AN EFFICIENT ALGORITHM FOR THE COMPUTATION OF RICCATI DIFFERENTIAL EQUATIONS

2021 ◽  
Vol 21 (1) ◽  
pp. 241
Author(s):  
Pius Tumba ◽  
Sunday J ◽  
Kwanamu J ◽  
Andest J ◽  
El M
Keyword(s):  
Differential Equations ◽  
Efficient Algorithm ◽  
Riccati Differential Equations

scholarly journals CANONICAL FORM OF THE EVOLUTION OPERATOR OF A TIME-DEPENDENT HAMILTONIAN IN THE THREE LEVEL SYSTEM

2011 ◽  
Vol 08 (03) ◽  
pp. 647-655
Author(s):  
KAZUYUKI FUJII
Keyword(s):  
Differential Equations ◽  
Canonical Form ◽  
Evolution Operator ◽  
Time Dependent ◽  
Level System ◽  
Riccati Differential Equations

In this paper we study the evolution operator of a time-dependent Hamiltonian in the three level system. The evolution operator is based on SU(3) and its dimension is eight, so we obtain three complex Riccati differential equations interacting with one another (which have been obtained by Fujii and Oike) and two real phase equations. This is a canonical form of the evolution operator.

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