Evolution of localized electron spin in a nuclear spin environment

Sigurdur I. Erlingsson*, Yuli V. Nazarov

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

75 Citations (Scopus)


Motivated by recent interest in the role of the hyperfine interaction in quantum dots, we study the dynamics of a localized electron spin coupled to many nuclei. An important feature of the model is that the coupling to an individual nuclear spin depends on its position in the quantum dot. We introduce a semiclassical description of the system valid in the limit of a large number of nuclei and analyze the resulting classical dynamics. Contrary to a natural assumption of chaoticity of such dynamics, the correlation functions of the electron spin with an arbitrary initial condition show no decay in time. Rather, they exhibit complicated undamped oscillations. This may be attributed to the fact that the system has many integrals of motion and is close to an integrable one. The correlation functions averaged over initial conditions do exhibit a slow decay (∼ 1/ln(t) at t → ∞).

Original languageEnglish
Article number205327
Pages (from-to)205327-1-205327-9
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number20
Publication statusPublished - Nov 2004

Bibliographical note

Funding Information:
The authors acknowledge financial support from FOM and S.I.E. would like to thank Oleg Jouravlev, Dmitri Bagrets, and Lieven Vandersypen for fruitful discussions.


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