Related papers: Superposition and higher-order spacing ratios in r…
New aspects of spectral fluctuations of (quantum) chaotic and diffusive systems are considered, namely autocorrelations of the spacing between consecutive levels or spacing autocovariances. They can be viewed as a discretized two point…
We analyze statistical properties of the complex system with conditions which manifests through specific constraints on the column/row sum of the matrix elements. The presence of additional constraints besides symmetry leads to new…
We derive exact equations for the spectral density of sparse networks with an arbitrary distribution of the number of single edges and triangles per node. These equations enable a systematic investigation of the effect of clustering on the…
We investigate the spectral statistics of Hermitian matrices in which the elements are chosen uniformly from U (1), called the uni-modular ensemble (UME), in the limit of large matrix size. Using three complimentary methods; a…
We apply the supersymmetry approach to one-dimensional quantum systems with spatially-dependent mass, by including their ordering ambiguities dependence. In this way we extend the results recently reported in the literature. Furthermore, we…
Random matrix theory (RMT) provides a successful model for quantum systems, whose classical counterpart has a chaotic dynamics. It is based on two assumptions: (1) matrix-element independence, and (2) base invariance. Last decade witnessed…
In this paper, we investigate the extremal values of (the logarithm of) the characteristic polynomial of a random unitary matrix whose spectrum is distributed according the Circular Beta Ensemble (C$\beta$E). More precisely, if $X_n$ is…
Exploiting quantum mechanics for sensing offers unprecedented possibilities. State of the art proposals for novel quantum sensors often rely on the creation of large superpositions and generally detect a field. However, what is the optimal…
The spurious interaction of quantum systems with their environment known as decoherence leads, as a function of time, to a decay of coherence of superposition states. Since the interactions between system and environment are local, they can…
Studies of disordered heterogeneous media and galaxy cosmology share a common goal: analyzing the distribution of particles at `microscales' to predict physical properties at `macroscales', whether for a liquid, composite material, or…
We consider random non-normal matrices constructed by removing one row and column from samples from Dyson's circular ensembles or samples from the classical compact groups. We develop sparse matrix models whose spectral measures match these…
Consider a string of $n$ positions, i.e. a discrete string of length $n$. Units of length $k$ are placed at random on this string in such a way that they do not overlap, and as often as possible, i.e. until all spacings between neighboring…
Quantum sensitivity is an important issue in the field of quantum metrology where sub-Planck scale structures play crucial role in the Heisenberg limited measurement. We investigate the mesoscopic superposition structures, particularly for…
Inspired by the quantization of classical quantities and Rankin Selberg convolution, we study the anticommutator operation $\{\cdot, \cdot\}$, where $\{A,B\} = AB + BA$, applied to real symmetric random matrix ensembles including Gaussian…
Arising as a fluctuation phenomenon, the equilibrium distribution of meandering steps with mean separation $<\ell>$ on a "tilted" surface can be fruitfully analyzed using results from RMT. The set of step configurations in 2D can be mapped…
While investigating quantum correlations in atomic systems, we note that single measurements contain information about these correlations. Using a simple model of measurement -- analogous to the one used in quantum optics -- we show how to…
Theoretical analysis of biological and artificial neural networks e.g. modelling of synaptic or weight matrices necessitate consideration of the generic real-asymmetric matrix ensembles, those with varying order of matrix elements e.g. a…
We study a simple one-dimensional quantum system on a circle with n scale free point interactions. The spectrum of this system is discrete and expressible as a solution of an explicit secular equation. However, its statistical properties…
This article is concerned with statistics of addition spectra for systems of identical charged particles. A classical model is suggested in order to study fluctuations of Coulomb blockade peak spacings in large two-dimensional semiconductor…
Consider the question: what statistical ensemble corresponds to minimal prior knowledge about a quantum system ? For the case where the system is in fact known to be in a pure state there is an obvious answer, corresponding to the unique…