In one paper (PRL 89, 144101 (2002)),(adsbygoogle = window.adsbygoogle || []).push({});

[tex]k=<Tr\sigma>_{p.v.}[/tex], (1)

where p.v. stipulates a principal-value evaluation and

[tex]<f>=^{def}lim_{t\rightarrow\infty}t^{-1}\int_{0}^{t}f(\bar{t})d\bar{t}[/tex].

[tex]\sigma_{n+1}=(\sigma_{n}^{-1}+T)^{-1}-\nabla\nabla f(q_{n+1})[/tex], (2)

then the author deduces the following equation:

[tex]k=lim_{N\rightarrow\infty}\sum_{n=0}^{N-1}ln|det(1+\sigma_{n}T)|[/tex] (3).

Can you show me how to deduce the equation (3)?

Thank you!

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# What is principal value integral?

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