A reduced dynamics representation is introduced which is tailored to a hierarchical, Mori-chain type representation of a bath of harmonic oscillators which are linearly coupled to a subsystem. We consider a spin-boson system where a single effective mode is constructed so as to absorb all system-environment interactions, while the residual bath modes are coupled bilinearly to the primary mode and among each other. Using a cumulant expansion of the memory kernel, correlation functions for the primary mode are obtained, which can be suitably approximated by truncated chains representing the primary-residual mode interactions. A series of reduced-dimensional bath correlation functions is thus obtained, which can be expressed as Fourier-Laplace transforms of spectral densities that are given in truncated continued-fraction form. For a master equation which is second order in the system-bath coupling, the memory kernel is re-expressed in terms of local-in-time equations involving auxiliary densities and auxiliary operators.

Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation / I. Burghardt, R. Martinazzo, K.H. Hughes. - In: THE JOURNAL OF CHEMICAL PHYSICS. - ISSN 0021-9606. - 137:14(2012 Oct), pp. 144107.144107-1-144107.144107-18. [10.1063/1.4752078]

Non-Markovian reduced dynamics based upon a hierarchical effective-mode representation

R. Martinazzo
Secondo
;
2012

Abstract

A reduced dynamics representation is introduced which is tailored to a hierarchical, Mori-chain type representation of a bath of harmonic oscillators which are linearly coupled to a subsystem. We consider a spin-boson system where a single effective mode is constructed so as to absorb all system-environment interactions, while the residual bath modes are coupled bilinearly to the primary mode and among each other. Using a cumulant expansion of the memory kernel, correlation functions for the primary mode are obtained, which can be suitably approximated by truncated chains representing the primary-residual mode interactions. A series of reduced-dimensional bath correlation functions is thus obtained, which can be expressed as Fourier-Laplace transforms of spectral densities that are given in truncated continued-fraction form. For a master equation which is second order in the system-bath coupling, the memory kernel is re-expressed in terms of local-in-time equations involving auxiliary densities and auxiliary operators.
boson systems ; Brownian motion ; Fourier transforms ; harmonic oscillators ; higher order statistics ; Laplace transforms ; master equation ; mathematical operators
Settore CHIM/02 - Chimica Fisica
ott-2012
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/210598
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