Universal relations between thermoelectrics and noise in mesoscopic transport across a tunnel Junction

I present a unified theory of weakly probed observables for currents and noise in transport experiments. Our findings uncover a set of universal relations between thermoelectric and noise properties of a system probed through a tunnel contact, with the Wiedemann-Franz law being just one example of such universality between charge and heat currents. We illustrate the general theory by applying it to various quantum systems, including multichannel Kondo, and Sachdev-Ye-Kitaev quantum dots, quantum Hall devices, resonant impurity, and two-stage Kondo models, and demonstrate that each of the microscopic theories is characterized by its set of universal relations connecting conductance and thermoelectrics with noise. Violations of these relations indicate additional energy scales emerging in a system. We further discuss extensions of this theory beyond the linear response regime.I present a unified theory of weakly probed observables for currents and noise in transport experiments. Our findings uncover a set of universal relations between thermoelectric and noise properties of a system probed through a tunnel contact, with the Wiedemann-Franz law being just one example of such universality between charge and heat currents. We illustrate the general theory by applying it to various quantum systems, including multichannel Kondo, and Sachdev-Ye-Kitaev quantum dots, quantum Hall devices, resonant impurity, and two-stage Kondo models, and demonstrate that each of the microscopic theories is characterized by its set of universal relations connecting conductance and thermoelectrics with noise. Violations of these relations indicate additional energy scales emerging in a system. We further discuss extensions of this theory beyond the linear response regime.