A gauge invariant theory for time dependent heat current

摘要: In this work, we develop a general gauge-invariant theory for AC heat current through multi-probe systems. Using the non-equilibrium Green's function, expression time-dependent electrothermal admittance is obtained where include internal potential due to Coulomb interaction explicitly. We show that condition satisfied if self-consistent considered. It known Onsager relation holds dynamic charge conductance. in work violated, except special case of quantum dot system with single energy level. apply our nano capacitor plays an essential role. find that, first order frequency, related electrochemical capacitance as well phase accumulated scattering event.