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• W2000447247 abstract "Non-Markovian processes can often be turned Markovian by enlarging the set of variables. Here we show, by an explicit construction, how this can be done for the dynamics of a Brownian particle obeying the generalized Langevin equation. Given an arbitrary bath spectral density $J_{0}$J0⁠, we introduce an orthogonal transformation of the bath variables into effective modes, leading stepwise to a semi-infinite chain with nearest-neighbor interactions. The transformation is uniquely determined by $J_{0}$J0 and defines a sequence $lbrace J_{n}rbrace _{nin mathbb {N}}${Jn}n∈N of residual spectral densities describing the interaction of the terminal chain mode, at each step, with the remaining bath. We derive a simple one-term recurrence relation for this sequence and show that its limit is the quasi-Ohmic expression provided by the Rubin model of dissipation. Numerical calculations show that, irrespective of the details of $J_{0}$J0⁠, convergence is fast enough to be useful in practice for an effective Ohmic reduction of the dissipative dynamics." @default.
• W2000447247 created "2016-06-24" @default.
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• W2000447247 date "2011-01-07" @default.
• W2000447247 modified "2023-10-14" @default.
• W2000447247 title "Communication: Universal Markovian reduction of Brownian particle dynamics" @default.
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• W2000447247 doi "https://doi.org/10.1063/1.3532408" @default.
• W2000447247 hasPubMedId "https://pubmed.ncbi.nlm.nih.gov/21218988" @default.
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