2007/11/30 by Dibyendu Roy, Abhishek Dhar · 45 citations
Engineering · Materials Science · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Boundary value problem #Chain (unit) #Condensed matter physics #Constant (computer programming) #Harmonic #Harmonic oscillator #Heat current #Langevin equation #Limit (mathematics) #Mathematical analysis #Mathematics #Ohmic contact #Physics #Quantum #Quantum mechanics #Statistical physics #Thermal Radiation and Cooling Technologies #Thermal conduction #Thermal properties of materials #cond-mat.dis-nn #cond-mat.stat-mech
paper · pdf · doi:10.1007/s10955-008-9487-1
published in Journal of Statistical Physics 131(3), 535-541 (Springer Science+Business Media) · 8 pages, 2 figures, published version
openalex publication_date 2008/01/31 · arxiv created 2008/04/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We consider heat conduction across an ordered oscillator chain with harmonic interparticle interactions and also onsite harmonic potentials. The onsite spring constant is the same for all sites excepting the boundary sites. The chain is connected to Ohmic heat reservoirs at different temperatures. We use an approach following from a direct solution of the Langevin equations of motion. This works both in the classical and quantum regimes. In the classical case we obtain an exact formula for the heat current in the limit of system size N to infinity. In special cases this reduces to earlier results obtained by Rieder, Lebowitz and Lieb and by Nakazawa. We also obtain results for the quantum mechanical case where we study the temperature dependence of the heat current. We briefly discuss results in higher dimensions.