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We study the asymptotic behavior of the trajectory of a nonautonomous evolution equation governed by a quasi-nonexpansive operator in Hilbert spaces. We prove the weak convergence of the trajectory to a fixed point of the operator by…
We study the Cooper instability in jellium model in the controlled regime of small to intermediate values of the Coulomb parameter $r_s \leq 2$. We confirm that superconductivity naturally emerges from purely repulsive interactions…
We have calculated the thermoelectric conductivity tensor $\varepsilon_{ij}$ and the thermal conductivity tensor $\lambda_{ij}$ of a unidirectional lateral superlattice (ULSL) ($i,j = x,y$, with the $x$-axis aligned to the principal axis of…
There have recently been several experiments studying induced superconductivity in semiconducting two-dimensional electron gases that are strongly coupled to thin superconducting layers, as well as probing possible topological phases…
Partial differential equations with random inputs have become popular models to characterize physical systems with uncertainty coming from, e.g., imprecise measurement and intrinsic randomness. In this paper, we perform asymptotic rare…
We consider the problem of determining a small elliptical conductivity anomaly in a unit disc from boundary measurements. The conductivity of the anomaly is assumed to be a small perturbation from the constant background. A measurement of…
Optimal estimates on asymptotic behaviors of weak solutions both at the origin and at the infinity are obtained to the following quasilinear elliptic equations \begin{eqnarray*} -\Delta_{p}u-\frac{\mu}{|x|^{p}}|u|^{p-2}u+m|u|^{p-2}u=f(u), &…
We consider time-dependent convection-diffusion problems with high P\'eclet number of order $\mathcal{O}(\varepsilon^{-1})$ in thin three-dimensional graph-like networks consisting of cylinders that are interconnected by small domains…
We study the low-temperature low-frequency conductivity sigma of an interacting one dimensional electron system in the presence of a periodic potential. The conductivity is strongly influenced by conservation laws, which, we argue, need be…
The temperature-dependent nonlinear conductance for transport of a Luttinger liquid through a barrier is calculated in the nonperturbative regime for $g=1/2-\epsilon$, where $g$ is the dimensionless interaction constant. To describe the…
We study the effect of Coulomb interactions on the conductance of a single-mode quantum wire connecting two bulk leads. When the density of electrons in the wire is very low, they arrange in a finite-length Wigner crystal. In this regime…
We study the behavior of steady state voltage potentials in two kinds of bidimensional media composed of material of complex permittivity equal to 1 (respectively $\alpha$) surrounded by a thin membrane of thickness $h$ and of complex…
A study of impedance spectroscopy was done for the electrical characterization of pyrochlore materials. The experiment consisted of measurements of the dependence of the impedance of such systems with the temperature during heating (25 to…
We study temperature dependence of diagonal conductivity at half filled Landau level by means of the theory of composite fermions in the weakly disordered regime $(k_{F}l>>1)$. At low temperatures we find the leading $\log T$ correction…
We compare the asymptotic behavior of Carmichael's lambda function composed with Euler's totient function to the asymptotic behavior of Carmichael's lambda function composed with itself. We establish the normal order of the logarithm of the…
Since Bardeen-Cooper-Schrieffer theory of superconductivity is non-linear, it is difficult to study superconducting properties analytically. There is a more tractable linear criterion which determines a temperature $T_l$ below which the…
We show that electron transport through a long multichannel wire, connected to leads by tunnel junctions, at low temperatures and voltages is dominated by inelastic cotunnelling. This mechanism results in experimentally observed power-law…
The conductance of disordered nano-wires at T=0 is calculated in one-particle approximation by reducing the original multi-dimensional problem for an open bounded system to a set of exactly one-dimensional non-Hermitian problems for mode…
The linear conductance of the single electron transistor is determined in the high temperature limit. Electron tunneling is treated nonperturbatively by means of a path integral formulation and the conductance is obtained from Kubo's…
We describe a phenomenological model for the conductance feature near $0.7 \times 2e^2/h$ that occurs in quantum point contacts. We focus on the transconductance at finite source-drain bias and contrast our model with the results expected…