Fractional quantization of Hall resistance as a consequence of\n mesoscopic feedback

2005/11/08 by Artur Sowa, Sowa, Artur
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Information and Cryptography #Quantum and electron transport phenomena #Surface and Thin Film Phenomena

paper · pdf · doi:10.48550/arxiv.cond-mat/0511204

openalex publication_date 2005/11/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A nonlinear single-particle model is introduced, which captures the\ncharacteristic of systems in the quantum Hall regime. The model entails the\nmagnetic Shr "odinger equation with spatially variable magnetic flux density.\nThe distribution of flux is prescribed via the postulates of the mesoscopic\nmechanics (MeM) introduced in my previous articles [cf. J. Phys. Chem. Solids,\n65 (2004), 1507-1515; J. Geom. Phys., Vol. 55/1 (2005), 1-18]. The model is\nfound to imply exact integer and fractional quantization of the Hall\nconductance. In fact, Hall resistance is found to be R_H =\n\(h)/(2e²)\(M)/(N) at the filling factor value N/M. The assumed\ngeometry of the Hall plate is rectangular. Special properties of the magnetic\nShr "odinger equation with the mesoscopic feedback loop allow us to demonstrate\nquantization of Hall resistance as a direct consequence of charge and flux\nquantization. I believe results presented here shed light at the overall status\nof the MeM in quantum physics, confirming its validity.\n

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