Abstract
AbstractMuch of the qualitative nature of physical systems can be predicted from the way it scales with system size. Contrary to the continuum expectation, we observe a profound deviation from logarithmic scaling in the impedance of a two-dimensional LC circuit network. We find this anomalous impedance contribution to sensitively depend on the number of nodes N in a curious erratic manner and experimentally demonstrate its robustness against perturbations from the contact and parasitic impedance of individual components. This impedance anomaly is traced back to a generalized resonance condition reminiscent of Harper’s equation for electronic lattice transport in a magnetic field, even though our circuit network does not involve magnetic translation symmetry. It exhibits an emergent fractal parametric structure of anomalous impedance peaks for different N that cannot be reconciled with a continuum theory and does not correspond to regular waveguide resonant behavior. This anomalous fractal scaling extends to the transport properties of generic systems described by a network Laplacian whenever a resonance frequency scale is simultaneously present.
Funder
Ministry of Education - Singapore
Publisher
Springer Science and Business Media LLC
Subject
General Physics and Astronomy
Reference113 articles.
1. Fisher, M. E. The theory of equilibrium critical phenomena. Rep. Prog. Phys. 30, 615–730 (1967).
2. Stanley, H. E. Scaling, universality, and renormalization: three pillars of modern critical phenomena. Rev. Mod. Phys. 71, S358–S366 (1999).
3. Hilfer, R. Scaling theory and the classification of phase transitions. Mod. Phys. Lett. B 06, 773–784 (1992).
4. Cardy, J. Scaling and Renormalization in Statistical Physics. Cambridge Lecture Notes in Physics (Cambridge University Press, 1996).
5. Frohlich, J. Scaling and Self-Similarity in Physics: Renormalization in Statistical Mechanics and Dynamics (Birkhauser, 1983).
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