Hostname: page-component-7b7567c8c-2n9c9 Total loading time: 0 Render date: 2026-11-15T18:10:55.552Z Has data issue: false hasContentIssue false
  • English
  • Français

Size Effects in Quasi-Static Energy Transport for Microscopic Quantum Systems

Published online by Cambridge University Press:  19 August 2014

George Y. Panasyuk,
Timothy J. Haugan and
Kirk L. Yerkes
George Y. Panasyuk
Affiliation:
Aerospace System Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, U.S.A.
Timothy J. Haugan
Affiliation:
Aerospace System Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, U.S.A.
Kirk L. Yerkes
Affiliation:
Aerospace System Directorate, Air Force Research Laboratory, Wright-Patterson Air Force Base, Ohio 45433, U.S.A.
Get access

Abstract

We consider finite size effects on energy transfer between nanoparticles mediated by quantum systems. The nanoparticles are considered as heat reservoirs with a finite number of modes. An expression for the quasi-static energy transport between the heat reservoirs having a finite mode frequency spacing Δ is derived. The resulting equations describing long-term (t ≥1/Δ) relaxation for the mode temperatures and the average temperatures of the nanoparticles are solved. The solutions depend on small number of measurable parameters and show unusual peculiarities in their temporal variations. As is shown, Fourier’s law in a chain of identical subsystems (nanoparticles) can be validated only on a short time scale. For a larger times, when t ∼ 1/Δ, the temperatures of different modes deviate from each other, thus preventing thermal equilibrium in each subsystem, and the validity of Fourier’s law cannot be established.

Keywords

thermal conductivitysimulationmicrostructure

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

REFERENCES

Hache, F., Ricard, D., and Flytzanis, C., J. Opt. Soc. Am. B 3, 1647 (1986).10.1364/JOSAB.3.001647CrossRefGoogle Scholar
Rautian, S. G., Sov. Phys. JETP 85, 451 (1997).10.1134/1.558330CrossRefGoogle Scholar
Panasyuk, G. Y., Schotland, J. C., and Markel, V. A., Phys. Rev. Lett. 100, 047402 (2008).10.1103/PhysRevLett.100.047402CrossRefGoogle Scholar
Govyadinov, A. A., Panasyuk, G. Y., Schotland, J. C., and Markel, V. A., Phys. Rev. B 84, 155461 (2011).10.1103/PhysRevB.84.155461CrossRefGoogle Scholar
Panasyuk, G. Y., Schotland, J. C., and Markel, V. A., Phys. Rev. B 84, 155460 (2011).10.1103/PhysRevB.84.155460CrossRefGoogle Scholar
Adiga, S. P., Adiga, V. P., Carpick, R. W., and Brenner, D. W., J. Phys. Chem. C 115, 21691 (2011).10.1021/jp207424mCrossRefGoogle Scholar
Sopu, D., Kotakoski, J., and Albe, K., Phys. Rev. B 83, 245416 (2011).10.1103/PhysRevB.83.245416CrossRefGoogle Scholar
Pohl, J., Stahl, C., and Albe Beilstein, K., J. Nanotechnol. 3, 1 (2012).Google Scholar
Cuansing, E. C., Li, H., and Wang, J. S., Phys. Rev. E 86, 031132 (2012).10.1103/PhysRevE.86.031132CrossRefGoogle Scholar
Panasyuk, G. Y. and Yerkes, K. L., Phys. Rev. E 87, 062118 (2013).10.1103/PhysRevE.87.062118CrossRefGoogle Scholar
Panasyuk, G. Y., Levin, G.A., and Yerkes, K. L., Phys. Rev. E 86, 021116 (2012).10.1103/PhysRevE.86.021116CrossRefGoogle Scholar
Nieuwenhuizen, Th. M. and Allahverdian, A. E., Phys. Rev. E 66, 036102 (2002).10.1103/PhysRevE.66.036102CrossRefGoogle Scholar