English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

The generalized Master equation of the Nakajima-Zwanzig (NZ) type has beenused extensively to investigate the coherence dynamics of the central spinmodel with the nuclear bath in a narrowed state characterized by a well definedvalue of the Overhauser field. We revisit the perturbative NZ approach andapply it to the exactly solvable case of a system with uniform hyperfinecouplings. This is motivated by the fact that the effective Hamiltonian-basedtheory suggests that the dynamics of the realistic system at low magneticfields and short times can be mapped onto the uniform coupling model. We showthat the standard NZ approach fails to reproduce the exact solution of thismodel beyond very short times, while the effective Hamiltonian calculationagrees very well with the exact result on timescales during which most of thecoherence is lost. Our key finding is that in order to extend the timescale ofapplicability of the NZ approach in this case, instead of using a singleprojection operator one has to use a set of correlated projection operatorswhich properly reflect the symmetries of the problem and greatly improve theconvergence of the theory. This suggests that the correlated projectionoperators are crucial for a proper description of narrowed state free inductiondecay at short times and low magnetic fields. Our results thus provideimportant insights toward the development of a more complete theory of centralspin decoherence applicable in a broader regime of timescales and magneticfields.

Master equation approach to the central spin decoherence problem: the uniform coupling model and the role of projection operators