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Eigenvalue Repulsion and Eigenfunction Localization in Sparse Non-Hermitian Random Matrices
Grace H. Zhang, David R. Nelson
Complex networks with directed, local interactions are ubiquitous in nature, and often occur with probabilistic connections due to both intrinsic stochasticity and disordered envir…
Non-Hermitian Quasi-Localization and Ring Attractor Neural Networks
Hidenori Tanaka, David R. Nelson
Eigenmodes of a broad class of "sparse" random matrices, with interactions concentrated near the diagonal, exponentially localize in space, as initially discovered in 1957 by Ander…
Non-Hermitian Localization in Biological Networks
Ariel Amir, Naomichi Hatano, David R. Nelson
We explore the spectra and localization properties of the N-site banded one-dimensional non-Hermitian random matrices that arise naturally in sparse neural networks. Approximately…
Transverse Meissner Physics of Planar Superconductors with Columnar Pins
Gil Refael, Walter Hofstetter, David R. Nelson
The statistical mechanics of thermally excited vortex lines with columnar defects can be mapped onto the physics of interacting quantum particles with quenched random disorder in o…
Vortex pinning by a columnar defect in planar superconductors with point disorder
Anatoli Polkovnikov, Yariv Kafri, David R. Nelson
We study the effect of a single columnar pin on a dimensional array of vortex lines in planar type II superconductors in the presence of point disorder. In large samples, t…
Population Dynamics and Non-Hermitian Localization
Karin A. Dahmen, David R. Nelson, Nadav M. Shnerb
We review localization with non-Hermitian time evolution as applied to simple models of population biology with spatially varying growth profiles and convection. Convection leads t…
Life and Death near a Windy Oasis
Karin A. Dahmen, David R. Nelson, Nadav M. Shnerb
We propose a simple experiment to study delocalization and extinction in inhomogeneous biological systems. The nonlinear steady state for, say, a bacteria colony living on and near…
Winding Numbers, Complex Currents, and Non-Hermitian Localization
Nadav M. Shnerb, David R. Nelson
The nature of extended states in disordered tight binding models with a constant imaginary vector potential is explored. Such models, relevant to vortex physics in superconductors…
Non-Hermitian Localization and Population Biology
David R. Nelson, Nadav M. Shnerb
The time evolution of spatial fluctuations in inhomogeneous d-dimensional biological systems is analyzed. A single species continuous growth model, in which the population disperse…