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add note about sub-processes

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Valentin Boettcher 2022-09-28 14:07:23 +02:00
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src/flow.tex
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@ -688,7 +688,16 @@ dynamics.
% 0 & τ \neq 0, % 0 & τ \neq 0,
% \end{cases} % \end{cases}
% \end{equation} % \end{equation}
% so that we end up with a process that is some approximation of white noise. % so that we end up with a process that is some approximation of white
% noise.
If one wants to obtain information about \emph{part} of the bath
\cref{eq:with_process} could become useful. The bath could be
decomposed into several sub-baths by virtue of expressing the spectral
density as a sum of functions with disjoint support, leading to
multiple stochastic processes which would add up to the original
process. In this way the hierarchy structure could remain unaltered,
while \cref{eq:with_process} could be evaluated for the sub-processes.
Also, this alternative method could be used as a convergence and Also, this alternative method could be used as a convergence and
consistency check, as expressions of the form~\cref{eq:with_process} consistency check, as expressions of the form~\cref{eq:with_process}
involve the hierarchy cutoff and the exponential expansion of the BCF involve the hierarchy cutoff and the exponential expansion of the BCF