相关论文: Symmetries of certain double integrals related to …
Jacobi's elliptic integrals and elliptic functions arise naturally from the Schwarz-Christoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalized elliptic integrals which arise from the…
We study monotonicity and convexity properties of functions arising in the theory of elliptic integrals, and in particular in the case of a Schwarz-Christoffel conformal mapping from a half-plane to a trapezoid. We obtain sharp monotonicity…
The edge states of a two-dimensional topological insulator are characterized by their helicity, a very remarkable property which is related to the time-reversal symmetry and the topology of the underlying system. We theoretically…
In this paper, we introduce certain new features of the shuffle algebra, that will allow us to obtain explicit formulas for the isomorphism between its Drinfeld double and the elliptic Hall algebra.
The in-plane (thermal) Hall effect is an unconventional transverse response when the applied magnetic field is in the (heat) current plane. In contrast to the normal Hall effect, the in-plane Hall effect requires the absence of certain…
In a recent study of how the output voltage of a Hall plate is affected by the shape of the plate and the size of its contacts, Udo Ausserlechner has come up with a remarkable double integral that can be viewed as a generalization of the…
Using a first-principles classical many-body simulation of a Hall bar, we study the necessary conditions for the formation of the Hall potential: (i) Ohmic contacts with metallic reservoirs, (ii) electron-electron interactions, and (iii)…
Algorithms for numerical computation of symmetric elliptic integrals of all three kinds are improved in several ways and extended to complex values of the variables (with some restrictions in the case of the integral of the third kind).…
The effect of spin-orbit interaction on electron transport properties of a cross-junction structure is studied. It is shown that it results in spin polarization of left and right outgoing electron waves. Consequently, incoming electron wave…
We show that the following double integral \[\int_{0}^\pi {\rm d}x \int_0^x {\rm d}y \frac{1}{\sqrt{1-\smash[b]{p}\cos x}\sqrt{1+\smash[b]{q\cos y}}}\]remains invariant as one trades the parameters $p$ and $q$ for $p'=\sqrt{1-p^2}$ and…
Toroidal sigma models of magneto-transport are analyzed, in which integer and fractional quantum Hall effects automatically are unified by a {holomorphic modular symmetry}. By exploiting a quantum equivalence called \emph{mirror symmetry},…
The electronic circulator, and its close relative the gyrator, are invaluable tools for noise management and signal routing in the current generation of low-temperature microwave systems for the implementation of new quantum technologies.…
We investigate the Hall effect in two different theoretical models of strongly correlated systems: a system made of weakly coupled Luttinger liquids, in the presence of umklapp scattering, and the 2D triangular lattice, with…
An oscillographic study of the Hall voltage with an unpolarized alternating current through a platinum sample revealed choral features of the Hall effect, which clearly demonstrate the presence of the spin Hall effect in metals with a…
We discuss the role of direct Coulomb interaction on the bulk insulator of the integer quantized Hall effect that bridges the topological insulators and the conductance quantization. We investigate the magneto-transport properties of a…
We derive an analytic representation of the ten-particle, two-loop double-box integral as an elliptic integral over weight-three polylogarithms. To obtain this form, we first derive a four-fold, rational (Feynman-)parametric representation…
Using a mapping of a layered three-dimensional system with significant inter-layer tunneling onto a spin-Hamiltonian, the phase diagram in the strong magnetic field limit is obtained in the semi-classical approximation. This phase diagram,…
The new integrable systems associated to the space of elliptic branched coverings are constructed. The relationship of these systems with elliptic Schlesinger's system is described. For the standard two-fold elliptic coverings the…
We investigate the spin Hall effect in a single-layer graphene device with disorder and interface-induced spin-orbit coupling. Our graphene device is connected to four semi-infinite leads that are embedded in a {Landauer-B\"uttiker} setup…
The analog of two seminal quantum optics experiments are considered in a condensed matter setting with single electron sources injecting electronic wave packets on edge states coupled through a quantum point contact. When only one electron…