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The existing doubling algorithms have been proven efficient for several important nonlinear matrix equations arising from real-world engineering applications. In a nutshell, the algorithms iteratively compute a basis matrix, in one of the…
A one-parameter random matrix model is proposed for describing the statistics of the local amplitudes and phases of electron eigenfunctions in a mesoscopic quantum dot in an arbitrary magnetic field. Comparison of the statistics obtained…
Composite quantum systems can be decomposed into subsystems in many different inequivalent ways. We call a particular decomposition a meronomic reference frame for the system. We apply the ideas of quantum reference frames to characterize…
A diagrammatic method is presented for averaging over the circular ensemble of random-matrix theory. The method is applied to phase-coherent conduction through a chaotic cavity (a ``quantum dot'') and through the interface between a normal…
The computation of light scattering by the superposition T-matrix scheme has been so far restricted to systems made of particles that are either sparsely distributed or of near-spherical shape. In this work, we extend the range of…
The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case…
Resonance counting is an intuitive and widely used tool in Random Matrix Theory and Anderson Localization. Its undoubted advantage is its simplicity: in principle, it is easily applicable to any random matrix ensemble. On the downside, the…
We discuss the scattering of a quantum particle by two independent successive point interactions in one dimension. The parameter space for two point interactions is given by $U(2)\times U(2)$, which is described by eight real parameters. We…
Using the tools of the J-matrix method, we absorb the 1/r singularity of the Yukawa potential in the reference Hamiltonian, which is handled analytically. The remaining part, which is bound and regular everywhere, is treated by an efficient…
Although the unitarity triangles ($UTs$) carry information about the Kobayashi-Maskawa (KM) quark mixing matrix, it explicitly contains just three parameters which is one short to completely fix the KM matrix. It has been shown recently, by…
Unitary transformations and density matrices are central objects in quantum physics and various tasks require to introduce them in a parameterized form. In the present article we present a parameterization of the unitary group…
The simultaneous quantum estimation of multiple parameters can provide a better precision than estimating them individually. This is an effect that is impossible classically. We review the rich background of multi-parameter quantum…
High-dimensional k-sample comparison is a common applied problem. We construct a class of easy-to-implement nonparametric distribution-free tests based on new tools and unexplored connections with spectral graph theory. The test is shown to…
Based on a dispersive approach, we apply the inverse amplitude method to unitarize one-loop SU(2) and SU(3) Chiral Perturbation Theory. Numerically, we find that this unitarization technique yields the correct complex analytic structure in…
This work deals with two groups of spectral analysis results for matrices arising in fully implicit Runge-Kutta methods used for linear time-dependent partial differential equations. These were applied for different formulations of the same…
Due to their conceptual simplicity, k-means algorithm variants have been extensively used for unsupervised cluster analysis. However, one main shortcoming of these algorithms is that they essentially fit a mixture of identical spherical…
A new unitarization approach is discussed and applied to study the elastic $\pi K$ scattering process. The existence of the light $\kappa$ resonance is firmly established if the scattering length in the I=1/2 channel does not deviate too…
Cumulant mapping employs a statistical reconstruction of the whole by sampling its parts. The theory developed in this work formalises and extends ad hoc methods of `multi-fold' or `multi-dimensional' covariance mapping. Explicit formulae…
Quantum machine learning techniques have been proposed as a way to potentially enhance performance in machine learning applications. In this paper, we introduce two new quantum methods for neural networks. The first one is a quantum…
In this paper, we establish a relation between two seemingly unrelated concepts for solving first-order hyperbolic quasilinear systems of partial differential equations in many dimensions. These concepts are based on a variant of the…