Related papers: Exact and approximate fluxonium array modes
We study numerically and analytically the properties of a one-dimensional array of parallel Josephson junctions in which every {\em alternate} junction is a $\pi$ junction. In the ground state of the array, each cell contains spontaneous…
We discuss the prospect of using quantum properties of large scale Josephson junction arrays for quantum manipulation and simulation. We study the collective vibrational quantum modes of a Josephson junction array and show that they provide…
Stationary compact fluxon profiles are shown to be exact solutions of the inductively coupled and dc-biased Josephson junction ladder. Such states do not exist in the parallel Josephson junction array which is described by the standard…
We consider quasinormal modes with complex energies from the point of view of the theory of quasi-exactly solvable (QES) models. We demonstrate that it is possible to find new potentials which admit exactly solvable or QES quasinormal modes…
Following the demonstration of semiconductor-based Josephson junctions which are fully tuneable by electrical means, new routes have been opened for the study of hybrid semiconductor-superconductor qubits. These include semiconductor-based…
In this paper, we develop an accurate and efficient framework for computing subwavelength guided modes in high-contrast periodic media with line defects, based on a tight-binding approximation. The physical problem is formulated as an…
In this paper, we consider the plasmon resonance in multi-layer structures. The conductivity problem associated with uniformly distributed background field is considered. We show that the plasmon mode is equivalent to the eigenvalue problem…
We present the Fast Chebyshev Transform (FCT), a fast, randomized algorithm to compute a Chebyshev approximation of functions in high-dimensions from the knowledge of the location of its nonzero Chebyshev coefficients. Rather than sampling…
We present an exact mathematical description of Josephson vortices and of the Meissner effect in periodic thin-layer superconductor/insulator structures with an arbitrary number of identical junctions N-1 (N is the number of superconducting…
An extended range of energy stable flux reconstruction schemes, developed using a summation-by-parts approach, is presented on quadrilateral elements for various sets of polynomial bases. For the maximal order bases, a new set of correction…
We propose a fast and stable method for constructing matrix approximations to fractional integral operators applied to series in the Chebyshev fractional polynomials. This method utilizes a recurrence relation satisfied by the fractional…
We derive a model problem for quasicontinuum approximations that allows a simple, yet insightful, analysis of the optimal-order convergence rate in the continuum limit for both the energy-based quasicontinuum approximation and the…
Circuit quantum electrodynamics, where photons are coherently coupled to artificial atoms built with superconducting circuits, has enabled the investigation and control of macroscopic quantum-mechanical phenomena in superconductors.…
The vertical modes of linearized equations of motion are widely used by the oceanographic community in numerous theoretical and observational contexts. However, the standard approach for solving the generalized eigenvalue problem using…
Electric vehicles with multiple motors provide a flexibility in meeting the driver torque demand, which calls for minimizing the battery energy consumption through torque allocation. In this paper, we present an approach to this problem…
We provide an exact infinite power series solution that describes the trajectory of a nonlinear simple pendulum undergoing librating and rotating motion for all time. Although the series coefficients were previously given in [V. Fair\'en,…
A recently proposed scheme for the analytical treatment of the dynamics of two-dimensional hybrid Josephson junction arrays is extended to a class of generalized hybrid arrays with ''horizontal'' shunts involving a capacitive as well as an…
Multi-mode superconducting circuits offer a promising platform for engineering robust systems for quantum computation. Previous studies indicate that single-mode devices cannot be engineered to simultaneously exhibit resilience against…
We investigated the plasmonic modes in a two-dimensional quasicrystalline array of metal nanoparticles. The polarization of the modes is in the array plane. A simplified eigen-decomposition method is presented with the help of rotational…
We consider the problem of deriving an explicit approximate solution of the nonlinear power equations that describe a balanced power distribution network. We give sufficient conditions for the existence of a practical solution to the power…