Two early-stage inverse power-law dyamics in nonlinear complex systems far-from equilibrium

TL;DR

This paper investigates the non-equilibrium charge carrier dynamics in a tunneling-enhanced percolation network, revealing two distinct inverse power-law relaxation regimes that resemble avalanche phenomena in disordered systems.

Contribution

It introduces the study of early-stage inverse power-law dynamics in a nonlinear complex system, highlighting two regimes and their relation to avalanche-like phenomena.

Findings

Two early-stage inverse power-law relaxations observed

Power-law regime violates Boltzmann's relaxation approximation

Beyond this regime, relaxation becomes exponential and single-scaled

Abstract

We consider the dynamics of the charge carriers in a tunneling-enhanced percolation network, named as a Random Resistor cum Tunneling-bond Network (RRTN), where we allow tunneling in the gap between two randomly thrown nearest neighbour metallic bonds only. Our earlier studies involve the dc and the ac nonlinear response, the percolative aspects, dielectric breakdown, low-temperature variable range hopping (VRH) conduction, etc. in the RRTN. Here we study the non-equilibrium dynamics of the carriers. With two far-from- equilibrium, initial inverse power-law relaxations extending over several decades, the dynamics has a lot of similarities with a wide variety of naturally occuring avalance-like, run-away phenomena in driven, disordered systems with statistically correlated randomness. In the power-law regime, the RRTN violates the Boltzmann's (or Debye) relaxation time approximation strongly. Beyond this regime, the response relaxes exponentially fast (acquires one time-scale) to a steady-state, and thus the relaxation approximation becomes exact.