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Matrix Models are the most effective way to describe strongly interacting systems with many degrees of freedom. They have proven successful in describing very different settings, from nuclei spectra to conduction in mesoscopic systems, from…
Recent experiments with nanopatterned thin films revealed an unusual quantum superconductor to metal phase transition (QSMT) with a linear in temperature resistivity. In contrast, most known examples of such transitions and standard…
In this thesis manuscript we explore different facets of random tensor models. These models have been introduced to mimic the incredible successes of random matrix models in physics, mathematics and combinatorics. After giving a very short…
We compute the statistics of thermal emission from systems in which the radiation is scattered chaotically, by relating the photocount distribution to the scattering matrix - whose statistical properties are known from random-matrix theory.…
Random impedance networks are widely used as a model to describe plasmon resonances in disordered metal-dielectric and other two-component nanocomposites. In the present work, the spectral properties of resonances in random networks are…
We consider a possible generalization of the random matrix theory, which involves the maximization of Tsallis' $q$-parametrized entropy. We discuss the dependence of the spacing distribution on $q$ using a non-extensive generalization of…
Topological models involving matter couplings to Donaldson-Witten theory are presented. The construction is carried using both, the topological algebra and its central extension, which arise from the twisting of $N=2$ supersymmetry in four…
In this preface to the Journal of Physics A, Special Edition on Random Matrix Theory, we give a review of the main historical developments of random matrix theory. A short summary of the papers that appear in this special edition is also…
Random Matrix Theory (RMT) is capable of making predictions for the spectral fluctuations of a physical system only after removing the influence of the level density by unfolding the spectra. When the level density is known, unfolding is…
We generalize the supersymmetry method in Random Matrix Theory to arbitrary rotation invariant ensembles. Our exact approach further extends a previous contribution in which we constructed a supersymmetric representation for the class of…
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…
We use ab initio electronic-structure methods to investigate random-matrix theory (RMT) universality in molecular electronic structure. Using single-reference electronic structure methods, including Hartree-Fock, configuration-interaction…
It is a classical result of Wigner that for an hermitian matrix with independent entries on and above the diagonal, the mean empirical eigenvalue distribution converges weakly to the semicircle law as matrix size tends to infinity. In this…
During last two decades it has been discovered that the statistical properties of a number of microscopically rather different random systems at the macroscopic level are described by {\it the same} universal probability distribution…
Starting from Gaussian random matrix models we derive a new supermatrix field theory model. In contrast to the conventional non-linear sigma models, the new model is applicable for any range of correlations of the elements of the random…
We review recent progress in analysing wave scattering in systems with both intrinsic chaos and/or disorder and internal losses, when the scattering matrix is no longer unitary. By mapping the problem onto a nonlinear supersymmetric…
We introduce and analyze the physics of "driving reversal" experiments. These are prototype wavepacket dynamics scenarios probing quantum irreversibility. Unlike the mostly hypothetical "time reversal" concept, a "driving reversal" scenario…
We expose an interesting connection between the distribution of local spectral density of states arising in the theory of disordered systems and the notion of superstatistics introduced by Beck and Cohen and recently incorporated in random…
The purpose of this review is to provide a comprehensive pedagogical introduction into Keldysh technique for interacting out-of-equilibrium fermionic and bosonic systems. The emphasis is placed on a functional integral representation of…
In these lectures, we review the D=11 supermembrane and supersymmetric matrix models at an introductory level. We also discuss some more recent developments in connection with non-perturbative string theory.