Thermalization of Interacting Quasi-One-Dimensional Systems

Area of Science:

• Statistical Mechanics
• Quantum Gases
• Condensed Matter Physics

Background:

• Many experimental systems feature quasi-one-dimensional structures with strong intrachain and weak interchain interactions.
• Integrable intrachain interactions necessitate interchain coupling for system thermalization.

Purpose of the Study:

• To develop a Boltzmann-equation formalism for asymptotically exact collision integrals in interacting integrable systems.
• To quantitatively model relaxation dynamics in the Newton's cradle setup of coupled Bose gases.

Main Methods:

• Development of a Boltzmann-equation formalism with an asymptotically exact collision integral.
• Application to analyze relaxation in coupled Bose-Einstein condensates (Newton's cradle).

Main Results:

• Identified a broad spectrum of timescales governing the relaxation process.
• Provided evidence that the late-time Markov process is gapless.
• Demonstrated generally nonexponential approaches to equilibrium, even for uniform perturbations.

Conclusions:

• The developed formalism accurately describes relaxation in coupled integrable systems.
• Nonexponential relaxation is a characteristic feature due to the gapless nature of the late-time dynamics.
• Findings are crucial for understanding thermalization in quasi-one-dimensional quantum systems.