Related papers: Universal gap fluctuations in the superconductor p…
We discuss the phenomenon of universal fluctuations in mesoscopic systems and nuclei. For this purpose we use Random Matrix Theory (RMT). The statistical $S$-matrix is used to obtain the physical observables in the case of Quantum Dots,…
This is a comprehensive review of the random-matrix approach to the theory of phase-coherent conduction in mesocopic systems. The theory is applied to a variety of physical phenomena in quantum dots and disordered wires, including universal…
Spatial fluctuations of the effective pairing interaction between electrons in a superconductor induce variations of the order parameter which in turn lead to significant changes in the density of states. In addition to an overall reduction…
A finite dimensional quantum system for which the quantum chaos conjecture applies has eigenstates, which show the same statistical properties than the column vectors of random orthogonal or unitary matrices. Here, we consider the different…
This is a cursory overview of applications of concepts from random matrix theory (RMT) to quantum electronics and classical & quantum optics. The emphasis is on phenomena, predicted or explained by RMT, that have actually been observed in…
One of the major themes of random matrix theory is that many asymptotic properties of traditionally studied distributions of random matrices are universal. We probe the edges of universality by studying the spectral properties of random…
We calculate the sample-to-sample fluctuations in the excitation gap of a chaotic dynamical system coupled by a narrow lead to a superconductor. Quantum fluctuations on the order of magnitude of the level spacing, predicted by random-matrix…
We consider an ensemble of fully connected networks of N oscillators coupled harmonically with random springs and show, using Random Matrix Theory considerations, that both the average phonon heat current and its variance are…
Random matrix theory of the transition strengths is applied to transport in the strongly localized regime. The crossover distribution function between the different ensembles is derived and used to predict quantitatively the {\sl universal}…
We study mesoscopic fluctuations in the supercurrent of a Josephson junction consisting of a topological insulator microbridge between two conventional superconductors. In the model, we account for the strong proximity effect when…
Superfluidity and superconductivity are genuine many-body manifestations of quantum coherence. For finite-size systems the associated pairing gap fluctuates as a function of size or shape. We provide a parameter free theoretical description…
The studies of fluctuations of the one-dimensional Kardar-Parisi-Zhang universality class using the techniques from random matrix theory are reviewed from the point of view of the asymmetric simple exclusion process. We explain the basics…
A Gaussian fluctuation formula is proved for linear statistics of complex random matrices in the case that the statistic is rotationally invariant. For a general linear statistic without this symmetry, Coulomb gas theory is used to predict…
The energy levels of a quasi-continuous spectrum in mesoscopic systems fluctuate in positions, and the distribution of the fluctuations reveals information about the microscopic nature of the structure under consideration. Here, we…
We study the fluctuation properties of transition intensities applying a recently proposed generalization of the random matrix theory, which is based on Beck and Cohen's superstatistics. We obtain an analytic expression for the distribution…
The conductance distribution of metallic mesoscopic systems is considered. The variance of this distribution describes the universal conductance fluctuations, yielding a Gaussian distribution of the conductance. We calculate…
A description of mesoscopic fluctuations of the pairing gap in finite-sized quantum systems based on periodic orbit theory is presented. The size of the fluctuations are found to depend on quite general properties. We distinguish between…
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…
The momentum spectrum of a periodic network (quantum graph) has a band-gap structure. We investigate the relative density of the bands or, equivalently, the probability that a randomly chosen momentum belongs to the spectrum of the periodic…
We calculate the system-size-over-wave-length ($M$) dependence of sample-to-sample conductance fluctuations, using the open kicked rotator to model chaotic scattering in a ballistic quantum dot coupled by two $N$-mode point contacts to…