Study on Duality of Wave and Particle of Turbulence Using CML Models

Abstract

A family of coupled map lattice (CML) models has been developed to simulate the evolutional mechanism of interactions of convection, diffusion, and dispersion in both weakly and strongly coupled cases. Not only coherent and turbulent properties as well as their relations, but also the transitional states between convection dominating, diffusion dominating and dispersion dominating are analyzed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. The duality of wave and particle characters of turbulence is illustrated in the numerical simulation; a sketch picture is given to explain the questions associated with the turbulent inverse cascade, which is the result of the mutual interactions among the physical factors of nonlinearity, dissipation and dispersion.

Quantum to Classical Transition by a Classically Small Interaction

“…These investigations stimulate us to explore the quantum-classical transition in condition that the classical motion is almost unaffected. In this paper, we make further investigation on the quantum-classical transition for the models analyzed in [16]. Our results show that the quantum-classical transition persists by decreasing the mass of the second KR, and at the same time, decreasing the effective Planck's constant and the interaction strength proportionally.…”

“…The system analyzed in [15] consists of two particles with very different masses, in which the particle of very small mass possesses little energy to affect the classical motion of the other one of larger mass. In a recent paper, [16] we showed that the coupling with a particle of very small mass can destroy dynamical localization of KR. The quantum-classical transition happens as the coupling strength increases.…”