Kicked-Harper model versus on-resonance double-kicked rotor model: From spectral difference to topological equivalence

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	Kicked-Harper model versus on-resonance double-kicked rotor model: From spectral difference to topological equivalence
	Wang, Hailong ; Ho, Derek Y. H. ; Lawton, Wayne ; Wang, Jiao ; Gong, Jiangbin ; Wang J(王矫)
刊名	http://dx.doi.org/10.1103/PhysRevE.88.052920
	2013
关键词	QUANTUM CHAOS LOCALIZATION ANTIRESONANCE DYNAMICS FIELD
英文摘要	NNSF [11275159, 10925525]; SRFDP of China [20100121110021]; ARF Tier I, MOE of Singapore [R-144-000-276-112]; Recent studies have established that, in addition to the well-known kicked-Harper model (KHM), an on-resonance double-kicked rotor (ORDKR) model also has Hofstadter's butterfly Floquet spectrum, with strong resemblance to the standard Hofstadter spectrum that is a paradigm in studies of the integer quantum Hall effect. Earlier it was shown that the quasienergy spectra of these two dynamical models (i) can exactly overlap with each other if an effective Planck constant takes irrational multiples of 2 pi and (ii) will be different if the same parameter takes rational multiples of 2 pi. This work makes detailed comparisons between these two models, with an effective Planck constant given by 2 pi M/N, where M and N are coprime and odd integers. It is found that the ORDKR spectrum (with two periodic kicking sequences having the same kick strength) has one flat band and N - 1 nonflat bands with the largest bandwidth decaying in a power law as similar to KN+2, where K is a kick strength parameter. The existence of a flat band is strictly proven and the power-law scaling, numerically checked for a number of cases, is also analytically proven for a three-band case. By contrast, the KHM does not have any flat band and its bandwidths scale linearly with K. This is shown to result in dramatic differences in dynamical behavior, such as transient (but extremely long) dynamical localization in ORDKR, which is absent in the KHM. Finally, we show that despite these differences, there exist simple extensions of the KHM and ORDKR model (upon introducing an additional periodic phase parameter) such that the resulting extended KHM and ORDKR model are actually topologically equivalent, i. e., they yield exactly the same Floquet-band Chern numbers and display topological phase transitions at the same kick strengths. A theoretical derivation of this topological equivalence is provided. These results are also of interest to our current understanding of quantum-classical correspondence considering that the KHM and ORDKR model have exactly the same classical limit after a simple canonical transformation.
语种	英语
出版者	AMER PHYSICAL SOC
内容类型	期刊论文
源URL	[http://dspace.xmu.edu.cn/handle/2288/91787]
专题	物理技术－已发表论文
推荐引用方式 GB/T 7714	Wang, Hailong,Ho, Derek Y. H.,Lawton, Wayne,et al. Kicked-Harper model versus on-resonance double-kicked rotor model: From spectral difference to topological equivalence[J]. http://dx.doi.org/10.1103/PhysRevE.88.052920,2013.
APA	Wang, Hailong,Ho, Derek Y. H.,Lawton, Wayne,Wang, Jiao,Gong, Jiangbin,&王矫.(2013).Kicked-Harper model versus on-resonance double-kicked rotor model: From spectral difference to topological equivalence.http://dx.doi.org/10.1103/PhysRevE.88.052920.
MLA	Wang, Hailong,et al."Kicked-Harper model versus on-resonance double-kicked rotor model: From spectral difference to topological equivalence".http://dx.doi.org/10.1103/PhysRevE.88.052920 (2013).