The standard Kubo formulas (current-current correlation functions) for the thermal transport coefficients are profoundly altered in the presence of a quantizing magnetic field. Quite general expressions are derived using quantum linear-response theory. They clearly reflect the role of magnetization in the electronic thermal transport. These fundamental corrections are of purely quantum-mechanical origin and vanish in the classical high-field limit.
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Oji et al. (1985) studied this question.
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