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- W1652359567 abstract "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 appea r to be associated with a new kind of energy gap �. Here I show that a microscopic quantum model that involves the Prime Number Theorem explains the MW power dependence of the energy gap �. The explanation involves remarkable convergence with the most ab stract ideas of modern mathematics. Two experimental groups have discovered giant magnetoresistance oscillations associated with low-field cyclotron resonance in two dimensional electron gases ((2DEG) immersed in a microwave (MW) bath that were previously used to study quantum Hall effects. In very high mobility samples the minima of these oscillations correspond to exponentially small resistance (ESR) 1-3 . The dependence of ESR on MW power P is anomalous 4,5 , exhibiting hysteresis similar to that found in many nucleation processes in materials science 6 . Starting from P = 0, there is an incubation regime at low power levels, where the resistance change very slowly with increasing power, followed by a steep decrease in ESR at a higher power levels above P = P 1. In the steeply decreasing (growth or formation) range P 1 P 2, ESR is maintained to a lower power level P' ~ P/2, and in the range P 1' < P' < P 2' the re sistivity is again linear in lnP ', but with a slope that is ~ 3 times larger." @default.
- W1652359567 created "2016-06-24" @default.
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- W1652359567 date "2003-07-12" @default.
- W1652359567 modified "2023-09-24" @default.
- W1652359567 title "Fermat's last theorem, the Riemann hypothesis, and synergistic glasses" @default.
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