Driven, underdamped Frenkel-Kontorova model on a quasiperiodic substrate

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Nonlinear dynamics

Background:

• Underdamped dynamics of atomic chains are crucial for understanding friction and transport phenomena.
• Quasiperiodic potentials introduce complex behaviors in driven systems.
• Incommensurate length scales lead to rich phenomena in condensed matter systems.

Purpose of the Study:

• To investigate the conditions under which static friction can be zero in a driven atomic chain system.
• To explore the role of incommensurate length scales and their mathematical relationships on static friction.
• To understand the depinning mechanisms and steady states in such systems.

Main Methods:

• Numerical simulations of underdamped atomic chains.
• Analysis of system dynamics under dc driving force and quasiperiodic substrate potential.
• Theoretical considerations based on standard map theory.

Main Results:

• Zero static friction is achievable when three mutually incommensurate length scales are related by the spiral mean (cubic irrational).
• Static friction remains nonzero for all interaction strengths when length scales are related by the golden mean (quadratic irrational).
• Zero static friction is generally possible for incommensurate ratios, but not for quadratic irrationals or commensurable scales.

Conclusions:

• The mathematical nature of the ratio between length scales dictates the possibility of zero static friction.
• Systems with quadratic irrational or commensurable length scales exhibit always nonzero static friction.
• Depinning mechanisms and steady states are influenced by the interplay of driving force, substrate potential, and interparticle interactions.