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Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium.
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The physical form of a substance changes on changing its temperature. For example, raising the temperature of a liquid causes the liquid to vaporize (convert into vapor). The process is called vaporization—a surface phenomenon. Vaporization occurs when the thermal motion of the molecules overcome the intermolecular forces, and the molecules (at the surface) escape into the gaseous state. When a liquid vaporizes in a closed container, gas molecules cannot escape. As these gas phase...
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In convection, thermal energy is carried by the large-scale flow of matter. Ocean currents and large-scale atmospheric circulation, which result from the buoyancy of warm air and water, transfer hot air from the tropics toward the poles and cold air from the poles toward the tropics. The Earth’s rotation interacts with those flows, causing the observed eastward flow of air in the temperate zones. Convection dominates heat transfer by air, and the amount of available space for the airflow...
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Thermalization of Interacting Quasi-One-Dimensional Systems.

Miłosz Panfil1, Sarang Gopalakrishnan2,3, Robert M Konik4

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|February 10, 2023
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This summary is machine-generated.

Weak interchain couplings drive thermalization in integrable quasi-one-dimensional systems. A new Boltzmann-equation approach reveals a broad spectrum of relaxation timescales, showing nonexponential approaches to equilibrium in coupled Bose gases.

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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.