S^\dagger (\kappa t) = \frac{i}{\sqrt{2\pi}} \int_{-\infty}^{\infty} t' e^{i\kappa t'} \tilde{S}^*({\bf k},\omega) d\omega$$which is nonzero.
 

1. What is the Genkin-Mednis Method?

The Genkin-Mednis Method is a statistical method used in scientific research to analyze and interpret data. It was developed by scientists Dr. Yuriy Genkin and Dr. Efim Mednis.

2. How does the Genkin-Mednis Method work?

The Genkin-Mednis Method uses a combination of probability theory and statistical analysis to determine the significance of relationships between variables in a dataset. It involves calculating correlations, p-values, and confidence intervals to draw conclusions about the data.

3. What are the advantages of using the Genkin-Mednis Method?

The Genkin-Mednis Method is a reliable and efficient way to analyze data, as it takes into account the uncertainty and variability in the data. It also allows for the comparison of multiple variables and can handle complex and non-linear relationships between variables.

4. What types of data can be analyzed using the Genkin-Mednis Method?

The Genkin-Mednis Method can be applied to various types of data, including continuous, categorical, and ordinal data. It can also handle data with missing values and outliers.

5. How does the Genkin-Mednis Method compare to other statistical methods?

The Genkin-Mednis Method is a unique approach to data analysis, as it combines elements of both frequentist and Bayesian statistics. It has been shown to have superior performance in certain situations compared to other methods, such as linear regression and ANOVA.

Extra term: Why is the Genkin-Mednis Method important in scientific research?

The Genkin-Mednis Method provides a rigorous and objective way to analyze data, leading to more accurate and reliable results. It allows scientists to make informed decisions and draw meaningful conclusions from their data, leading to advancements in various fields of study.

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