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https://elib.belstu.by/handle/123456789/36308
Title: | On solving coherent dynamics equations with discrete mathematics method for quantum systems under laser excitation |
Authors: | Savva, Vadim Alexandrovich Banjak, Sary |
Keywords: | Coherent laser excitation of quantum systems Fourier spectra Discrete orthogonal polynomials Laser excitation когерентное лазерное возбуждение квантовых систем спектры Фурье дискретные ортогональные полиномы лазерное возбуждение |
Issue Date: | 2020 |
Publisher: | БГТУ |
Citation: | Savva, V. A. On solving coherent dynamics equations with discrete mathematics method for quantum systems under laser excitation / V. A. Savva, S. Banjak // Труды БГТУ. Сер. 3, Физико-математические науки и информатика. - Минск : БГТУ, 2020. - № 2 (236). - 12-17. - Bibliogr.: 13 nam. - il. |
Abstract: | Molecular coherent excitation calculations are performed using a simple model of quantum N + 1-levels systems. An exact solution of the corresponding system of differential equations is obtained without their integration. For this, the discrete Fourier transform is applied: the sought-for functions – probability amplitudes a[n](t) of a quantum system are represented with Fourier images F[n] (ω) ,i.e. spectra that are described by some corresponding system of discrete orthogonal polynomials. Fourier spectra are calculated using the polynomials constructed. We find the required a[n](t) by calculating the final sum from 0 to N. Based on a one-to-one correspondence: polynomial characteristics vs equations coefficients, we find all the characteristics of quantum systems, the dynamics of which are described by the obtained solution. The construction of various polynomial systems of a discrete variable makes it possible to obtain solutions for quantum systems with various characteristics, including systems with non-equidistant arrangement of energy levels, which are typical for real molecules. |
URI: | https://elib.belstu.by/handle/123456789/36308 |
Appears in Collections: | выпуск журнала постатейно |
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2. V. A. Savva, S. Banjak.pdf | 624.09 kB | Adobe PDF | View/Open |
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