Quantum theory of nonlinear thermal response

The linear behavior of thermal transport has been widely explored, both theoretically and experimentally. On the other hand, nonlinear response not fully discussed. In light vector potential theory [Tatara, Phys. Rev. Lett. 114, 196601 (2015)], we develop a general formulation to calculate dynamic responses. DC limit, recover well-known Mott relation Wiedemann-Franz (WF) law at order response, which link thermoelectric conductivity $\ensuremath{\eta}$, $\ensuremath{\kappa}$, electric $\ensuremath{\sigma}$ together. To be specific, describes $\ensuremath{\eta}$ is proportional first derivative with respect Fermi energy (for brevity call derivative, others are similar); WF shows $\ensuremath{\kappa}$ zero (i.e., itself). We found there higher-order relations laws follow an order-dependent relation. At second order, indicates that $\ensuremath{\eta}$; but $\ensuremath{\kappa}$. third increases once. Although only did explicit calculations up third-order can deduce $n\text{th-order}$ ($n\ensuremath{-}2$)th for relation; ($n\ensuremath{-}1$)th law. Since second-order Hall effect studied in experiment, our may tested by measuring as well. Our presented explicitly fermions, it also applied bosons. As example, magnons strained collinear antiferromagnet on honeycomb, disappears.