Partially asymmetric exclusion models with quenched disorder

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Non-equilibrium Systems

Background:

• The one-dimensional partially asymmetric exclusion process models systems with interacting particles and directional bias.
• Random variations in particle hopping rates introduce disorder, significantly impacting system dynamics.
• Understanding particle transport under disorder is crucial for various physical phenomena.

Purpose of the Study:

• To investigate the impact of random hopping rates on particle transport in a 1D partially asymmetric exclusion process.
• To precisely determine the dynamical exponent (z) governing particle displacement over time.
• To explore the relationship between particlewise and sitewise disorder in this system.

Main Methods:

• Utilizing extreme value statistics to analyze particle behavior.
• Employing an asymptotically exact strong disorder renormalization group method.
• Calculating the dynamical exponent for particlewise disorder (z(PW)).

Main Results:

• The accumulated particle distance (x) scales with time (t) as x ~ t(1/z), with z > 0.
• The dynamical exponent for particlewise disorder, z(PW), was exactly calculated.
• A relationship z(SW) = z(PW)/2 was established for sitewise disorder.
• In the symmetric case (zero drift), ultraslow, logarithmic diffusion was observed.

Conclusions:

• Random hopping rates lead to anomalous diffusion characterized by a dynamical exponent.
• The renormalization group method provides an exact solution for the disordered exclusion process.
• The findings offer insights into transport phenomena in disordered non-equilibrium systems.