Very Persistent Random Walkers Reveal Transitions in Landscape Topology

Area of Science:

• Statistical Mechanics
• Disordered Systems
• Complex Systems

Background:

• Understanding the behavior of random walkers is crucial in statistical mechanics.
• Mean-field disordered systems exhibit complex energy landscapes.
• Ergodicity breaking and dynamical glass transitions are key phenomena in these systems.

Purpose of the Study:

• To investigate the behavior of random walkers on the microcanonical configuration space of mean-field disordered systems.
• To analyze the role of persistence in random walks within these systems.
• To explore the relationship between ergodicity-breaking transitions and the topology of configuration space.

Main Methods:

• Studying passive and persistent random walks.
• Analyzing the microcanonical configuration space.
• Investigating models with well-understood energy landscapes.
• Examining the limit of infinite persistence time.

Main Results:

• Passive walks show an ergodicity-breaking transition at the dynamical glass transition energy density.
• Persistent walks remain ergodic at lower energies.
• In specific models, the ergodicity-breaking transition coincides with a topological transition in configuration space.

Conclusions:

• A correspondence between ergodicity-breaking and topological transitions is proposed.
• This correspondence can be used to determine topological transition energy in ambiguous cases.
• The findings offer insights into the nature of disordered systems and random walks.