In this paper we present a consolidated equation for all low-field transport coefficients, based on a reservoir approach developed for non-interacting quasiparticles. This formalism allows us to treat the two distinct types of charged (fermionic and
bosonic) quasiparticles that can be simultaneously present, as for example in superconductors. Indeed, in the underdoped cuprate superconductors these two types of carriers result in two onset temperatures with distinct features in transport: $T^*$, where the fermions first experience an excitation (pseudo)gap, and $T_c$, where bosonic conduction processes are dominant and often divergent. This provides the central goal of this paper, which is to address the challenges in thermoelectric transport that stem from having two characteristic temperatures as well as two types of charge carriers whose contributions can in some instances enhance each other and in others compete. We show how essential features of the cuprates (their bad-metal character and the presence of Fermi arcs) provide an explanation for the classic pseudogap onset signatures at $T^*$ in the longitudinal resistivity, $rho_{xx}$. Based on the fits to the temperature-dependent $rho_{xx}$, we present the implications for all of the other thermoelectric transport properties.
We study quantum geometric contributions to the Berezinskii-Kosterlitz-Thouless (BKT) transition temperature, $T_{mathrm{BKT}}$, in the presence of fluctuations beyond BCS theory. Because quantum geometric effects become progressively more important
with stronger pairing attraction, a full understanding of 2D multi-orbital superconductivity requires the incorporation of preformed pairs. We find it is through the effective mass of these pairs that quantum geometry enters the theory and this suggests that the quantum geometric effects are present in the non-superconducting pseudogap phase as well. Increasing these geometric contributions tends to raise $T_{mathrm{BKT}}$ which then competes with fluctuation effects that generally depress it. We argue that a way to physically quantify the magnitude of these geometric terms is in terms of the ratio of the pairing onset temperature $T^*$ to $T_{mathrm{BKT}}$. Our paper calls attention to an experimental study demonstrating how both temperatures and, thus, their ratio may be currently accessible. They can be extracted from the same voltage-current measurements which are generally used to establish BKT physics. We use these observations to provide rough preliminary estimates of the magnitude of the geometric contributions in, for example, magic angle twisted bilayer graphene.
In this paper, we study the boundary feedback stabilization of a quasilinear hyperbolic system with partially dissipative structure. Thanks to this structure, we construct a suitable Lyapunov function which leads to the exponential stability to the e
quilibrium of the $H^2$ solution. As an application, we also obtain the feedback stabilization for the Saint-Venant-Exner model under physical boundary conditions.
