K. Nakamura et al., WEAK CHAOS IN ONE-DIMENSIONAL QUANTUM TRANSPORT - THE 1 F2 LAW AND THE BREAKDOWN OF THE LAW OF LARGE NUMBERS/, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 50(2), 1994, pp. 1700-1703
We study quantum transports in the one-dimensional Kronig-Penny model
in a static electric field. S matrices as a function of the number of
barriers are examined in the complex plane. They show a stagnant chaos
around torus in a weak field case, while, in a strong field case, wan
dering from one stagnant region to another in an unpredictable way. Th
e power spectra of transmission coefficients show a universal 1/f2 beh
avior with the exponent independent on both the strength of field and
width of barriers. The Allan variance indicates a breakdown of the law
of large numbers.