Condition of Correspondence between Quantum and Classical Dynamics for a Chaotic System

1996 ◽  
Vol 76 (3) ◽  
pp. 340-343 ◽  
Author(s):  
A. R. Kolovsky
Keyword(s):  
Chaotic System ◽  
Classical Dynamics

Quantum simulations

2017 ◽  
Author(s):  
Michael P. Allen ◽  
Dominic J. Tildesley
Keyword(s):  
Ab Initio ◽  
Quantum Monte Carlo ◽  
Degrees Of Freedom ◽  
Small Region ◽  
Time Correlation ◽  
Ab Initio Molecular Dynamics ◽  
Classical Dynamics ◽  
Integral Methods ◽  
Quantum Time ◽  
Low Mass

This chapter covers the introduction of quantum mechanics into computer simulation methods. The chapter begins by explaining how electronic degrees of freedom may be handled in an ab initio fashion and how the resulting forces are included in the classical dynamics of the nuclei. The technique for combining the ab initio molecular dynamics of a small region, with classical dynamics or molecular mechanics applied to the surrounding environment, is explained. There is a section on handling quantum degrees of freedom, such as low-mass nuclei, by discretized path integral methods, complete with practical code examples. The problem of calculating quantum time correlation functions is addressed. Ground-state quantum Monte Carlo methods are explained, and the chapter concludes with a forward look to the future development of such techniques particularly to systems that include excited electronic states.

Dynamics, Synchronization and Electronic Implementations of a New Lorenz-like Chaotic System with Nonhyperbolic Equilibria

2019 ◽  
Vol 29 (14) ◽  
pp. 1950197 ◽  
Author(s):  
P. D. Kamdem Kuate ◽  
Qiang Lai ◽  
Hilaire Fotsin
Keyword(s):  
Chaotic System ◽  
Chaotic Systems ◽  
Lorenz System ◽  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Period Doubling ◽  
Adaptive Synchronization ◽  
The Novel ◽  
Algebraic Equations ◽  
The Lorenz System

The Lorenz system has attracted increasing attention on the issue of its simplification in order to produce the simplest three-dimensional chaotic systems suitable for secure information processing. Meanwhile, Sprott’s work on elegant chaos has revealed a set of 19 chaotic systems all described by simple algebraic equations. This paper presents a new piecewise-linear chaotic system emerging from the simplification of the Lorenz system combined with the elegance of Sprott systems. Unlike the majority, the new system is a non-Shilnikov chaotic system with two nonhyperbolic equilibria. It is multiplier-free, variable-boostable and exclusively based on absolute value and signum nonlinearities. The use of familiar tools such as Lyapunov exponents spectra, bifurcation diagrams, frequency power spectra as well as Poincaré map help to demonstrate its chaotic behavior. The novel system exhibits inverse period doubling bifurcations and multistability. It has only five terms, one bifurcation parameter and a total amplitude controller. These features allow a simple and low cost electronic implementation. The adaptive synchronization of the novel system is investigated and the corresponding electronic circuit is presented to confirm its feasibility.

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