Related papers: Is the K-matrix approach adequate for describing o…
We make use of the improved K-matrix algorithm to obtain unitarized amplitudes in $R+\alpha R^2$ gravity (the so-called Starobisnsky model, of cosmological relevance). The procedure is of some complexity because infrared divergences are…
A numerical matrix methodology is applied to quantum problems with periodic potentials. The procedure consists essentially in replacing the true potential by an alternative one, restricted by an infinite square well, and in expressing the…
Overlapping clustering problem is an important learning issue in which clusters are not mutually exclusive and each object may belongs simultaneously to several clusters. This paper presents a kernel based method that produces overlapping…
The convergence of the Rayleigh-Ritz method with nonlinear parameters optimized through minimization of the trace of the truncated matrix is demonstrated by a comparison with analytically known eigenstates of various quasi-solvable systems.…
We explore the set of unitary matrices characterized by a given structure in the context of their applications in the field of Quantum Information. In the first part of the Thesis we focus on classification of special classes of unitary…
A K-matrix formalism is used to relate single-channel and multi-channel fits. We show how the single-channel formalism changes as new hadronic channels become accessible. These relations are compared to those commonly used to fit…
Recently, untrained neural networks (UNNs) have shown satisfactory performances for MR image reconstruction on random sampling trajectories without using additional full-sampled training data. However, the existing UNN-based approach does…
Ultrasound 3D compounding is important for volumetric reconstruction, but as of yet there is no consensus on best practices for compounding. Ultrasound images depend on probe direction and the path sound waves pass through, so when multiple…
A new method is proposed for fitting non-relativistic binary-scattering data and for extracting the parameters of possible quantum resonances in the compound system that is formed during the collision. The method combines the well-known…
A method is presented which makes considerably more transparent possible patterns behind low-energy scattering data. In particular, structures associated with resonances, such as locations, widths and heights, become visible with a naked…
Complex quantum systems consisting of large numbers of strongly coupled states exhibit characteristic level repulsion, leading to a non-Poisson spacing distribution which can be described by Random Matrix Theory. Scattering resonances…
We present a method for resolving spatial mode overlaps in coupled microresonators based on Kerr and thermal cross-phase modulation. Through a pump-probe setup, we measure experimental overlap in a three-ring resonator with good agreement…
Analyses of betatron coupling can be broadly divided into two categories: the matrix approach that decouples the single-turn matrix to reveal the normal modes and the hamiltonian approach that evaluates the coupling in terms of the action…
This paper is dedicated to the problem of verification of matrices for unitary similarity. For the case of nonderogatory matrices, we have been able to present the new solution for this problem based on geometric approach. The main…
A matrix balanced version of the Recursive Centered T Matrix Algorithm (RCTMA) applicable to systems possessing resonant inter-particle couplings is presented. Possible domains of application include systems containing interacting localized…
Resonances of cylindrical symmetric microwave cavities are analyzed in R-matrix theory which transforms the input channel conditions to the output channels. Single and interfering double resonances are studied and compared with experimental…
Clustering partitions a dataset such that observations placed together in a group are similar but different from those in other groups. Hierarchical and $K$-means clustering are two approaches but have different strengths and weaknesses.…
We investigate an efficient, generic method for evaluating the performance of quantum annealing devices that does not require the prior knowledge of the true ground state of the benchmark problem. This approach exploits symmetry properties…
We investigate a numerical method for studying resonances in quantum mechanics. We prove rigorously that this method yields accurate approximations to resonance energies and widths for shape resonances in the semiclassical limit.
For coupled-channel resonance scattering we derive a model with a closed form solution for the $T$-matrix that satisfies unitarity and analyticity. The two-channel case is handled explicitly for an arbitrary number of resonances. The method…