TY - JOUR

T1 - Quantum diffusion in the generalized Harper equation

AU - Jeon, Gun Sang

AU - Kim, Beom Jun

AU - Yu, Sang Wook

AU - Choi, M. Y.

PY - 1998/2/6

Y1 - 1998/2/6

N2 - We study numerically the dynamic and spectral properties of a one-dimensional quasi-periodic system, where site energies are given by ∈k = V cos 2π f cursive Greek chik with cursive Greek chik denoting the kth quasiperiodic lattice site. When 2π f is given by the reciprocal lattice vector G(m, n) with n and m being successive Fibonacci numbers, the variance of the wavepacket is found to grow quadratically in time, regardless of the potential strength V. For other values of f, there exists a critical value of V beyond which the growth of the wavepacket variance is bounded. In particular an anomalous diffusion takes place for 2π f corresponding to G(m, n) with generic integers m and n. The level-spacing distribution is also examined, and the corresponding exponent β is observed to decrease with V.

AB - We study numerically the dynamic and spectral properties of a one-dimensional quasi-periodic system, where site energies are given by ∈k = V cos 2π f cursive Greek chik with cursive Greek chik denoting the kth quasiperiodic lattice site. When 2π f is given by the reciprocal lattice vector G(m, n) with n and m being successive Fibonacci numbers, the variance of the wavepacket is found to grow quadratically in time, regardless of the potential strength V. For other values of f, there exists a critical value of V beyond which the growth of the wavepacket variance is bounded. In particular an anomalous diffusion takes place for 2π f corresponding to G(m, n) with generic integers m and n. The level-spacing distribution is also examined, and the corresponding exponent β is observed to decrease with V.

UR - http://www.scopus.com/inward/record.url?scp=0040426416&partnerID=8YFLogxK

U2 - 10.1088/0305-4470/31/5/006

DO - 10.1088/0305-4470/31/5/006

M3 - Article

AN - SCOPUS:0040426416

SN - 0305-4470

VL - 31

SP - 1353

EP - 1364

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

IS - 5

ER -