| FUNDAMENTAL AREAS OF PHENOMENOLOGY(INCLUDING APPLICATIONS) |
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Quantum Scars in Microwave Dielectric Photonic Graphene Billiards |
| Xiao Wang1**, Guo-Dong Wei2 |
1Department of Computer Science and Technology, Taiyuan University of Science and Technology, Taiyuan 030024
2School of Applied Science, Taiyuan University of Science and Technology, Taiyuan 030024
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| Cite this article: |
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Xiao Wang, Guo-Dong Wei 2020 Chin. Phys. Lett. 37 014201 |
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Abstract In the band structure of graphene, the dispersion relation is linear around a Dirac point at the corners of the Brillouin zone. The closed graphene system has proven to be the ideal model to investigate relativistic quantum chaos phenomena. The electromagnetic material photonic graphene (PG) and electronic graphene not only have the same structural symmetry, but also have the similar band structure. Thus, we consider a stadium shaped resonant cavity filled with PG to demonstrate the relativistic quantum chaos phenomenon by numerical simulation. It is interesting that the relativistic quantum scars not only are identified in the PG cavities, but also appear and disappear repeatedly. The wave vector difference between repetitive scars on the same orbit is analyzed and confirmed to follow the quantization rule. The exploration will not only demonstrate a visual simulation of relativistic quantum scars but also propose a physical system for observing valley-dependent relativistic quantum scars, which is helpful for further understanding of quantum chaos.
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Received: 31 October 2019
Published: 23 December 2019
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| PACS: |
42.70.Qs
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(Photonic bandgap materials)
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05.45.Pq
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(Numerical simulations of chaotic systems)
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72.10.-d
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(Theory of electronic transport; scattering mechanisms)
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| Fund: Supported by the National Natural Science Foundation of China under Grant No. 11847067, the Natural Science Foundation of Shanxi Province under Grant No. 201801D221178, the Science and Technology Innovation Project of Shanxi Higher Education under Grant No. 2019L0648, and Taiyuan University of Science and Technology Scientific Research Initial Funding under Grant No. 20152044. |
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| [1] | Mcdonald S W and Kaufman A N 1979 Phys. Rev. Lett. 42 1189 | | [2] | Mcdonald S W and Kaufman A N 1988 Phys. Rev. A 37 3067 | | [3] | Heller E J 1984 Phys. Rev. Lett. 53 1515 | | [4] | Bogomolny E B 1988 Physica D 31 169 | | [5] | Berry M 1989 Proc. R. Soc. A 423 219 | | [6] | Castro Neto A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2009 Rev. Mod. Phys. 81 109 | | [7] | Geim A K and Novoselov K S 2007 Nat. Mater. 6 183 | | [8] | Beenakker C W J 2008 Rev. Mod. Phys. 80 1337 | | [9] | Huang L, Lai Y C, Ferry D K, Goodnick M S and Akis R 2009 Phys. Rev. Lett. 103 054101 | | [10] | Cabosart D, Felten A, Reckinger N, Iordanescu A, Toussaint S, Faniel S and Hackens B 2017 Nano Lett. 17 1344 | | [11] | Ni X, Huang L, Lai Y C and Grebogi C 2012 Phys. Rev. E 86 016702 | | [12] | Xu H Y, Huang L, Lai Y C and Grebogi C 2013 Phys. Rev. Lett. 110 064102 | | [13] | Ying L, Wang G L, Huang L and Lai Y C 2014 Phys. Rev. B 90 224301 | | [14] | Yang R, Huang L, Lai Y C and Pecora M 2012 Appl. Phys. Lett. 100 093105 | | [15] | Yang R, Huang L, Lai Y C, Grebogi C and Pecora L M 2013 Chaos 23 013125 | | [16] | Wallace P R 1947 Phys. Rev. 71 622 | | [17] | Bittner S, Dietz B, Miski-Oglu M, Oria Iriarte P, Richter A and Schäfer F 2010 Phys. Rev. B 82 014301 | | [18] | Kuhl U, Barkhofen S, Tudorovskiy T, Stöckmann H J, Hossain T, de Forges de Parny L and Mortessagne F 2010 Phys. Rev. B 82 094308 | | [19] | Bellec M, Kuhl U, Montambaux G, Montambaux G and Mortessagne F 2013 Phys. Rev. Lett. 110 033902 | | [20] | Bittner S, Dietz B, Miski-Oglu M and Richter A 2012 Phys. Rev. B 85 064301 | | [21] | Wang X, Jiang H T, Yan C, Sun Y, Li Y H, Shi Y L and Chen H 2013 Europhys. Lett. 103 17003 | | [22] | Wang X, Jiang H T, Yan C, Deng F S, Sun Y, Li Y H, Shi Y L and Chen H 2014 Europhys. Lett. 108 14002 | | [23] | Wang X, Jiang H T, Li Y, Yan C, Deng F S, Sun Y, Li Y H, Shi Y L and Chen H 2015 Opt. Express 23 5126 | | [24] | Zandbergen S R and De dood M J A 2010 Phys. Rev. Lett. 104 043903 | | [25] | Plotnik Y, Rechtsman M C, Song D, Heinrich M, Zeuner J M, Nolte S, Lumer Y, Malkova N, Xu J, Szameit A, Chen Z and Segev M 2014 Nat. Mater. 13 57 | | [26] | Lai Y C, Xu H Y, Huang L and Grebogi C 2018 Chaos 28 052101 | | [27] | Ponomarenko L A, Schedin F, Katsnelson M I, Yang R, Hill E W, Novoselov K S and Geim A K 2008 Science 320 356 | | [28] | Miao F, Wijeratne S, Zhang Y, Coskun U C, Bao W and Lau C N 2007 Science 317 1530 | | [29] | Huang L, Xu H Y, Grebogi C and Lai Y C 2018 Phys. Rep. 753 1 | | [30] | Dietz B, Klaus T, Miski-Oglu M and Richter A 2015 Phys. Rev. B 91 035411 | | [31] | Dietz B and Richter A 2015 Chaos 25 097601 | | [32] | Dietz B, Klaus T, Miski-Oglu M, Richer A, Wunderle M and Bouazza C 2016 Phys. Rev. Lett. 116 023901 | | [33] | Dietz B and Richter A 2019 Phys. Scr. 94 014002 | | [34] | Song M Y, Li Z Y, Xu H Y, Huang L and Hai Y C 2019 Phys. Rev. Res. 1 033008 | | [35] | Zhang H F 2018 Chin. Phys. B 27 014205 | | [36] | Deng F S, Sun Y, Wang X, Xue R, Li Y, Jiang H T, Shi Y L, Chang Kai and Chen H 2014 Opt. Express 22 23605 | | [37] | Gutzwiller M C 1971 J. Math. Phys. 12 343 | | [38] | Wang C Z, Huang L and Chang K 2017 New J. Phys. 19 013018 | | [39] | Berry M V and Mondragon R J 1987 Proc. R. Soc. A 412 53 |
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