ON SOLVING COHERENT DYNAMICS EQUATIONS WITH DISCRETE MATHEMATICS METHOD FOR QUANTUM SYSTEMS UNDER LASER EXCITATION

UDC 535.35+535.33+517.925+621.373.8

  • Savva Vadim Alexandrovich – DSc (Physics and Mathematics), Associate Professor, Professor, the Department of Higher Mathematics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: savva@belstu.by kordikova@tut.by

  • Banjak Sary – PhD student, the Department of Higher Mathematics. Belarusian State Technological University (13a, Sverdlova str., 220006, Minsk, Republic of Belarus). E-mail: bnjk_sary@yahoo.com

Key words: coherent laser excitation of quantum systems, Fourier spectra, discrete orthogonal polynomials in Fourier space, exact solutions of differential equations systems.

For 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 ( ) n a t of a quantum system are represented with Fourier images ( ), Fn 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 ( ) n a 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.

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07.04.2020