Heat Transport in an Ordered Harmonic Chain in Presence of a Uniform Magnetic Field

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 expr...

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Bibliographic Details
Published in:Journal of statistical physics 2022, Vol.186 (1), Article 2
Main Authors: Bhat, Junaid Majeed, Cane, Gaëtan, Bernardin, Cédric, Dhar, Abhishek
Format: Article
Language:English
Subjects:
Boundary conditions
Chains
Charged particles
Condensed Matter
Free boundaries
Green's functions
Magnetic fields
Magnetism
Mathematical and Computational Physics
Mathematical Physics
Mathematics
Phonons
Physical Chemistry
Physics
Physics and Astronomy
Probability
Quantum Physics
Statistical Mechanics
Statistical Physics and Dynamical Systems
Theoretical
Thermodynamics
Transverse waves
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Summary: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 ω , the effective transmission has the frequency-dependence ω 3 / 2 and ω 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 ω 2 and ω 0 for the two boundary conditions respectively, and can be understood as arising from the quadratic low frequency phonon dispersion.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-021-02848-5