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مقاله پژوهشی: تحول زمانی مدل تنگابست در حضور میدان الکتریکی | ||
| فیزیک کاربردی ایران | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 23 اردیبهشت 1404 | ||
| نوع مقاله: مقاله پژوهشی | ||
| شناسه دیجیتال (DOI): 10.22051/ijap.2025.49828.1446 | ||
| نویسنده | ||
| سعید انصاری* | ||
| استادیار، گروه علوم مهندسی و فیزیک، مرکز آموزش عالی فنی و مهندسی بوئین‌زهرا، بوئین‌زهرا، ایران | ||
| چکیده | ||
| با وجود اینکه نظریه‌های گوناگونی در مورد ویژگی‌های در حال تعادل یک سامانه کوانتومی وجود دارد، اما رفتار دینامیکی چنین سامانه‌هایی کم‌تر شناخته شده است. نشان داده شده است که انرژی آزاد دینامیکی نقش مهمی در مشخص کردن اثر دینامیک غیرتعادلی در گذار فاز دینامیکی دارد. در حقیقت، وجود تکینگی‌ها در تحول زمانی یک کمیت فیزیکی سبب می‌شود که رفتار دینامیکی سامانه جالب توجه باشد. این رفتار حتی در مورد یک سامانه تک ذره‌ای چون الگوی تنگابست نیز می‌تواند رخ دهد. در این مقاله دینامیک غیرتعادلی شبکه تنگابست یک‌بعدی با شرط مرزی تناوبی ، که تحت‌تأثیر میدان الکتریکی خارجی DC و AC است، با استفاده از مفهوم گذار فاز کوانتومی دینامیکی بررسی می‌شود. اگر سامانه در میدان الکتریکی ثابت قرار داشته باشد، با بهره‌مندی از حل تحلیلی، در ابتدا می‌توان نشان داد که شرط وجود گذار فاز این است که شدت میدان از یک مقدار حدی ضعیف‌تر باشد. سپس، زمان‌های بحرانی گذارفاز دینامیکی سامانه نیز به‌صورت تحیلی قابل پیش‌بینی است. در حضور میدان الکتریکی صرفاً تناوبی افزون بر روش عددی می‌توان برخی از زمان‌های بحرانی را با استفاده از حل تحلیلی مشخص کرد. در حالت کلی که هر دو میدان ثابت و تناوبی وجود دارند، با اینکه مشخص کردن گذار فاز با روش‌های عددی امکان‌پذیر است، اما می‌توان دوره تناوب انرژی آزاد دینامیکی و همچنین ناوردایی آن تحت تبدیل وارونیزمان را به روش تحلیلی نشان داد. | ||
| کلیدواژه‌ها | ||
| الگوی تنگابست؛ سامانه‌‌های دور از تعادل؛ گذارفاز دینامیکی | ||
| عنوان مقاله [English] | ||
| Research Paper:Time Evolution of Tight-Binding Model in the Presence of Electric Field | ||
| نویسندگان [English] | ||
| Saeid Ansari | ||
| Assistant Professor, Department of Engineering Scinece and Physics, Buein Zahra Technical University, Buein Zahra, Iran | ||
| چکیده [English] | ||
| Although many theorems exist about the characteristics of equilibrium quantum systems, the dynamical behavior of out-of-equilibrium systems is far less understood. It is demonstrated that dynamical free energy is important in determining the non-equilibrium dynamic signature in dynamical phase transitions. The presence of singularities in the time evolution of a physical quantity makes the dynamic behavior of the system interesting. This behavior can occur even in the case of a single-particle system such as the tight-binding model. In this paper, we study non-equilibrium dynamics of the one-dimensional tight-binding lattice with periodic boundary conditions under the influence of DC and AC electric fields, utilizing dynamical quantum phase transitions. Given that such a system has an exact non-perturbative solution, we can analytically predict the conditions for the existence of a dynamical phase transition in the presence of various electrical fields, as well as the corresponding critical times. If the system is placed in a constant electric field, utilizing analytical solutions, firstly, we show that the phase transition only occurs when the field strength is weaker than a certain value. Secondly, the critical times of the system's dynamical phase transition can also be analytically predicted. In the presence of a purely periodic electric field, in addition to numerical methods, some of the critical times can be determined analytically. When constant and periodic fields, both, are present, it is possible to show that the periodicity of the dynamical free energy and its invariance under time-reversal transformations. | ||
| کلیدواژه‌ها [English] | ||
| Tight-Binding Model, Non-equilibrium Systems, Dynamical Phase Transition | ||
| مراجع | ||
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[1] Dirac, P.A.M.,"Bakerian lecture-the physical interpretation of quantum mechanics", Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences 180(980), 1-40, 1942. https://doi.org/10.1098/rspa.1942.0023 [2] Bender, C.M. and Boettcher, S., "Real spectra in non-Hermitian Hamiltonians having P T symmetry", Physical review letters 80(24), 5243, 1998. https://doi.org/10.1103/PhysRevLett.80.5243 [3] Bender, C.M., Brody, D.C. and Jones, H.F., "Complex extension of quantum mechanics" Physical review letters 89(27), 270401, 2002. https://doi.org/10.1103/PhysRevLett.89.270401 [4] Bender, C.M., "Making sense of non-Hermitian Hamiltonians" Reports on Progress in Physics 70(6), 947, 2007. https://doi.org/10.1088/0034-4885/70/6/R03 [5] Ashida, Y., Gong, Z. and Ueda, M., "Non-hermitian physics", Advances in Physics 69(3), 249-435, 2020. https://doi.org/10.1080/00018732.2021.1876991 [6] Lee, T.E., "Anomalous edge state in a non-Hermitian lattice", Physical review letters 116(13), 133903, 2016. https://doi.org/10.1103/PhysRevLett.116.133903 [7] Longhi, S., "Topological Phase Transition in non-Hermitian Quasicrystals", Phys. Rev. Lett., 122, 237601, 2019. https://doi.org/10.1103/PhysRevLett.122.237601. [8] Longhi, S., "Phase transitions in a non-Hermitian Aubry-André-Harper model", Phys. Rev. B, 103, 054203, 2021. https://doi.org/10.1103/PhysRevB.103.054203. [9] Yao, S., Song, F., and Wang, Z., "Non-Hermitian Chern Bands", Phys. Rev. Lett., 121, 136802, 2018. https://doi.org/10.1103/PhysRevLett.121.136802. [10] Yang, Z., Zhang, K., Fang, C., and Hu, J., "Non-Hermitian Bulk-Boundary Correspondence and Auxiliary Generalized Brillouin Zone Theory", Phys. Rev. Lett., 125, 226402, 2020. https://doi.org/10.1103/PhysRevLett.125.226402. [11] Lee, C. H. and Thomale, R., "Anatomy of skin modes and topology in non-Hermitian systems", Phys. Rev. B, 99, 201103, 2019. https://doi.org/10.1103/PhysRevB.99.201103. [12] Liu, Y., Wang, Y., Zheng, Z., and Chen, S., "Non-Hermitian mobility edges in one-dimensional quasicrystals with parity-time symmetry", Phys. Rev. B, 103, 134208, 2021. https://doi.org/10.1007/s11433-0211802-4 [13] Helbig, T., Hofmann, T., Imhof, S., Abdelghany, M., Kiessling, T., Molenkamp, L., Lee, C., Szameit, A., Greiter, M., and Thomale, R., "Generalized bulk–boundary correspondence in non-Hermitian topolectrical circuits", NAT. Phys., 16, 747, 2020. https://doi.org/10.1038/s41567-020--09229. [14] Zhang, X-X. and Franz, M., "Non-Hermitian Exceptional Landau Quantization in Electric Circuits", Phys. Rev. Lett., 124, 046401, 2020. https://doi.org/10.1103/PhysRevLett.124.046401. [15] Schomerus, H., "Topologically protected midgap states in complex photonic lattices", Opt. Lett., 38, 1912, 2013., https://doi.org/10.1364/ol.38.001912. [16] Liang, Q., Xie, D., Dong, Z., Li, H., Li, H., Gadway, B., Yi W., and Yan, B., "Dynamic Signatures of Non-Hermitian Skin Effect and Topology in Ultracold Atoms", Phys. Rev. Lett., 129, 070401, 2022. https://doi.org/10.1103/PhysRevLett.129.070401. [17] Li, J., Harter, A. K., Liu, J., de Melo, L., Joglekar, Y. N. and Luo, L., "Observation of parity-time symmetry breaking transitions in a dissipative Floquet system of ultracold atoms", Nat. Commun., 10, 855, 2019. https://doi.org/10.1038/s41467-019-08596-1. [18] Weidemann, S., Kremer, M., Helbig, T., Hofmann, T., Stegmaier, A., Greiter, M., Thomale, R., and Szameit, A., "Topological funneling of light", Science, 368, 311, 2020. https://doi.org/10.1126/science.aaz8727. [19] Zhang, W., Ouyang, X., Huang, X., Wang, X., Zhang, H., Yu Y., Chang, X., Liu, Y., Deng, D-L., and Duan, L-M., "Observation of Non-Hermitian Topology with Nonunitary Dynamics of Solid-State Spins", Phys.Rev. Lett., 127, 090501, 2021. https://doi.org/10.1103/PhysRevLett.127.090501. [20] Akulin, V. M., "Coherent Dynamics of Complex Quantum Systems", Springer-Verlag, Berlin, 2006. [21] Dunlap, D. H. and Kenkre, V. M., "Dynamic localization of a charged particle moving under the influence of an electric field", Phys. Rev. B, 34, 3625, 1986. https://doi.org/10.1103/PhysRevB.34.3625. [22] Grossmann, F., Dittrich, T., Jung, P., and Hänggi, P., "Coherent destruction of tunneling", Phys. Rev. Lett., 67, 516, 1991. https://doi.org/10.1103/PhysRevLett.67.516. [23] Heyl, M., Polkovnikov, A., and Kehrein, S., "Dynamical Quantum Phase Transitions in the Transverse-Field Ising Model", Phys. Rev. Lett., 110, 135704, 2013. https://doi.org/10.1103/PhysRevLett.110.135704. [24] Heyl, M., "Scaling and Universality at Dynamical Quantum Phase Transitions", Phys. Rev. Lett., 115, 140602, 2015. https://doi.org/10.1103/PhysRevLett.115.140602. [25] Budich, J. C. and Heyl, M., "Dynamical topological order parameters far from equilibrium", Phys. Rev. B, 93, 085416, 2016. https://doi.org/10.1103/PhysRevB.93.085416. [26] Huang, Z. and Balatsky, A. V., "Dynamical Quantum Phase Transitions: Role of Topological Nodes in Wave Function Overlaps", Phys. Rev. Lett., 117, 086802, 2016. https://doi.org/10.1103/PhysRevLett.117.086802. [27] Zamani, S., Naji, J., Jafari, R., Langari, A., "Scaling and universality at ramped quench dynamical quantum phase transitions", J. Phys. Condens. Matter, 36, 355401, 2024. https://doi.org/10.1088/1361-648X/ad4df9. [28] Ansari, S., Akbari, A., Jafari, R., "Dynamics of steered quantum coherence and magic resource under sudden quench", Quantum Inf. Process. 23, 212, 2024. https://doi.org/10.1007/s11128-024-04414-w. [29] Jafari, R., Langari, A., Eggert, S., Johannesson, H., "Dynamical quantum phase transitions following a noisy quench", Phys. Rev. B, 109, 180303, 2024. https://doi.org/10.1103/PhysRevB.109.L180303. [30] Ansari, S. and Jafari, R., "One-dimensional p-wave superconductivity with long-range hopping and pairing", Iran. J. Phys. Res, 21, 81, 2021. https://doi.org/10.47176/ijpr.20.2.35211. (in Persian) [31] Ansari, S. and Jafari, R., "Dynamical phase transition in n-cluster spin model", Res. Many. Sys., 9, 29, 2019. https://doi.org/10.22055/jrmbs.2019.14922. (in Persian) [32] Jafari, R., "Quantum phase transition in the one-dimensional extended quantum compass model in a transverse field", Phys. Rev. B, 84, 035112, 2011. https://doi.org/10.1103/PhysRevB.84.035112. [33] Gorin, T., Prosen, T., Seligman, T. H., and Znidaric, M., "Dynamics of Loschmidt echoes and fidelity decay", Phys. Rep., 435, 33, 2006. https://doi.org/10.1016/j.physrep.2006.09.003. [34] Quan, H. T., Song, Z., Liu, X. F., Zanardi, P., and Sun, C. P., "Decay of Loschmidt Echo Enhanced by Quantum Criticality", Phys. Rev. Lett., 96, 140604, 2006. https://doi.org/10.1103/PhysRevLett.96.140604. [35] Jafari, R.and Johannesson, H., "Loschmidt Echo Revivals: Critical and Noncritical", Phys. Rev. Lett., 118, 015701, 2017. https://doi.org/10.1103/PhysRevLett.118.015701. [36] Halimeh, J. C. and Zauner-Stauber, V., "Dynamical phase diagram of quantum spin chains with long-range interactions", Phys. Rev. B, 96, 134427, 2017. https://doi.org/10.1103/PhysRevB.96.134427. [37] Hickey, J. M., "Timescales, dynamical phase transitions and 3rd order phase transitions in the 1d anisotropic XY model", arXiv:1403.5515, 2014. [38] Vajna, S. and Dóra, B., "Disentangling dynamical phase transitions from equilibrium phase transitions", Phys. Rev. B, 89, 161105R, 2014. https://doi.org/10.1103/PhysRevB.89.161105. [39] Lang, J., Frank, B., and Halimeh, J. C., "Dynamical Quantum Phase Transitions: A Geometric Picture", Phys. Rev. Lett., 121, 130603, 2018. https://doi.org/10.1103/PhysRevLett.121.130603. [40] Jafari, R., Johannesson H., Langari, A., Martin-Delgado, M. A., "Quench dynamics and zero-energy modes: The case of the Creutz model", Phys. Rev. B, 99, 054302, 2018. https://doi.org/10.1103/PhysRevB.99.054302. [41] Sharma, S., Suzuki, S., and Dutta, A., "Quenches and dynamical phase transitions in a nonintegrable quantum Ising model", Phys. Rev. B, 92, 104306, 2015. https://doi.org/10.1103/PhysRevB.92.104306. [42] Schmitt, M. and Kehrein, S., "Dynamical quantum phase transitions in the Kitaev honeycomb model", Phys. Rev. B, 92, 075114, 2015. https://doi.org/10.1103/PhysRevB.92.075114. [43] Budich, J. C. and Heyl, M., "Dynamical topological order parameters far from equilibrium", Phys. Rev. B, 93, 085416, 2016. https://doi.org/10.1103/PhysRevB.93.085416. [44] Sharma, S., Divakaran, U., "Polkovnikov A., and Dutta A., Slow quenches in a quantum Ising chain: Dynamical phasetransitions and topology", Phys. Rev. B, 93, 144306, 2016. https://doi.org/10.1103/PhysRevB.93.144306. [45] Peng, Y., Jie, J., Yu, D., and Wang, Y., "Manipulating non-Hermitian skin effect via electric fields", Phys. Rev. B, 106, 161402, 2022. https://doi.org/10.1103/PhysRevB.106.L161402. [45] Graham, R., Schlautmann, M., and Zoller, P., "Dynamical localization of atomic-beam deflection by a modulated standing light wave", Phys. Rev. A, 45, 19, 1992. https://doi.org/10.1103/PhysRevA.45.R19. [46] Waschke, C., Roskos, H., Schwedler, R., Leo, K., Kurz, H., Kohler, K., "Coherent submillimeter-wave emission from Bloch oscillations in a semiconductor superlattice", Phys. Rev. Lett., 70, 3319, 1993. https://doi.org/10.1103/PhysRevLett.70.3319. [47] Faisal, F. H. M. and Kaminski, J. Z., "Generation and control of high harmonics by laser interaction with transmission electrons in a thin crystal", Phys. Rev. A, 54, R1769, 1996. https://doi.org/10.1103/PhysRevA.54.R1769. | ||
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