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xylai
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In one paper (PRL 89, 144101 (2002)),
[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!
[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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