law in one-dimensional quantum transport: an example of weak chaos in quantum systems

Quantum transport is studied in the one-dimensional (1D) Kronig-Penny model in the applied electric field. S matrices in the phase-amplitude plane are examined as a function of the number of barriers. In a weak field regime, matrix elements show stagnant chaos around the torus, whereas in a strong field regime they wander from one stagnant region to another irregularly. The power spectra of the transmission coefficients show a universal behaviour with the exponent independent of both the strength of the field and width of barriers. The results are confirmed by the universal feature of the Allan variance.