Random-Matrix Theory of Quantum Size Effects on Nuclear Magnetic Resonance in Metal Particles
C.W.J. Beenakker (Instituut-Lorentz, Leiden, The Netherlands)
TL;DR
This paper uses random-matrix theory to analyze quantum size effects on NMR in metal particles, showing exact results for local density of states and universal reduction in Knight shift variance when time-reversal symmetry is broken.
Contribution
It provides an exact computation of the local density of states distribution for the Wigner-Dyson ensemble and confirms supersymmetry theory predictions for NMR lineshape in disordered metals.
Findings
Exact distribution function for local density of states computed.
Agreement with supersymmetry theory for NMR lineshape.
Universal reduction of Knight shift variance by 2/3 when time-reversal symmetry is broken.
Abstract
The distribution function of the local density of states is computed exactly for the Wigner-Dyson ensemble of random Hamiltonians. In the absence of time-reversal symmetry, precise agreement is obtained with the "supersymmetry" theory by Efetov and Prigodin of the NMR lineshape in disordered metal particles. Upon breaking time-reversal symmetry, the variance of the Knight shift in the smallest particles is reduced by a universal factor of 2/3. ***To be published in Physical Review B.****
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