Dynamical mean-field solution of coupled quantum wells: a bifurcation analysis

Area of Science:

• Quantum mechanics
• Nonlinear dynamics
• Computational physics

Background:

• Discrete models of quantum systems are crucial for understanding complex phenomena.
• Quantum wells exhibit rich dynamical behavior influenced by electrostatic interactions.
• Characterizing chaos in quantum systems is essential for theoretical advancements.

Purpose of the Study:

• To analyze the time evolution of a discrete model of three quantum wells.
• To investigate the role of localized mean-field electrostatic interaction on system dynamics.
• To explore chaotic behavior using numerical simulation and bifurcation techniques.

Main Methods:

• Numerical simulation of the discrete Schrödinger equation.
• Application of bifurcation theory to identify dynamical organizing centers.
• Analysis of frequency spectrum and Lyapunov exponents to detect chaos.
• Investigation of rotating periodic solutions and their bifurcations.

Main Results:

• The discrete model exhibits chaotic behavior, similar to its continuum counterpart.
• Bifurcations of rotating periodic solutions act as organizing centers for the dynamics.
• Subharmonic bifurcations lead to the emergence of nonsymmetric periodic solutions.
• A novel bifurcation involving characteristic multipliers splitting from the unit circle was identified.
• The system's chaotic behavior is directly linked to its nonintegrability.

Conclusions:

• The discrete three-quantum-well model demonstrates complex, chaotic dynamics.
• Bifurcation analysis provides a framework for understanding the organizing principles of this chaos.
• The findings contribute to the understanding of chaos in discrete quantum systems.