najoNanosystems: Physics, Chemistry, MathematicsНаносистемы: физика, химия, математика2220-80542305-7971Университет ИТМО10.17586/2220-8054-2024-15-4-457-464najo-36Research ArticlePHYSICSФИЗИКАFast forward problem for adiabatic quantum dynamics: Estimation of the energy cost.Ускорения эволюции адиабатической квантовой динамики: Оценка энергетической стоимостиhttps://orcid.org/0000-0001-5741-9003МатрасуловЖ. Д.MatrasulovJ. D.

J. D. Matrasulov –  Faculty of Physics

Vuzgorodok, Tashkent 100174

Institute of Fundamental and Applied Research

Kori Niyoziy 39, Tashkent 100000

jasur1362@gmail.comhttps://orcid.org/0000-0003-1758-6805ЮсуповЖ. Р.YusupovJ. R.

R. Yusupov – Kimyo International University in Tashkent

156 Usman Nasyr Str., 100121, Tashkent

Faculty of Physics

Vuzgorodok, Tashkent 100174

j.yusupov@ytit.uzhttps://orcid.org/0000-0002-6642-5488МатякубовХ. Ш.MatyokubovKh. Sh.

Kh. Sh. Matyokubov

1 Gurlan str., 220100, Urgench; 14 H. Olimjon Str., 220100, Urgench

hikmat.shuhratovich@gmail.comNational University of Uzbekistan; National Research University TIIAMEUzbekistanNational University of UzbekistanUzbekistanUrgench State Pedagogical Institute; Urgench State UniversityUzbekistan202431052025154457464Copyright © Matrasulov J.D., Yusupov J.R., Matyokubov K.S., 20252025Матрасулов Ж.Д., Юсупов Ж.Р., Матякубов Х.Ш.Matrasulov J.D., Yusupov J.R., Matyokubov K.S.This work is licensed under a Creative Commons Attribution 4.0 License.https://nanojournal.ifmo.ru/jour/article/view/36

We consider the problem of energy cost needed for acceleration (deceleration) of the evolution of a quantum system using the Masuda–Nakamura’s fast forward protocol. In particular, we focus on dynamics by considering models for a quantum box with a moving wall and harmonic oscillator with time-dependent frequency. For both models we computed the energy needed for acceleration (deceleration) as a function of time. The results obtained are compared with those of other acceleration (deceleration) protocols.

Рассматривается задача о затратах энергии, необходимой для ускорения (замедления) эволюции квантовой системы с использованием протокола быстрой перемотки Масуда-Накамуры. В частности, мы фокусируемся на динамике, рассматривая модели квантового ящика с движущейся стенкой и гармонического осциллятора с зависящей от времени частотой. Для обеих моделей мы рассчитали энергию, необходимую для ускорения (замедления) в зависимости от времени. Полученные результаты сравниваются с результатами других протоколов ускорения (замедления).

Кратчайшие пути к адиабатичностиадиабатическая квантовая динамикаУравнение Шрёдингераenergetic costshortcuts to adiabaticitystatistical physics and thermodynamicsThis work is supported by the grant of the Agency of Innovative Development of the Republic of Uzbekistan, World Bank Project “Modernizing Uzbekistan National Innovation System” (Ref. Nr. REP-05032022/235).ReferencesMasuda S. and Nakamura K. Fast-forward problem in quantum mechanics. Phys. Rev. A, 2008, 78, P. 062108.Masuda S. and Nakamura K. Fast-forward problem in quantum mechanics. Phys. Rev. A, 2008, 78, P. 062108.Masuda S. and Nakamura K. Fast-forward of adiabatic dynamics in quantum mechanics. Proc. R. Soc. A, 2010, 466, P. 1135.Masuda S. and Nakamura K. Fast-forward of adiabatic dynamics in quantum mechanics. Proc. R. Soc. A, 2010, 466, P. 1135.Masuda S. and Nakamura K. Acceleration of adiabatic quantum dynamics in electromagnetic fields. Phys. Rev. A, 2011, 84, P. 043434.Masuda S. and Nakamura K. Acceleration of adiabatic quantum dynamics in electromagnetic fields. Phys. Rev. A, 2011, 84, P. 043434.Khujakulov A. and Nakamura K. Scheme for accelerating quantum tunneling dynamics. Phys. Rev. A, 2016, 93, P. 022101.Khujakulov A. and Nakamura K. Scheme for accelerating quantum tunneling dynamics. Phys. Rev. A, 2016, 93, P. 022101.I. Setiawan, Bobby Eka Gunara, S. Masuda and K. Nakamura. Fast forward of the adiabatic spin dynamics of entangled states. Phys. Rev. A, 2017, 96, P. 052106.I. Setiawan, Bobby Eka Gunara, S. Masuda and K. Nakamura. Fast forward of the adiabatic spin dynamics of entangled states. Phys. Rev. A, 2017, 96, P. 052106.Nakamura K., Khujakulov A., Avazbaev S. and Masuda S. Fast forward of adiabatic control of tunneling states. Phys. Rev.A, 2017, 95, P. 062108.Nakamura K., Khujakulov A., Avazbaev S. and Masuda S. Fast forward of adiabatic control of tunneling states. Phys. Rev.A, 2017, 95, P. 062108.Babajanova G., Matrasulov J., Nakamura K. Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of state. Phys. Rev. E, 2018, 97, P. 042104.Babajanova G., Matrasulov J., Nakamura K. Quantum gas in the fast forward scheme of adiabatically expanding cavities: Force and equation of state. Phys. Rev. E, 2018, 97, P. 042104.Nakamura K., Matrasulov J., and Izumida Y. Fast-forward approach to stochastic heat engine. Phys. Rev. E, 2020, 102, P. 012129.Nakamura K., Matrasulov J., and Izumida Y. Fast-forward approach to stochastic heat engine. Phys. Rev. E, 2020, 102, P. 012129.Matrasulov J., Yusupov J.R., Saidov A.A. Fast forward evolution in heat equation: Tunable heat transport in adiabatic regime, Nanosystems: Physics, Chemistry, Mathematics, 2023, 14, P. 421–427.Matrasulov J., Yusupov J.R., Saidov A.A. Fast forward evolution in heat equation: Tunable heat transport in adiabatic regime, Nanosystems: Physics, Chemistry, Mathematics, 2023, 14, P. 421–427.Setiawan I., Sugihakim R., Gunara B.E., Masuda S., Nakamura K. Fast-forward generation of non-equilibrium steady states of a charged particle under the magnetic field. Progress of Theoretical and Experimental Physics, 2023, 2023, 063A04.Setiawan I., Sugihakim R., Gunara B.E., Masuda S., Nakamura K. Fast-forward generation of non-equilibrium steady states of a charged particle under the magnetic field. Progress of Theoretical and Experimental Physics, 2023, 2023, 063A04.Zheng Y., Campbell S., De Chiara G., Poletti D. Cost of counterdiabatic driving and work output. Phys. Rev. A, 2016, 94, P. 042132.Zheng Y., Campbell S., De Chiara G., Poletti D. Cost of counterdiabatic driving and work output. Phys. Rev. A, 2016, 94, P. 042132.Obinna Abah, Ricardo Puebla, Anthony Kiely, Gabriele De Chiara, Mauro Paternostro and Steve Campbell. Energetic cost of quantum control protocols. New J. Phys., 2019, 21, P. 103048.Obinna Abah, Ricardo Puebla, Anthony Kiely, Gabriele De Chiara, Mauro Paternostro and Steve Campbell. Energetic cost of quantum control protocols. New J. Phys., 2019, 21, P. 103048.Chen X., et al. Fast Optimal Frictionless Atom Cooling in Harmonic Traps: Shortcut to Adiabaticity. Phys. Rev. Lett., 2010, 104, P. 063002.Chen X., et al. Fast Optimal Frictionless Atom Cooling in Harmonic Traps: Shortcut to Adiabaticity. Phys. Rev. Lett., 2010, 104, P. 063002.Gu´ery-Odelin D., Ruschhaup A., Kiel A., Torrontegui E., Mart´ınez-Garaot S., Muga J.G. Shortcuts to adiabaticity: Concepts, methods, and applications. Rev. Mod. Phys., 2019, 91, P. 045001.Gu´ery-Odelin D., Ruschhaup A., Kiel A., Torrontegui E., Mart´ınez-Garaot S., Muga J.G. Shortcuts to adiabaticity: Concepts, methods, and applications. Rev. Mod. Phys., 2019, 91, P. 045001.Erik Torrontegui, et al. Chapter 2 Shortcuts to Adiabaticity. Advances in atomic, molecular, and optical physics, 2013, 62, P. 117.Erik Torrontegui, et al. Chapter 2 Shortcuts to Adiabaticity. Advances in atomic, molecular, and optical physics, 2013, 62, P. 117.Martınez-Garaot S., et al. Vibrational Mode Multiplexing of Ultracold Atoms. Phys. Rev. Lett., 2013, 111, P. 213001.Martınez-Garaot S., et al. Vibrational Mode Multiplexing of Ultracold Atoms. Phys. Rev. Lett., 2013, 111, P. 213001.A. del Campo. Shortcuts to Adiabaticity by Counterdiabatic Driving. Phys. Rev. Lett., 2013, 111, P. 100502.A. del Campo. Shortcuts to Adiabaticity by Counterdiabatic Driving. Phys. Rev. Lett., 2013, 111, P. 100502.Demirplak M., Rice S.A. Adiabatic Population Transfer with Control Fields. J. Phys. Chem. A., 2003, 107, P. 9937.Demirplak M., Rice S.A. Adiabatic Population Transfer with Control Fields. J. Phys. Chem. A., 2003, 107, P. 9937.Berry M.V. Transitionless quantum driving. Journal of Physics A: Mathematical and Theoretical, 2009, 42, P. 365303.Berry M.V. Transitionless quantum driving. Journal of Physics A: Mathematical and Theoretical, 2009, 42, P. 365303.Christopher Jarzynski, Sebastian Deffner, Ayoti Patra, and Yiˇgit Subas¸ı. Fast forward to the classical adiabatic invariant. Phys. Rev. E, 2017, 95, P. 032122.Christopher Jarzynski, Sebastian Deffner, Ayoti Patra, and Yiˇgit Subas¸ı. Fast forward to the classical adiabatic invariant. Phys. Rev. E, 2017, 95, P. 032122.

The authors declare that there are no conflicts of interest present.