Transverse single-file diffusion and enhanced longitudinal diffusion near a subcritical bifurcation

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• Quasi-one-dimensional systems of repelling particles are fundamental models in physics.
• Configurational phase transitions are critical phenomena influencing system behavior.
• Understanding particle interactions and confinement effects is key to predicting emergent properties.

Purpose of the Study:

• To investigate the configurational phase transition in a quasi-one-dimensional system of repelling particles.
• To analyze the impact of a decreasing transverse confining potential on system symmetry and stability.
• To explore the effects of subcriticality on thermal motion and diffusion coefficients.

Main Methods:

• Theoretical analysis of a quasi-one-dimensional system with repelling particles.
• Identification of the system's behavior as a subcritical pitchfork bifurcation for short-range interactions.
• Examination of the stability of the homogeneous zigzag pattern within a specific amplitude range [h_{C1},h_{C2}].

Main Results:

• A configurational phase transition occurs, leading to two symmetric staggered raw patterns below a potential threshold.
• The homogeneous zigzag pattern becomes unstable in the range [h_{C1},h_{C2}] due to subcritical pitchfork bifurcation.
• Transverse fluctuations exhibit strongly subdiffusive behavior (similar to single-file diffusion) near bifurcation limits, while longitudinal fluctuations are enhanced (diffusion coefficient more than doubled).

Conclusions:

• The subcriticality of the pitchfork bifurcation significantly affects thermal motions and diffusion.
• A transverse vibrational soft mode is induced near bifurcation thresholds, altering fluctuation dynamics.
• Measuring thermal fluctuations provides a precise method for determining bifurcation thresholds.