Related papers: S-matrix network models for coherent waves in rand…
Diffusion-driven instability is a fundamental mechanism underlying pattern formation in spatially extended systems. In almost all existing works, diffusion across the links of the underlying network is modeled through scalar weights,…
It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed according to a power…
The Random Coupling Model (RCM) is a statistical approach for studying the scattering properties of linear wave chaotic systems in the semi-classical regime. Its success has been experimentally verified in various over-moded wave settings,…
You might've heard about various mathematical properties of scattering amplitudes such as analyticity, sheets, branch cuts, discontinuities, etc. What does it all mean? In these lectures, we'll take a guided tour through simple scattering…
The relation between the R- and P-matrix approaches and the harmonic oscillator representation of the quantum scattering theory (J-matrix method) is discussed. We construct a discrete analogue of the P-matrix that is shown to be equivalent…
We propose an information-theoretic model for the transport of waves through a chaotic cavity in the presence of absorption. The entropy of the S-matrix statistical distribution is maximized, with the constraint $<Tr SS^{\dagger}> =\alpha…
While renormalization groups are fundamental in physics, renormalization of complex networks remains vague in its conceptual definition and methodology. Here, we propose a novel strategy to renormalize complex networks. Rather than…
Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the…
We measure the transmission and reflection amplitudes of microwaves in a resonator coupled to two antennas at room temperature in the regime of weakly overlapping resonances and in a frequency range of 3 to 16 GHz. Below 10.1 GHz the…
This paper presents a unified and computationally efficient framework for modeling antennas embedded in spherically stratified media, applicable to implantable biomedical antennas and radome-enclosed systems. The method separates the…
We study the spectral properties of a class of random matrices where the matrix elements depend exponentially on the distance between uniformly and randomly distributed points. This model arises naturally in various physical contexts, such…
We consider two different stationary random processes whose probability distributions are very close and indistinguishable by standard tests for large but limited statistics. Yet we demonstrate that these processes can be reliably…
We develop the scattering theory of general conformally compact metrics. For low frequencies, the domain of the scattering matrix is shown to be frequency dependent. In particular, generalized eigenfunctions exhibit L^2 decay in directions…
Networks constitute efficient tools for assessing universal features of complex systems. In physical contexts, classical as well as quantum, networks are used to describe a wide range of phenomena, such as phase transitions, intricate…
We investigate systematically sample-to sample fluctuations of the probability $\tau$ of no return into a given entrance channel for wave scattering from disordered systems. For zero-dimensional ("quantum chaotic") and quasi one-dimensional…
We describe a random matrix approach that can provide generic and readily soluble mean-field descriptions of the phase diagram for a variety of systems ranging from QCD to high-T_c materials. Instead of working from specific models, phase…
Quantum mechanical systems with some degree of complexity due to multiple scattering behave as if their Hamiltonians were random matrices. Such behavior, while originally surmised for the interacting many-body system of highly excited…
Low-rank matrix approximations, such as the truncated singular value decomposition and the rank-revealing QR decomposition, play a central role in data analysis and scientific computing. This work surveys and extends recent research which…
We explore the scattering of waves in designed asymmetric one-dimensional waveguide networks. We show that the reflection between two ports of an asymmetric network can be identical over a broad frequency range, as if the network was…
We derive the off-shell scattering matrix for a spherical scatterer. The result obtained generalizes the off-on-shell matrix commonly used in the theory of scalar waves propagation in random media.