title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð´Ð²Ð¾Ð¹Ð½Ð¾Ð³Ð¾ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÑÐ¾Ð³Ð¾ ÑÐµÐ·Ð¾Ð½Ð°Ð½ÑÐ° Ð² ÑÑÑÑ ÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ðµ
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of a program for modeling double parametric resonance in a three-level quantum system
Creators: name: Ð¥Ð»Ð¾Ð±ÑÑÑÐ¾Ð², ÐÐ²Ð°Ð½
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2024
Subjects: Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
Fortran
Python
Ð´Ð²Ð¾Ð¹Ð½Ð¾Ð¹ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ·Ð¾Ð½Ð°Ð½Ñ
Ð¼ÐµÑÐ¾Ð´ ÑÑÐ°Ð¿ÐµÑÐ¸Ð¹
modeling
double parametric resonance
trapezoid method

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐµÐ¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°ÑÑ Ð´Ð²Ð¾Ð¹Ð½Ð¾Ð¹ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ·Ð¾Ð½Ð°Ð½Ñ Ð² ÑÑÑÑÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ðµ. ÐÑÐ¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½Ð¸Ð¸ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð¸ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ Ð¼ÐµÑÐ¾Ð´Ñ Ð½Ð° ÑÐµÑÑÐ¾Ð²Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ðµ Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹. ÐÐ»Ñ Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ»Ð¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð½Ð° ÑÐ·ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ fortran Ð´Ð»Ñ ÐºÐ°Ð¶Ð´Ð¾Ð³Ð¾ Ð¼ÐµÑÐ¾Ð´Ð°. ÐÐ¾ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÐ°Ð¼ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ð±ÑÐ» Ð²ÑÐ±ÑÐ°Ð½ Ð¼ÐµÑÐ¾Ð´ ÑÑÐ°Ð¿ÐµÑÐ¸Ð¹. ÐÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð° Ð´Ð»Ñ Ð¼ÐµÑÐ¾Ð´Ð° ÑÑÐ°Ð¿ÐµÑÐ¸Ð¸ Ð² Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐ¼ Ð±ÑÐ»Ð° Ð¼Ð¾Ð´Ð¸ÑÐ¸ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð° Ð´Ð»Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸Ñ Ñ ÐºÐ¾Ð¼Ð¿Ð»ÐµÐºÑÐ½ÑÐ¼Ð¸ ÑÐ¸ÑÐ»Ð°Ð¼Ð¸. ÐÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð½Ð° Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸, Ð¿ÑÐ¸Ð±Ð»Ð¸Ð¶ÐµÐ½Ð½Ð¾Ð¹ Ðº Ð¿Ð¾ÑÑÐ°Ð½Ð¾Ð²Ð¾ÑÐ½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐµ, Ð½Ð¾ Ð¸Ð¼ÐµÑÑÐµÐ¹ ÑÑÐ°Ð»Ð¾Ð½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ, Ð´Ð»Ñ Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐ¹ Ð´Ð¾ÑÐ°Ð±Ð¾ÑÐºÐ¸ Ñ ÑÐµÐ»ÑÑ ÑÐµÑÐµÐ½Ð¸Ñ Ð¾ÑÐ½Ð¾Ð²Ð½Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸. Ð¢Ð°Ðº Ð¶Ðµ Ð² ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ»Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ð° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð° Ð½Ð° ÑÐ·ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python, ÐºÐ¾ÑÐ¾ÑÐ°Ñ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÐ»Ð° Ð¾Ð±ÑÐ°Ð±Ð°ÑÑÐ²Ð°ÑÑ, Ð¿Ð¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð² ÑÐµÐºÑÑÐ¾Ð²Ð¾Ð¼ Ð²Ð¸Ð´Ðµ, Ð´Ð»Ñ Ð³ÑÐ°ÑÐ¸ÑÐµÑÐºÐ¾Ð³Ð¾ Ð¿ÑÐµÐ´ÑÑÐ°Ð²Ð»ÐµÐ½Ð¸Ñ ÑÐµÑÐµÐ½Ð¸Ð¹. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð¼ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÑÑÑÑ Ð´Ð²Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð½Ð° ÑÐ·ÑÐºÐ°Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Fortran Ð¸ Python, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°ÑÑ Ð´Ð²Ð¾Ð¹Ð½Ð¾Ð¹ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¸ÑÐµÑÐºÐ¸Ð¹ ÑÐµÐ·Ð¾Ð½Ð°Ð½Ñ Ð² ÑÑÑÑÑÑÐ¾Ð²Ð½ÐµÐ²Ð¾Ð¹ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¹ ÑÐ¸ÑÑÐµÐ¼Ðµ.
description: This work is devoted to the development of programs that allow the simulation of double parametric resonance in a three-level quantum system. During the execution of the work, a study of methods was carried out on a test system of differential equations. To carry out the research, programs in the fortran programming language were developed for each method. According to the results of the study, the trapezoid method was chosen. The program for the trapezoid method was later modified for use with complex numbers. A study was conducted on a mathematical model that is close to the posed problem, but has a reference solution, for further refinement in order to solve the main problem. Also, in the course of the work, a program was developed in the Python programming language, which allowed processing the results in text form for graphical representation of solutions. The result of this work are two programs in the programming languages Fortran and Python, which allow you to simulate a double parametric resonance in a three-level quantum system.