物理学报2016，Vol.65Issue(16)：160501-1-160501-8,8.DOI:10.7498/aps.65.160501
广义Fib onacci时间准周期量子行走波包扩散的动力学特性∗
Dynamic b ehaviors of spreading in generalized Fib onacci time quasip erio dic quantum walks
摘要
Abstract
Quantum walk (QW), the quantum mechanical counterpart of classical random walk, has recently been studied in various fields. The evolution of the discrete time quantum walk can be described as follows: the walker changes its spin state by the coin operator C, then takes one step left or right according to its spin state. For homogeneous quantum walk, the coin operator is independent of time and the standard deviation of the position grows linearly in time. It is quadratically faster than that in the classical random walk. In this work, we numerically study the dynamical behaviors of spreading in a one-dimensional discrete time quasiperiodic quantum walk (DTQQW). The DTQQW is that the coin operator is dependent on time and takes two different coins C(α) and C(β) arranged in generalized Fibonacci (GF) sequences. The GF sequences are constructed from A by the recursion relation: A → AmBn, B → A, for m, n are positive integers. They can be classified into two classes according to the wandering exponentω. Forω<0, they belong to the first class, and for ω > 0, they belong to the second class. For one dimensional system, the behaviors of two classes of GF systems are different either for the electronic spectrum of an electron in quasiperiodic potentials or for the quantum phase transitions of the quasiperiodic spin chains. In this paper, we discuss the cases of two different C operators (C(α), C(β)) arranged in GF sequences and find that the spreading behaviors are superdiffusion (the standard deviation of the positionσ∼tγ, 0.5<γ<1) for the two classes of GF DTQQW. For the second class of GF DTQQW, the exponent valuesγ are larger than those of the first class of GF DTQQW in the case of two identical C operators. By exploring the probability distribution in the real space, we find that for the first class of GF DTQQW, the probability distributions are almost the same for different initial states and are similar to the classical Gaussian distribution. For the probability distributions of the second class of GF DTQQW, there are two peaks at the two edges and the height of the two peaks can be different for different initial states. They are similar to the ballistic distribution of the homogeneous quantum walk. Therefore, we conclude that for the first class of GF DTQQW, the spreading behaviors are close to those of the classical random walk (γ = 0.5) while for the second class of GF DTQQW, they are close to those of the homogeneous quantum walk (γ = 1). This result is quite different from the characteristics of the quantum phase transitions in two classes of GF quasiperiodic quantum spin chains.关键词
量子行走/时间准周期/超扩散Key words
quantum walk/time quasiperiodic/superdiffusion引用本文复制引用
王文娟,童培庆..广义Fib onacci时间准周期量子行走波包扩散的动力学特性∗[J].物理学报,2016,65(16):160501-1-160501-8,8.基金项目
国家自然科学基金(批准号:11175087,11575087)资助的课题.* Project supported by the National Natural Science Foundation of China (Grant Nos.11175087,11575087) （批准号:11175087,11575087）
