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Methods to Quantify Pharmacologically Induced Alterations in Motor Function in Human Incomplete SCI

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Incomplete Thermalization from Trap-Induced Integrability Breaking: Lessons from Classical Hard Rods.

Xiangyu Cao¹, Vir B Bulchandani¹, Joel E Moore^1,2

¹Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA.

Physical Review Letters

|May 15, 2018

Summary

We studied a 1D hard rod gas in a harmonic potential, finding initial, chaotic, and stationary dynamics. The system shows broken integrability, leading to chaotic behavior and a stationary hydrodynamic state.

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Area of Science:

Statistical Mechanics
Condensed Matter Physics
Nonlinear Dynamics

Background:

Integrable systems offer analytical solutions but lack broad applicability.
Hard rod gases exhibit complex behavior due to strong interparticle interactions.
Harmonic potentials introduce nonuniformity, breaking system integrability.

Purpose of the Study:

Investigate the dynamics of a 1D hard rod gas under a harmonic potential.
Analyze the consequences of broken integrability on particle systems.
Identify distinct dynamical regimes and their characteristics.

Main Methods:

Simulated a one-dimensional gas of hard rods.
Applied a harmonic potential to break integrability.
Analyzed phase-space distribution functions and particle dynamics.
Examined system behavior over a timescale of 10^4 natural units.

Main Results:

Identified three dynamical regimes: initial, chaotic, and stationary.
Observed breakdown of hydrodynamics for finite particle numbers.
Dynamics became chaotic after a characteristic timescale.
System failed to thermalize within the studied timescale.
Time-averaged ensemble reached a stationary hydrodynamic state.

Conclusions:

Broken integrability in 1D hard rod gases leads to complex dynamics.
Chaotic behavior emerges, preventing thermalization over studied timescales.
Stationary states of hydrodynamic evolution are attainable.
Results provide insights for quantum particle systems.