Quantum diffusion in the generalized Harper equation

Gun Sang Jeon, Beom Jun Kim, Sang Wook Yu, M. Y. Choi

Research output: Contribution to journalArticlepeer-review

8 Scopus citations


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.

Original languageEnglish
Pages (from-to)1353-1364
Number of pages12
JournalJournal of Physics A: Mathematical and General
Issue number5
StatePublished - 6 Feb 1998


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