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Bond-disordered Anderson model in two dimensions on a square lattice is studied numerically near the band center by calculating density of states (DoS), multifractal properties of eigenstates and the localization length. DoS divergence at…
A stationary Josephson effect in a weak-link between misorientated nonunitary triplet superconductors is investigated theoretically. The non-self-consistent quasiclassical Eilenberger equation for this system has been solved analytically.…
In this paper, an $\mathbb{R}$-analytical function and the sequence of its Taylor polynomials (which are Lyapunov functions different from those of Vanelli & Vidyasagar (1985, Automatica, 21(1):6 9--80)) is presented, in order to determine…
We develop a fractional-order Ginzburg-Landau (GL) framework for nonreciprocal superconducting transport in Josephson junctions formed by fractal superconductors or superconducting media with nonlocal correlations, separated by a…
Two-fluxon state in an annular Josephson junction in the presence of external magnetic field is studied analytically, numerically and experimentally. We obtain an analytical expression for the potential of interaction between the fluxons…
For a family $(F_{t,a} : x \mapsto x + t + a\phi(x))$ of increasing homeomorphisms of $\mathbb R$ with $\phi$ being Lipschitz continuous of period 1, there is a parameter space consisting of the values $(t,a)$ such that the map $F_{t,a}$ is…
We argue that a locally time-reversal symmetry breaking state can occur at Josephson junctions between unconventional superconductors. Order parameters induced by the proximity effect can combine with the bulk order parameter to form such a…
In a very recent work, G. E. Andrews defined the combinatorial objects which he called {\it singular overpartitions} with the goal of presenting a general theorem for overpartitions which is analogous to theorems of Rogers--Ramanujan type…
Probing the superconducting order parameter symmetry is a crucial step towards understanding the pairing mechanism in unconventional superconductors. Inspired by the recent discoveries of superconductivity in various van der Waals…
We study the properties of the normal modes of a chain of Josephson junctions in the simultaneous presence of disorder and absorption. We consider the superconducting regime of small phase fluctuations and focus on the case where the…
Time-reversal symmetry breaking superconductivity is a quintessential unconventional quantum state. In Josephson junctions, time-reversal symmetry breaking manifests itself in the supercurrent interference pattern as the invariance of the…
We consider the first order differential equation with a sinusoidal nonlinearity and periodic time dependence, that is, the periodically driven overdamped pendulum. The problem is studied in the case that the explicit time-dependence has…
We discuss the change of the Kondo effect in the Josephson junction formed by the indirect coupling between a one-dimensional \emph{DIII}-class topological and s-wave superconductors via a quantum dot. By performing the Schrieffer-Wolff…
Using a generalization of the non-crossing approximation which incorporates Andreev reflection, we study the properties of an infinite-U Anderson impurity coupled to two superconducting leads. In the regime where $\Delta$ and $T_K$ are…
Topological defects such as vortices, dislocations or domain walls define many important effects in superconductivity, superfluidity, magnetism, liquid crystals, and plasticity of solids. Here we address the breakdown of the…
Local superlinear convergence of the semismooth Newton method usually necessitates assumptions on the uniform invertibility of the utilized, generalized Jacobian matrices, such as, e.g., BD- or CD-regularity. For certain composite-type…
The curvature of the noncommutative torus $T^2_\theta$ ($\theta$ irrational) endowed with a noncommutative conformal metric has been the focus of attention of several recent works. Continuing the approach taken in the paper [A. Connes and…
Reference [1] established an index theory for a class of linear selfadjoint operator equations covering both second order linear Hamiltonian systems and first order linear Hamiltonian systems as special cases. In this paper based upon this…
The methods of spectral geometry are useful for investigating the metric aspects of noncommutative geometry and in these contexts require extensive use of pseudo-differential operators. In a foundational paper, Connes showed that, by direct…
The properties of Josephson tunneling between a single band s-wave superconductor and a two band $s_\pm$ superconductor are studied, in relation to recent experiments involving iron-based superconductors. We study a single junction and tune…