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Geometric Quantum Noise of Spin
Copyright policy )American Physical Society (APS)Geometric Quantum Noise of Spin
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 (nano-magnets) 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-Sch\"on (AES) 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.
Comment: 8 pages including Supplemental Material
- Moscow Institute of Physics and Technology Russian Federation
- Karlsruhe Institute of Technology (KIT) Germany
- Karlsruhe Institute of Technology Germany
- Weizmann Institute of Science Israel
- University of Cologne Germany
Microsoft Academic Graph classification: Classical mechanics Physics Geometric phase Spin-½ Langevin equation Quantum dynamics Quantum mechanics Quantum Semiclassical physics Bloch sphere Quantum noise
General Physics and Astronomy, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), FOS: Physical sciences, Condensed Matter - Mesoscale and Nanoscale Physics
General Physics and Astronomy, Mesoscale and Nanoscale Physics (cond-mat.mes-hall), FOS: Physical sciences, Condensed Matter - Mesoscale and Nanoscale Physics
Microsoft Academic Graph classification: Classical mechanics Physics Geometric phase Spin-½ Langevin equation Quantum dynamics Quantum mechanics Quantum Semiclassical physics Bloch sphere Quantum noise
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citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).14 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average citations This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).14 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!
- Moscow Institute of Physics and Technology Russian Federation
- Karlsruhe Institute of Technology (KIT) Germany
- Karlsruhe Institute of Technology Germany
- Weizmann Institute of Science Israel
- University of Cologne Germany
- Landau Institute for Theoretical Physics Russian Federation
- Departement für Physik Universität Basel Switzerland
- International Centre for Theoretical Physics Italy
- University of Basel Switzerland
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 (nano-magnets) 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-Sch\"on (AES) 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.
Comment: 8 pages including Supplemental Material