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 -