|
|
|
Resonance and antiresonance characteristics in linearly delayed Maryland model |
| Hsinchen Yu(于心澄)1,2,3, Dong Bai(柏栋)4, Peishan He(何佩珊)1,2, Xiaoping Zhang(张小平)1,2,†, Zhongzhou Ren(任中洲)4,5,‡, and Qiang Zheng(郑强)6 |
1 State Key Laboratory of Lunar and Planetary Sciences, Macau University of Science and Technology, Macau 999078, China;
2 CNSA Macau Center for Space Exploration and Science, Macau, China;
3 Department of Physics, Nanjing University, Nanjing 210008, China;
4 School of Physics Science and Engineering, Tongji University, Shanghai 200092, China;
5 Key Laboratory of Advanced Micro-Structure Materials(MOE), Tongji University, Shanghai 200092, China;
6 School of Physical Science and Technology, Tiangong University, Tianjin 300387, China |
|
|
|
|
Abstract The Maryland model is a critical theoretical model in quantum chaos. This model describes the motion of a spin-1/2 particle on a one-dimensional lattice under the periodical disturbance of the external delta-function-like magnetic field. In this work, we propose the linearly delayed quantum relativistic Maryland model (LDQRMM) as a novel generalization of the original Maryland model and systematically study its physical properties. We derive the resonance and antiresonance conditions for the angular momentum spread. The "characteristic sum" is introduced in this paper as a new measure to quantify the sensitivity between the angular momentum spread and the model parameters. In addition, different topological patterns emerge in the LDQRMM. It predicts some additions to the Anderson localization in the corresponding tight-binding systems. Our theoretical results could be verified experimentally by studying cold atoms in optical lattices disturbed by a linearly delayed magnetic field.
|
Received: 12 January 2022
Revised: 19 April 2022
Accepted manuscript online: 18 June 2022
|
|
PACS:
|
05.45.-a
|
(Nonlinear dynamics and chaos)
|
| |
05.45.Mt
|
(Quantum chaos; semiclassical methods)
|
|
| Fund: Project supported by the Science and Technology Development Fund (FDCT) of Macau, China (Grant Nos. 0014/2022/A1 and 0042/2018/A2) and the National Natural Science Foundation of China (Grant Nos. 11761161001, 12035011, and 11975167). |
Corresponding Authors:
Xiaoping Zhang, Zhongzhou Ren
E-mail: xpzhangnju@gmail.com;zren@tongji.edu.cn
|
Cite this article:
Hsinchen Yu(于心澄), Dong Bai(柏栋), Peishan He(何佩珊), Xiaoping Zhang(张小平), Zhongzhou Ren(任中洲), and Qiang Zheng(郑强) Resonance and antiresonance characteristics in linearly delayed Maryland model 2022 Chin. Phys. B 31 120502
|
[1] Chirikov B V 1979 Phys. Rep. 52 263
[2] Fishman S, Grempel D R and Prange R E 1982 Phys. Rev. Lett. 49 509
[3] Grempel D R, Prange R E and Fishman S 1984 Phys. Rev. A 29 1639
[4] Grempel D R, Fishman S and Prange R E 1982 Phys. Rev. Lett. 49 833
[5] Prange R E, Grempel D R and Fishman S 1984 Phys. Rev. B 29 6500
[6] Simon B 1985 Ann. Phys. 159 157
[7] Berry M 1984 Physica D 10 369
[8] Altland A and Zirnbauer M R 1996 Phys. Rev. Lett. 77 4536
[9] Dana I and Dorofeev D L 2006 Phys. Rev. E 73 026206
[10] Casati G and Ford J 1979 Stochastic Behavior in Classical and Quantum Hamiltonian Systems, Lecture Notes in Physics (Berlin, Heidelberg: Springer)
[11] Khanna F and Matrasulov D 2006 Non-linear dynamics and fundamental interactions, chaotic dynamics of the relativistic kicked rotor (Dordrecht: Springer)
[12] Sokolov V V, Zhirov O V, Alonso D and Casati G 2000 Phys. Rev. Lett. 84 3566
[13] Billam T P and Gardiner S A 2009 Phys. Rev. A 80 023414
[14] Zhang Z J, Tong P Q, Gong J B and Li B W 2012 Phys. Rev. Lett. 108 070603
[15] Zhao W L, Gong J B, Wang W G, Casati G L, Liu J and Fu L B 2016 Phys. Rev. A 94 053631
[16] Moore F L, Robinson J C, Bharucha C F, Sundaram B and Raizen M G 1995 Phys. Rev. Lett. 75 4598
[17] D'Arcy M B, Godun R M, Oberthaler M K, Cassettari D and Summy G S 2001 Phys. Rev. Lett. 87 74102
[18] Kanem J F, Maneshi S, Partlow M, Spanner M and Steinberg A M 2007 Phys. Rev. Lett. 98 083004
[19] Duffy G J, Parkins S, Müller T, Sadgrove M, Leonhardt R and Wilson A C 2004 Phys. Rev. E 70 056206
[20] Dittrich T and Graham R 1990 Europhys. Lett. 11 589
[21] Ammann H, Gray R, Shvarchuck I and Christensen N 1998 Phys. Rev. Lett. 80 4111
[22] Sadgrove M, Wimberger S, Parkins S and Leonhardt R 2005 Phys. Rev. Lett. 94 174103
[23] Sadgrove M, Hilliard A, Mullins T, Parkins S and Leonhardt R 2004 Phys. Rev. E 70 036217
[24] Williams M E, Sadgrove M P, Daley A J, Gray R N, Tan S M, Parkins A S, Christensen N and Leonhardt R 2004 J. Opt. B: Quantum Semiclass. Opt. 6 28
[25] McDowall P, Hilliard A, McGovern M, Grünzweig T and Andersen M 2009 New J. Phys. 11 123021
[26] Manai I, Clément J F, Chicireanu R, Hainaut C, Garreau J C, Szriftgiser P and Delande D 2015 Phys. Rev. Lett. 115 240603
[27] Vant K, Ball G and Christensen N 2000 Phys. Rev. E 61 5994
[28] Cohen D 1991 Phys. Rev. A 43 639
[29] Ott E, Antonsen T M and Hanson J D 1984 Phys. Rev. Lett. 53 2187
[30] Cohen D 1991 Phys. Rev. A 44 2292
[31] Cohen D 1991 Phys. Rev. Lett. 67 1945
[32] Shiokawa K and Hu B L 1995 Phys. Rev. E 52 2497
[33] Schomerus H and Lutz E 2008 Phys. Rev. A 77 062113
[34] Borgonovi F and Shepelyansky D L 1996 Europhys. Lett. 35 517
[35] Cohen D 1994 J. Phys. A 27 4805
[36] Dittrich T and Graham R 1990 Ann. Phys. 200 363
[37] Dittrich T and Graham R 1990 Phys. Rev. A 42 4647
[38] Dyrting S and Milburn G J 1995 Phys. Rev. A 51 3136
[39] Benvenuto F, Casati G, Pikovsky A S and Shepelyansky D L 1991 Phys. Rev. A 44 R3423
[40] Shepelyansky D L 1993 Phys. Rev. Lett. 70 1787
[41] Pikovsky A S and Shepelyansky D L 2008 Phys. Rev. Lett. 100 094101
[42] García-Mata I and Shepelyansky D L 2009 Phys. Rev. E 79 026205
[43] Flach S, Krimer D O and Skokos C 2009 Phys. Rev. Lett. 102 024101
[44] Mulansky M, Ahnert K, Pikovsky A and Shepelyansky D L 2009 Phys. Rev. E 80 056212
[45] Ermann L and Shepelyansky D L 2014 J. Phys. A 47 335101
[46] Mieck B and Graham R 2004 J. Phys. A 37 L581
[47] Gligorić G, Bodyfelt J D and Flach S 2011 Europhys. Lett. 96 30004
[48] Zhao Q F, Müller C A and Gong J B 2014 Phys. Rev. E 90 022921
[49] Rozenbaum E B and Galitski V 2017 Phys. Rev. B 95 064303
[50] Graham R and Kolovsky A R 1996 Phys. Lett. A 222 47
[51] Klappauf B G, Oskay W H, Steck D A and Raizen M G 1998 Phys. Rev. Lett. 81 1203
[52] d'Arcy M B, Godun R M, Oberthaler M K, Summy G S, Burnett K and Gardiner S A 2001 Phys. Rev. E 64 056233
[53] Zhang C, Liu J, Raizen M G and Niu Q 2004 Phys. Rev. Lett. 92 054101
[54] Gadway B, Reeves J, Krinner L and Schneble D 2013 Phys. Rev. Lett. 110 190401
[55] Yu H C, Ren Z Z and Zhang X 2019 Chin. Phys. B 28 020504 |
| No Suggested Reading articles found! |
|
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
Cited |
|
|
|
|
Altmetric
|
|
blogs
Facebook pages
Wikipedia page
Google+ users
|
Online attention
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.
View more on Altmetrics
|
|
|
