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Analytic solution for heat flow through a general harmonic network.

Nahuel Freitas1, Juan Pablo Paz1

  • 1Departamento de Física, FCEyN, UBA, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina and Instituto de Física de Buenos Aires, UBA CONICET, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|November 7, 2014
PubMed
Summary
This summary is machine-generated.

We developed a new method to calculate heat current in harmonic networks, providing exact formulas for heat flow and local temperatures. This approach works even without weak coupling or Markovian approximations, revealing system-size dependent heat current scaling in disordered crystals.

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Area of Science:

  • Physics
  • Condensed Matter Physics
  • Statistical Mechanics

Background:

  • Understanding heat transport in complex systems is crucial for materials science and nanotechnology.
  • Traditional methods often rely on approximations like weak coupling and Markovian dynamics, limiting their applicability.
  • Harmonic networks coupled to reservoirs present a fundamental model for studying thermal properties.

Purpose of the Study:

  • To derive an analytic expression for heat current in general harmonic networks coupled to Ohmic reservoirs.
  • To develop a method for calculating stationary states using eigenvectors and eigenvalues of a generalized cubic eigenvalue problem.
  • To investigate nonequilibrium processes without common approximations and apply the method to disordered crystalline systems.

Main Methods:

  • Formulating an analytic expression for heat current.
  • Utilizing a generalized cubic eigenvalue problem to determine stationary states.
  • Calculating exact formulas for heat current and local temperatures.

Main Results:

  • Exact formulas for heat current and local temperature were obtained.
  • The method successfully bypasses weak coupling and Markovian approximations.
  • For small systems, heat current scaling with system size was found to strongly depend on reservoir interaction strength.

Conclusions:

  • The presented method offers a robust way to study heat transport in harmonic networks.
  • The findings highlight a counterintuitive dependence of heat current scaling on reservoir coupling in small disordered systems.
  • This work provides new insights into thermal conduction in nanostructured materials.