Description of the Simplest Non-Markov Process Using a Differential Equation for the Quantum State Vector
- Авторлар: Ozhigov Y.I.1,2, Victorova N.B.3
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Мекемелер:
- Lomonosov Moscow State University
- Valiev Institute of Physics and Technology of the Russian Academy of Sciences
- Russian State University for the Humanities
- Шығарылым: Том 10, № 2 (2023)
- Беттер: 9-15
- Бөлім: MATHEMATICAL MODELING, NUMERICAL METHODS AND COMPLEX PROGRAMS
- URL: https://journals.eco-vector.com/2313-223X/article/view/568050
- DOI: https://doi.org/10.33693/2313-223X-2023-10-2-9-15
- EDN: https://elibrary.ru/AIXNRU
- ID: 568050
Дәйексөз келтіру
Аннотация
The Jaynes–Cummings model with one atom and a photon is considered. A photon leaks out of the cavity (optical resonator). An atom can be in an excited and ground state. Usually, the dynamics of the probability of finding a photon in a cavity is considered using the basic quantum Lindblad equation, in which the density matrix acts as an unknown function. The Lindblad equation describes a quantum Markov random process. The article attempts to replace the equation from the density matrix with an ersatz of the Lindblad equation, which is a differential equation from the state wave vector. The quantum master equation involves the use of a matrix with a dimension equal to the dimension of the state space, which increases the complexity of the calculations, since it requires a quadratically large memory. For example, for the dimension of the main space equal to a billion, the memory required to solve the basic quantum equation will be about a quintillion, which is a problem even for supercomputers. Whereas a billion-long column fits easily into the memory of a personal computer and can be easily processed on a personal laptop. The ersatz of the quantum master equation, which we are constructing, cannot accurately describe the dynamics of the density matrix and therefore cannot serve as an exact replacement for the quantum master equation. Our ersatz will describe a special process of exchange with the environment.
Толық мәтін
Авторлар туралы
Yuri Ozhigov
Lomonosov Moscow State University; Valiev Institute of Physics and Technology of the Russian Academy of Sciences
Хат алмасуға жауапты Автор.
Email: ozhigov@cs.msu.ru
Doctor of Physics and Mathematics; Professor at the Department of Supercomputers and Quantum Informatics of the Faculty of Computational Mathematics and Cybernetics of the Lomonosov Moscow State University; leading researcher at the Valiev Institute of Physics and Technology of Russian Academy of Sciences
Ресей, Moscow; MoscowNadezda Victorova
Russian State University for the Humanities
Email: nbvictorova@list.ru
Candidate of Physics and Mathematics; associated professor at the Department of Fundamental and Applied Mathematics of the Faculty of Information Systems and Security of the Institute of IT and Security Technologies of the Russian State University for the Humanities
Ресей, MoscowӘдебиет тізімі
- Ozhigov Yu., You J. Description of the non-Markovian dynamics of atoms in terms of a pure state. Computational Mathematics and Modeling. 2023. URL: https://arxiv.org/pdf/2305.00564.pdf
- Jaynes E.T., Cummings F.W. Comparison of quantum and semiclassical radiation theories with application to the beam maser. Proc. IEEE. 1963. Vol. 51. No. 1. Pp. 89–109. DOI: 1.0.1109/PROC.1963.1664
- Cummings F.W. Reminiscing about thesis work with E.T. Jaynes at Stanford in the 1950s. Journal of Physics B: Atomic, Molecular and Optical Physics. 2013. Vol. 46. No. 22. P. 220202(3pp). doi: 10.1088/0953-4075/46/22/220202
- Ozhigov Y. Quantum computer. Moscow: Max Press, 2020. 172 p. ISBN: 9788-5-317-06405-7
- Scovoroda N.A., Ozhigov Yu.I., Victorova N.B. Quantum revivals of a non-rabi type in a Jaynes–Cummings model. Theoretical and Mathematical Physics. 2016. No. 189 (2). Pp. 1673–1679.
- Viktorova N., Ozhigov Yu.I., Skovoroda N.A., Skurat K.N. Analytical solution of the quantum master equation for the Jaynes–Cummings model. Computational Mathematics and Modeling. 2019. Vol. 30. No. 1. Pp. 68–79. URL: https://rdcu.be/bfRRR