Related papers: 3-Cocycles and the Operator Product Expansion
We construct a rational extension of a recently studied nonlinear quantum oscillator model. Our extended model is shown to retain exact solvability, admitting a discrete spectrum and corresponding closed-form solutions that are expressed…
Longitudinal non-dissipative current states in bilayer electron-hole systems in the presence of potential barriers that divide the system into left and right sides was investigated. The consideration is performed both for the case of weak…
We establish a topological criterion for connection between reducibility to constant rotations and dual localization, for the general family of analytic quasiperiodic Jacobi operators. As a corollary, we obtain the sharp arithmetic phase…
Previous works have considered the leading correction term to the scaled limit of various correlation functions and distributions for classical random matrix ensembles and their $\beta$ generalisations at the hard and soft edge. It has been…
We study the spectral multiplicity of Jacobi operators on star-like graphs with $m$ branches. Recently, it was established that the multiplicity of the singular continuous spectrum is at most $m$. Building on these developments and using…
A Josephson junction (JJ) is a key device in the development of superconducting circuits, wherein a supercurrent in the JJ is controlled by the phase difference between the two superconducting electrodes. Recently, it has been shown that…
We describe a suite of fast algorithms for evaluating Jacobi polynomials, applying the corresponding discrete Sturm-Liouville eigentransforms and calculating Gauss-Jacobi quadrature rules. Our approach is based on the well-known fact that…
The geometric approach [1312.1262] to iterated variations of local functionals -- e.g., of the (master-)action functional -- resulted in an extension of the deformation quantisation technique to the set-up of Poisson models of field theory…
Gauge-invariant phase difference and critical currents of cross-type Josephson junctions with thin and narrow superconducting strips exposed to three-dimensional magnetic fields are theoretically investigated. When a sandwich-type Josephson…
We introduce some basic concepts for Jacobi-Jordan algebras such as: representations, crossed products or Frobenius/metabelian/co-flag objects. A new family of solutions for the quantum Yang-Baxter equation is constructed arising from any…
We study orthogonal polynomials with periodically modulated Jacobi parameters in the case when $0$ lies on the soft edge of the spectrum of the corresponding periodic Jacobi matrix. We determine when the orthogonality measure is absolutely…
We apply a Gutzwiller-like variational technique to study Josephson conduction across a quantum dot with an odd number of electrons connected to two superconducting leads. We show that, for small values of the superconducting gap, Kondo…
In this second paper of the series we specify general theory developed in the first paper. Here we study the structure of Jacobi fields in the case of an analytic system and piece-wise analytic control. Moreover, we consider only…
We treat the Cooper pairs in the superconducting electrodes of a Josephson junction (JJ) as an open system, coupled via Andreev scattering to external baths of electrons. The disequilibrium between the baths generates the direct-current…
We study Majorana devices featuring a competition between superconductivity and multi-channel Kondo physics. Our proposal extends previous work on single-channel Kondo systems to a topologically nontrivial setting of non-Fermi liquid type,…
Spectral properties of Jacobi operators $J$ are intimately related to an asymptotic behavior of the corresponding orthogonal polynomials $P_{n}(z)$ as $n\to\infty$. We study the case where the off-diagonal coefficients $a_{n}$ and,…
For a long time it has been a challenging goal to identify all orthogonal polynomial systems that occur as eigenfunctions of a linear differential equation. One of the widest classes of such eigenfunctions known so far, is given by…
The quarkonic contributions to the three-loop heavy-quark form factors for vector, axial-vector, scalar and pseudoscalar currents are described by closed form difference equations for the expansion coefficients in the limit of small…
We consider a realization of supersymmetric quantum mechanics where supercharges are differential-difference operators with reflections. A supersymmetric system with an extended Scarf I potential is presented and analyzed. Its…
We study a Josephson junction (JJ) in the regime of incoherent Cooper pair tunneling, capacitively coupled to a nonequilibrium noise source. The current-voltage (I-V) characteristics of the JJ are sensitive to the excess voltage…