Related papers: Random matrix description of decaying quantum syst…
This paper is centred on the spectral study of a Random Fourier matrix, that is an $n\times n$ matrix $A$ whose $(j, k)$ entries are $\exp(2i\pi m X_jY_k)$, with $X_j$ and $Y_k$ two i.i.d sequences of random variables and $1\leq m\leq n$ is…
We theoretically investigate parameter quantum estimation in quantum chaotic systems. Our analysis is based on an effective description of non-integrable quantum systems in terms of a random matrix Hamiltonian. Based on this approach we…
In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…
Metastability and its relaxation mechanisms challenge our understanding of the stability of quantum many-body systems, revealing a gap between the microscopic dynamics of the individual components and the effective descriptions used for…
We study theoretically and numerically a new kind of spatial correlation for waves in disordered media. We define $C_{\Gamma}$ as the correlation function of the fluorescent decay rate of an emitter at two different positions inside the…
In this article we investigate no-resonance conditions for quantum many body chaotic systems and random matrix models. No-resonance conditions are properties of the spectrum of a model, usually employed as a theoretical tool in the analysis…
Probabilistic machine learning models are distinguished by their ability to integrate prior knowledge of noise statistics, smoothness parameters, and training data uncertainty. A common approach involves modeling data with Gaussian…
We present an analytical modal description of the rich physics involved in hybrid plasmonic-photonic devices that is confirmed by full dipole solutions of Maxwell's equations. Strong frequency-dependence for the spontaneous emission decay…
For any graph consisting of $k$ vertices and $m$ edges we construct an ensemble of random pure quantum states which describe a system composed of $2m$ subsystems. Each edge of the graph represents a bi-partite, maximally entangled state.…
Highly degenerate chaotic radiation has a Gaussian density matrix and a large occupation number of modes $f $. If it is passed through a weakly transmitting barrier, its counting statistics is close to Poissonian. We show that a second…
We investigate the spatial statistics of the energy eigenfunctions on large quantum graphs. It has previously been conjectured that these should be described by a Gaussian Random Wave Model, by analogy with quantum chaotic systems, for…
A strong optical nonlinearity arises when coherent light is scattered by a semiconductor quantumdot (QD) coupled to a nano-photonic waveguide. We exploit the Fano effect in such a waveguide to control the phase of the quantum interference…
Random factor graphs provide a powerful framework for the study of inference problems such as decoding problems or the stochastic block model. Information-theoretically the key quantity of interest is the mutual information between the…
In this work the information loss in deterministic, memoryless systems is investigated by evaluating the conditional entropy of the input random variable given the output random variable. It is shown that for a large class of systems the…
A computational model study for complete frequency redistribution linear incoherent two-level atomic radiation trapping in optically dense media using the multiple scattering representation is presented. This model study discuss at length…
In data science, individual observations are often assumed to come independently from an underlying probability space. Kernel matrices formed from large sets of such observations arise frequently, for example during classification tasks. It…
Statistical properties of coherent radiation propagating in a quasi - 1D random media is studied in the framework of random matrix theory. Distribution functions for the total transmission coefficient and the angular transmission…
Quantum states inevitably decay with time into a probabilistic mixture of classical states, due to their interaction with the environment and measurement instrumentation. We present the first measurement of the decoherence dynamics of…
The study of nanostructured artificial media for optics has expanded rapidly over the last few decades, coupled with improvements of fabrication technology that have enabled investigation of previously unrealisable optical scattering…
A method of resummation of infinite series of perturbation theory diagrams is applied for studying the properties of random band matrices. The topological classification of Feynman diagrams, which was actively used in last years for matrix…