Markovian approximation in a coarse-grained description of atomic systems

Area of Science:

• * Computational physics
• * Statistical mechanics
• * Physical chemistry

Background:

• * The Markovian assumption, neglecting memory effects, is fundamental in coarse-graining theories.
• * Coarse-graining simplifies complex systems by focusing on larger-scale dynamics.

Purpose of the Study:

• * To investigate the impact of different inter-oscillator potentials on the coarse-graining dynamics of a 1D chain.
• * To determine whether the Markovian assumption holds for harmonic versus nonlinear potentials.

Main Methods:

• * Theoretical analysis of a one-dimensional chain of oscillators grouped into clusters.
• * Examination of dynamics under Hookean spring interactions.
• * Examination of dynamics under nonlinear Lennard-Jones type potentials.

Main Results:

• * Coarse-graining with Hookean springs results in non-Markovian cluster dynamics.
• * Coarse-graining with Lennard-Jones potentials leads to Markovian cluster dynamics.
• * Persistence of sound waves in the harmonic case, suppressed in the nonlinear case, explains the differing behaviors.

Conclusions:

• * The nature of inter-oscillator interactions critically affects the validity of the Markovian assumption in coarse-graining.
• * Nonlinear potentials are more amenable to Markovian descriptions in coarse-grained models of oscillator chains.