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Chin. Phys. B, 2019, Vol. 28(2): 020504    DOI: 10.1088/1674-1056/28/2/020504
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Dynamical stable-jump-stable-jump picture in a non-periodically driven quantum relativistic kicked rotor system

Hsincheng Yu(于心澄)1, Zhongzhou Ren(任中洲)1,2, Xin Zhang(张欣)1
1 Department of Physics, Nanjing University, Nanjing 210008, China;
2 School of Physics Science and Engineering, Tongji University, Shanghai 200092, China

We study a non-periodically driven kicked rotor based on the one-dimensional quantum relativistic kicked rotor (QRKR). In our model, we add a small constant to the interval of the one-dimensional QRKR after each kick process. It is found that the momentum spreading is stable in finite kicked times, it then jumps up or down and becomes stable again. This interesting phenomenon is understood by quantum resonance. Moreover, the stable-jump-stable-jump phenomenon persists, even though the interval of kick process is randomly increased. This result means that the quantum resonance is independent of the periodic perturbation in the QRKR model.

Keywords:  quantum chaos      dynamical localization      quantum resonance  
Received:  23 October 2018      Revised:  07 December 2018      Published:  05 February 2019
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Mt (Quantum chaos; semiclassical methods)  

Project supported by the National Natural Science Foundation of China (Grant Nos. 11535004, 11761161001, 11375086, 11120101005, 11175085, and 1235001), the National Major State Basic Research and Development Program of China (Grant No. 2016YFE0129300), and the Science and Technology Development Fund of Macau (Grant No. 068/2011/A).

Corresponding Authors:  Zhongzhou Ren     E-mail:

Cite this article: 

Hsincheng Yu(于心澄), Zhongzhou Ren(任中洲), Xin Zhang(张欣) Dynamical stable-jump-stable-jump picture in a non-periodically driven quantum relativistic kicked rotor system 2019 Chin. Phys. B 28 020504

[1] Casati G, Chirikov B V, Izraelev F M and Ford J 1979 Lecture Notes in Physics, Vol. 93 (Berlin: Springer)
[2] Fishman S, Grempel D R and Prange R E 1982 Phys. Rev. Lett. 49 509
[3] Fishman S, Prange R E and Griniasty M 1989 Phys. Rev. A 39 1628
[4] Grempel D R, Prange R E and Fishman S 1984 Phys. Rev. A 29 1639
[5] Kohmoto M, Kadanoff L P and Tang C 1983 Phys. Rev. Lett. 50 1870
[6] Zhang Z J, Tong P Q, Gong J B and Li B W 2012 Phys. Rev. Lett. 108 070603
[7] Satija I I, Sundaram B and Ketoja J A 1999 Phys. Rev. E 60 453
[8] Wang J, Guarneri I, Casati G and Gong J B 2011 Phys. Rev. Lett. 107 234104
[9] Guarneri I, Casati G and Karle V 2014 Phys. Rev. Lett. 113 174101
[10] Anderson P W 1958 Phys. Rev. 109 1492
[11] Berry M V 1984 Physica D: Nonlinear Phenomena 10 369
[12] Zhao W L, Gong J B, Wang W G, Casati G, Liu J and Fu L B 2016 Phys. Rev. A 94 053631
[13] Guarneri I 2017 Phys. Rev. E 95 032206
[14] Lepers M, Zehnlé V and Garreau J C 2008 Phys. Rev. A 77 043628
[15] Sokolov V V, Zhirov O V, Alonso D and Casati G 2000 Phys. Rev. Lett. 84 3566
[16] d'Arcy M B, Godun R M, Oberthaler M K, Cassettari D and Summy G S 2001 Phys. Rev. Lett. 87 074102
[17] Daley A J, Parkins A S, Leonhardt R and Tan S M 2002 Phys. Rev. E 65 035201
[18] Zhao Q F, Müller C A and Gong J B 2014 Phys. Rev. E 90 022921
[19] Abal G, Donangelo R, Romanelli A, Sicardi S A C and Siri R 2002 Phys. Rev. E 65 046236
[20] Matrasulov D U, Milibaeva G M, Salomov U R and Sundaram B 2005 Phys. Rev. E 72 016213
[21] Rozenbaum E B and Galitski V 2017 Phys. Rev. B 95 064303
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