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 (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-Schön (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.

arXiv comment8 pages including Supplemental Material

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• The fractional Landau-Lifshitz-Gilbert equation
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• Spin pumping and torque statistics in the quantum noise limit
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• A thermally driven spin-transfer-torque system far from equilibrium: enhancement of the thermoelectric current via pumping current
• Dynamical exchange and phase induced switching of a localized molecular spin
• Inelastic electron scattering off a quantum dot in the cotunneling regime: the signature of mesoscopic Stoner instability
• Seven Etudes on dynamical Keldysh Model
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• Breaking of Coulomb blockade by macrospin-assisted tunneling
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• Spin-Noise and Damping in Individual Metallic Ferromagnetic Nanoparticles
• Coulomb blockade of chiral Majorana and complex fermions far from equilibrium