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We review the ideas of how random matrix theory has to be properly applied to quantum physics; particularly we focus on how the spectrum has to be properly prepared and the random matrix correctly identified before the random matrix and the…
We introduce a procedure to generate scattering states which display trajectory-like wave function patterns in wave transport through complex scatterers. These deterministic scattering states feature the dual property of being eigenstates…
This course aims to introduce the student to random matrix models for decoherence and fidelity decay. They present a very powerful alternate approach, that emphasizes the disordered character of many environments and uncontrollable…
This paper provides an analysis of radio wave scattering for frequencies ranging from the microwave to the Terahertz band (e.g., 1 GHz - 1 THz), by studying the scattering power reradiated from various types of materials with different…
The formalism of the scattering matrix is applied to describe the transmission properties of multilayered structures with deep variations of the refractive index and arbitrary arrangements of the layers. We show that there is an exact…
Software-defined metasurfaces (SDMs) comprise a dense topology of basic elements called meta-atoms, exerting the highest degree of control over surface currents among intelligent panel technologies. As such, they can transform impinging…
The scattering properties of randomly layered optical media with ${\cal PT}$-symmetric index of refraction are studied using the transfer-matrix method. We find that the transmitance decays exponentially as a function of the system size,…
In this work we present a method for generating random matrices describing electromagnetic scattering from disordered media containing dielectric particles with prescribed single particle scattering characteristics. Resulting scattering…
The application of random-matrix theory (RMT) to compound-nucleus (CN) reactions is reviewed. An introduction into the basic concepts of nuclear scattering theory is followed by a survey of phenomenological approaches to CN scattering. The…
Siegert pseudostates are purely outgoing states at some fixed point expanded over a finite basis. With discretized variables, they provide an accurate description of scattering in the s wave for short-range potentials with few basis states.…
The atomic structure of amorphous materials is believed to be well described by the continuous random network model. We present an algorithm for the generation of large, high-quality continuous random networks. The algorithm is a variation…
For a class of negative slowly decaying potentials, including $V(x):=-\gamma|x|^{-\mu}$ with $0<\mu<2$, we study the quantum mechanical scattering theory in the low-energy regime. Using modifiers of the Isozaki-Kitada type we show that…
We study S-matrix correlations for random matrix ensembles with a Hamiltonian which is the sum of a given deterministic part and of a random matrix with a Gaussian probability distribution. Using Efetov's supersymmetry formalism, we show…
We develop a quasi-normal mode theory (QNMT) to calculate a system's scattering $S$ matrix, simultaneously satisfying both energy conservation and reciprocity even for a small truncated set of resonances. It is a practical reduced-order…
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…
We present an algorithm for the calculation of eigenstates with definite linear momentum in quantum lattices. Our method is related to the Density Matrix Renormalization Group, and makes use of the distribution of multipartite entanglement…
The restriction imposed on the J-matrix method of using specific L2 bases is lifted without compromising any of the advantages that it offers. This opens the door to a wider range of application of the method to physical problems beyond the…
We analyze further a recently proposed S-matrix description of transplanckian scattering in the specific case of axisymmetric collisions of extended sources, where some of the original approximations are not necessary. We confirm the claim…
We propose a scheme for recycling Gaussian random vectors into structured matrices to approximate various kernel functions in sublinear time via random embeddings. Our framework includes the Fastfood construction as a special case, but also…
An S matrix approach is developed to describe elastic scattering resonances of systems where the scattered particle is asymptotically confined and the scattering potential lacks continuous symmetry. Examples are conductance resonances in…