Global minimization via classical tunneling assisted by collective force field formation

Area of Science:

• Complex systems
• Network dynamics
• Emergent phenomena

Background:

• Simple interacting elements can exhibit complex emergent behaviors like synchronization and phase transitions.
• Many systems can be modeled effectively by reduced models, highlighting universal principles.
• Memristor-based systems offer a platform for exploring novel network dynamics.

Purpose of the Study:

• To demonstrate emergent behavior in a memristor-inspired network model.
• To identify and characterize a novel collective effect driving systems toward global minima.
• To explore the potential applications of this mechanism in computation and optimization.

Main Methods:

• Development of a memristor-inspired network model.
• Analysis of system dynamics under weak and strong driving conditions.
• Interpretation of escape from local minima as an unstable tunneling mechanism.

Main Results:

• Under weak driving, the system dynamics are governed by an effective potential.
• Strong driving induces instabilities, leading to escapes from local minima.
• A collective, nonperturbative effect termed "Lyapunov force" was identified.
• This force effectively steers the system towards the global minimum, irrespective of numerous local minima.

Conclusions:

• The "Lyapunov force" provides a mechanism for navigating complex potential landscapes in driven systems.
• This phenomenon has significant implications for nanoscale physics and device design.
• Potential applications include enhanced optimization algorithms, Monte Carlo methods, and machine learning architectures.