Abstract
We consider heat transport across a harmonic chain of charged particles, with transverse degrees of freedom, in the presence of a uniform magnetic field. For an open chain connected to heat baths at the two ends we obtain the nonequilibrium Green’s function expression for the heat current. This expression involves two different Green’s functions which can be identified as corresponding respectively to scattering processes within or between the two transverse waves. The presence of the magnetic field leads to two phonon bands of the isolated system and we show that the net transmission can be written as a sum of two distinct terms attributable to the two bands. Exact expressions are obtained for the current in the thermodynamic limit, for the the cases of free and fixed boundary conditions. In this limit, we find that at small frequency \(\omega \), the effective transmission has the frequency-dependence \(\omega ^{3/2}\) and \(\omega ^{1/2}\) for fixed and free boundary conditions respectively. This is in contrast to the zero magnetic field case where the transmission has the dependence \(\omega ^2\) and \(\omega ^0\) for the two boundary conditions respectively, and can be understood as arising from the quadratic low frequency phonon dispersion.
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Acknowledgements
A.D. and J.M.B. acknowledge support of the Department of Atomic Energy, Government of India, under Project No. RTI4001. The work of C.B. and G.C. has been supported by the projects LSD ANR-15-CE40-0020-01 of the French National Research Agency (ANR), by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovative programme (Grant Agreement No. 715734) and the French-Indian UCA project ‘Large deviations and scaling limits theory for non-equilibrium systems’.
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Communicated by Giulio Biroli.
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Bhat, J.M., Cane, G., Bernardin, C. et al. Heat Transport in an Ordered Harmonic Chain in Presence of a Uniform Magnetic Field. J Stat Phys 186, 2 (2022). https://doi.org/10.1007/s10955-021-02848-5
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DOI: https://doi.org/10.1007/s10955-021-02848-5