Abstract
We generalize the many-body formalism for the Peltier effect to the nonlinear/nonequilibrium regime corresponding to large amplitude (spatially uniform but time-dependent) electric fields. We find a relationship between the expectation values for the charge current and for the part of the heat current that reduces to the Jonson-Mahan theorem in the linear-response regime. The nonlinear-response Peltier effect has an extra term in the heat current that is related to Joule heating (we are unable to fully analyze this term). The formalism holds in all dimensions and for arbitrary many-body systems that have local interactions. We illustrate it for the Falicov-Kimball, Hubbard, and periodic Anderson models.
Highlights
Introduction to heat transport and theJonson-Mahan theoremIn 1834, Peltier introduced the notion that an electrical current carries heat current with it [1]
We find a relationship between the expectation values for the charge current and for the part of the heat current that reduces to the Jonson-Mahan theorem in the linear-response regime
The Jonson-Mahan theorem is important for two reasons: (i) first, it shows that all the manybody effects for charge transport are essentially the same for heat transport, so even though the operators are quite different, the correlation functions retain the relationship they have for noninteracting systems, and (ii) second, the theorem allows for a consistent approximation scheme for charge and thermal transport – if one has an approximate result for the charge transport, the use of the Jonson-Mahan theorem will produce the most reasonable approximation for the thermal transport
Summary
In 1834, Peltier introduced the notion that an electrical current carries heat current with it [1]. The Jonson-Mahan theorem is important for two reasons: (i) first, it shows that all the manybody effects for charge transport are essentially the same for heat transport, so even though the operators are quite different, the correlation functions (including all effects of vertex corrections) retain the relationship they have for noninteracting systems, and (ii) second, the theorem allows for a consistent approximation scheme for charge and thermal transport – if one has an approximate result for the charge transport, the use of the Jonson-Mahan theorem will produce the most reasonable approximation for the thermal transport In this contribution, we are interested in nonlinear-response effects. One can even make contact with Kubo-like formulas by adding a gravitational field to the Hamiltonian, which couples to the energy current, and showing the equivalence of the response to a gravitational field with the response to a temperature gradient [9] Such a procedure is difficult to generalize to the nonequilibrium/nonlinear-response regime, so we focus here on the Peltier effect, which occurs due to the presence of an external electric field at a constant temperature
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