Thermal equilibration in infinite harmonic crystals View Full Text


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Article Info

DATE

2019-03-12

AUTHORS

Vitaly A. Kuzkin

ABSTRACT

We study transient thermal processes in infinite harmonic crystals having a unit cell with an arbitrary number of particles. Initially, particles have zero displacements and random velocities such that spatial distribution of temperature is uniform. Initial kinetic and potential energies are different and therefore the system is far from thermal equilibrium. Time evolution of kinetic temperatures, corresponding to different degrees of freedom of the unit cell, is investigated. It is shown that the temperatures oscillate in time and tend to generally different equilibrium values. The oscillations are caused by two physical processes: equilibration of kinetic and potential energies and redistribution of temperature among degrees of freedom of the unit cell. An exact formula describing these oscillations is obtained. At large times, a crystal approaches thermal equilibrium, i.e., a state in which the temperatures are constant in time. A relation, referred to as the non-equipartition theorem, between equilibrium values of the temperatures and initial conditions is derived. For illustration, transient thermal processes in a diatomic chain and graphene lattice are considered. Analytical results are supported by numerical solution of lattice dynamics equations. More... »

PAGES

1-23

References to SciGraph publications

  • 2011-12. Discrete breathers in deformed graphene in JETP LETTERS
  • 1977-06. Stationary non-equilibrium states of infinite harmonic systems in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2018-12. Slow thermal equilibration in methylammonium lead iodide revealed by transient mid-infrared spectroscopy in NATURE COMMUNICATIONS
  • 2019. The Ballistic Heat Equation for a One-Dimensional Harmonic Crystal in CLIMATE CHANGE AND COASTAL RESOURCES IN TANZANIA
  • 2018-02-28. One-Dimensional Heat Conduction and Entropy Production in ADVANCES IN MECHANICS OF MICROSTRUCTURED MEDIA AND STRUCTURES
  • 2006-08. Macroscopic Behavior of Microscopic Oscillations in Harmonic Lattices via Wigner-Husimi Transforms in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2017-02. High-frequency thermal processes in harmonic crystals in DOKLADY PHYSICS
  • 1986-05. One-dimensional harmonic lattice caricature of hydrodynamics in JOURNAL OF STATISTICAL PHYSICS
  • 1975. Time evolution and ergodic properties of harmonic systems in DYNAMICAL SYSTEMS, THEORY AND APPLICATIONS
  • 2015-09. Heat transfer in infinite harmonic one-dimensional crystals in DOKLADY PHYSICS
  • 2014-09. Energy oscillations in a one-dimensional crystal in DOKLADY PHYSICS
  • 2017-03. Transverse discrete breathers in unstrained graphene in THE EUROPEAN PHYSICAL JOURNAL B
  • 2019-01. Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply in CONTINUUM MECHANICS AND THERMODYNAMICS
  • 1969-09. Entropy, information theory, and the approach to equilibrium of coupled harmonic oscillator systems in JOURNAL OF STATISTICAL PHYSICS
  • 2017-05. An analytical description of transient thermal processes in harmonic crystals in PHYSICS OF THE SOLID STATE
  • 2015. Linear Oscillations of Suspended Graphene in SHELL AND MEMBRANE THEORIES IN MECHANICS AND BIOLOGY
  • 1983-01. Convergence to stationary states for infinite harmonic systems in JOURNAL OF STATISTICAL PHYSICS
  • 2017-07. Localized heat perturbation in harmonic 1D crystals: Solutions for the equation of anomalous heat conduction in PHYSICAL MESOMECHANICS
  • 2011-08. Thermal properties of graphene and nanostructured carbon materials in NATURE MATERIALS
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    http://scigraph.springernature.com/pub.10.1007/s00161-019-00758-2

    DOI

    http://dx.doi.org/10.1007/s00161-019-00758-2

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1112703006


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