2003/07/12 by J. C. Phillips, Phillips, J. C.
Mathematics · Medicine · Physics and Astronomy · #Calculus (dental) #FOS: Physical sciences #History and Theory of Mathematics #Mathematical economics #Mathematics #Medicine #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Pure mathematics #Riemann hypothesis #advanced mathematical theories #cond-mat.mes-hall
paper · pdf · doi:10.48550/arxiv.cond-mat/0307301
5 pages
arxiv created 2003/07/12 · openalex publication_date 2003/07/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The synergistic formation of zero (exponentially small) resistance states (ESRS) in high mobility two-dimensional electron systems (2DES) in a static magnetic field B and exposed to strong microwave (MW) radiation exhibits hysteresis and an anomalous logarithmic dependence on MW power. These synergistically organized states appear to be associated with a new kind of energy gap Δ. Here I show that a microscopic quantum model that involves the Prime Number Theorem explains the MW power dependence of the energy gap Δ. The explanation involves remarkable convergence with the most abstract ideas of modern mathematics.