A1 Vertaisarvioitu alkuperäisartikkeli tieteellisessä lehdessä

Symmetry and block structure of the Liouvillian superoperator in partial secular approximation




TekijätCattaneo M, Giorgi GL, Maniscalco S, Zambrini R

KustantajaAMER PHYSICAL SOC

Julkaisuvuosi2020

JournalPhysical Review A

Tietokannassa oleva lehden nimiPHYSICAL REVIEW A

Lehden akronyymiPHYS REV A

Artikkelin numeroARTN 042108

Vuosikerta101

Numero4

Sivujen määrä15

ISSN2469-9926

DOIhttps://doi.org/10.1103/PhysRevA.101.042108

Rinnakkaistallenteen osoitehttps://research.utu.fi/converis/portal/detail/Publication/46992723


Tiivistelmä
We address the structure of the Liouvillian superoperator for a broad class of bosonic and fermionic Markovian open systems interacting with stationary environments. We show that the accurate application of the partial secular approximation in the derivation of the Bloch-Redfield master equation naturally induces a symmetry on the superoperator level, which may greatly reduce the complexity of the master equation by decomposing the Liouvillian superoperator into independent blocks. Moreover, we prove that, if the steady state of the system is unique, one single block contains all the information about it, and that this imposes a constraint on the possible steady-state coherences of the unique state, ruling out some of them. To provide some examples, we show how the symmetry appears for two coupled spins interacting with separate baths, as well as for two harmonic oscillators immersed in a common environment. In both cases the standard derivation and solution of the master equation is simplified, as well as the search for the steady state. The block diagonalization does not appear when a local master equation is chosen.

Ladattava julkaisu

This is an electronic reprint of the original article.
This reprint may differ from the original in pagination and typographic detail. Please cite the original version.





Last updated on 2024-26-11 at 17:48