Related papers: Quasiperiodic Elliptic Operators: Projection Metho…
We study some classes of symmetric operators for the discrete series representations of the quantum algebra U_q(su_{1,1}), which may serve as Hamiltonians of various physical systems. The problem of diagonalization of these operators…
Qubit-efficient optimization studies how large combinatorial problems can be addressed with quantum circuits whose width is far smaller than the number of logical variables. In quadratic unconstrained binary optimization (QUBO), objective…
We define the computational task of detecting projectors in finite dimensional associative algebras with a combinatorial basis, labelled by representation theory data, using combinatorial central elements in the algebra. In the first…
Quasi-Periodic Oscillations (QPOs) are very puzzling since they remain totally unexplained by popular earlier models of accretion disks. The significant rms value in power density spectrum implies that the oscillation involves in the…
We present an approach to calculate the optical absorption spectra that combines the quasiparticle self-consistent GW method [Phys. Rev. B, 76 165106 (2007)] for the electronic structure with the solution of the ladder approximation to the…
A number of black hole X-ray transients show quasi-periodic oscillations (QPOs) in the optical (ultraviolet) and X-ray bands at the same frequency, which challenge models for production of radiation at these wavelengths. We propose a model…
This article provides a survey of recent research efforts on the application of quasi-Monte Carlo (QMC) methods to elliptic partial differential equations (PDEs) with random diffusion coefficients. It considers, and contrasts, the uniform…
The integral of the Wigner function of a quantum mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval…
A variety of physical phenomena, such as amplification, absorption, and radiation, can be effectively described using non-Hermitian operators. However, the introduction of non-uniform non-Hermiticity can lead to the formation of exceptional…
High-dimensional nonlinear mechanical systems admit quasi-periodic solutions that are essential for the understanding of the dynamical systems. These quasi-periodic solutions stay on some invariant tori governed by complex PDEs in…
Observables of a quantum system, described by self-adjoint operators in a von Neumann algebra or affiliated with it in the unbounded case, form a conditionally complete lattice when equipped with the spectral order. Using this…
This study analyzes the nonasymptotic convergence behavior of the quasi-Monte Carlo (QMC) method with applications to linear elliptic partial differential equations (PDEs) with lognormal coefficients. Building upon the error analysis…
We analyze combined Quasi-Monte Carlo quadrature and Finite Element approximations in Bayesian estimation of solutions to countably-parametric operator equations with holomorphic dependence on the parameters as considered in [Cl.~Schillings…
We try to understand the quasi-periodic oscillations (QPOs) in low-mass neutron-star and black-hole X-ray binaries by a resonance model in warped disks with precession. Our main concern is high-frequency QPOs, hectohertz QPOs, and…
We study the quasi-periodic Schr\"odinger operator $$ -\psi"(x) + V(x) \psi(x) = E \psi(x), \qquad x \in \mathbb{R} $$ in the regime of "small" $V(x) = \sum_{m\in\mathbb{Z}^\nu}c(m)\exp (2\pi i m\omega x)$, $\omega = (\omega_1, \dots,…
Koopman operators and transfer operators represent nonlinear dynamics in state space through its induced action on linear spaces of observables and measures, respectively. This framework enables the use of linear operator theory for…
Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…
Quasi-elliptic cohomology is a variant of Tate K-theory. It is the orbifold K-theory of a space of constant loops. For global quotient orbifolds, it can be expressed in terms of equivariant K-theories. In this paper we show how this theory…
This paper presents a groundbreaking advancement in the theory of operators defined on octonionic Hilbert spaces, successfully resolving a fundamental challenge that has persisted for over six decades. Due to the intrinsic non-associative…
Kilohertz Quasi-Periodic Oscillations (QPOs) have been detected in many accreting X-ray binaries. It has been suggested that the highest QPO frequencies observed in the modulation of the X-ray flux reflect a non-linear resonance between two…