title: Geometric quantum noise of spin.
abstract: The presence of geometric phases is known to affect the dynamics of the systems involved. Here, we consider a quantum degree of freedom, moving in a dissipative environment, whose dynamics is described by a Langevin equation with quantum noise. We show that geometric phases enter the stochastic noise terms. Specifically, we consider small ferromagnetic particles (nanomagnets) or quantum dots close to Stoner instability, and investigate the dynamics of the total magnetization in the presence of tunneling coupling to the metallic leads. We generalize the Ambegaokar-Eckern-Schön effective action and the corresponding semiclassical equations of motion from the U(1) case of the charge degree of freedom to the SU(2) case of the magnetization. The Langevin forces (torques) in these equations are strongly influenced by the geometric phase. As a first but nontrivial application, we predict low temperature quantum diffusion of the magnetization on the Bloch sphere, which is governed by the geometric phase. We propose a protocol for experimental observation of this phenomenon.
authors.affiliation: Institut für Theorie der Kondensierten Materie and DFG-Center for Functional Nanostructures (CFN), Karlsruhe Institute of Technology, D-76128 Karlsruhe, Germany.|L.D. Landau Institute for Theoretical Physics RAS, Kosygina street 2, 119334 Moscow, Russia.
authors.forename: Alexander
authors.initials: A
authors.lastname: Shnirman
authors.affiliation: Department of Condensed Matter Physics, Weizmann Institute of Science, 76100 Rehovot, Israel.|Institut für Nanotechnologie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany.
authors.forename: Yuval
authors.initials: Y
authors.lastname: Gefen
authors.affiliation: Department of Physics, University of Basel, CH-4056 Basel, Switzerland.
authors.forename: Arijit
authors.initials: A
authors.lastname: Saha
authors.affiliation: L.D. Landau Institute for Theoretical Physics RAS, Kosygina street 2, 119334 Moscow, Russia.|Moscow Institute of Physics and Technology, 141700 Moscow, Russia.
authors.forename: Igor S
authors.initials: IS
authors.lastname: Burmistrov
authors.affiliation: International Center for Theoretical Physics, Strada Costiera 11, I-34014 Trieste, Italy.
authors.forename: Mikhail N
authors.initials: MN
authors.lastname: Kiselev
authors.affiliation: Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, D-50937 Köln, Germany.
authors.forename: Alexander
authors.initials: A
authors.lastname: Altland