Related papers: Matrix elements for the quantum cat map: Fluctuati…

Planck-scale quantum spacetime undergoes probabilistic local curvature fluctuations whose distributions cannot explicitly depend on position otherwise vacuum's small-scale quantum structure would fail to be statistically homogeneous. Since…

We calculate the probability to find exactly $n$ eigenvalues in a spectral interval of a large random $N \times N$ matrix when this interval contains $s \ll N$ eigenvalues on average. The calculations exploit an analogy to the problem of…

We consider the properties of an observable (such as a single spin component that squares to the identity) when expressed as a matrix in the basis of energy eigenstates, and then truncated to a microcanonical slice of energies of varying…

This paper is devoted to the statistics of the quantum eigenfunctions in an ensemble of finite disordered systems (metallic grains). We focus on moments of inverse participation ratio. In the universal random matrix limit that corresponds…

We investigate the eigenvalue spectrum of the staggered Dirac matrix in SU(3) gauge theory and in full QCD as well as in quenched U(1) theory. As a measure of the fluctuation properties of the eigenvalues, we consider the nearest-neighbor…

We study semi-classical limits of eigenfunctions of a quantized linear hyperbolic automorphism of the torus ("cat map"). For some values of Planck's constant, the spectrum of the quantized map has large degeneracies. Our first goal in this…

Using the diagrammatic method, we derive a set of self-consistent equations that describe eigenvalue distributions of large correlated asymmetric random matrices. The matrix elements can have different variances and be correlated with each…

We set up a covariant renormalisation group equation on a foliated spacetime which preserves background diffeomorphism symmetry. As a first application of the new formalism, we study the effect of quantum fluctuations in Lorentz symmetry…

We study the eigenvector mass distribution of an $N\times N$ Wigner matrix on a set of coordinates $I$ satisfying $| I | \ge c N$ for some constant $c >0$. For eigenvectors corresponding to eigenvalues at the spectral edge, we show that the…

This paper calculates the fluctuations of eigenvalues of polynomials on large Haar unitaries cut by finite rank deterministic matrices. When the eigenvalues are all simple, we can give a complete algorithm for computing the fluctuations.…

Typical eigenstates of quantum systems, whose classical limit is chaotic, are well approximated as random states. Corresponding eigenvalue spectra is modeled through appropriate ensemble of random matrix theory. However, a small subset of…

While the notion of quantum chaos is tied to random matrix spectral correlations, also eigenstate properties in chaotic systems are often assumed to be described by random matrix theory. Analytic insights into eigenstate correlations can be…

Spectral statistics and correlations are the usual way to study the presence or absence of quantum chaos in quantum systems. We present our investigation on the study of the fluctuation average and variance of certain correlation functions…

Motivated by the Dirac idea that fundamental constant are dynamical variables and by conjectures on quantum structure of spacetime at small distances, we consider the possibility that Planck constant $\hbar$ is a time depending quantity,…

Starting from a critical analysis of recently reported surprisingly large uncertainties in length and position measurements deduced within the framework of quantum gravity, we embark on an investigation both of the correlation structure of…

Using a \emph{gedanken} experiment providing presumably a minimal inaccuracy the uncertainty contributions to the space-time measurement are precisely evaluated for clock and mirror respectively. The resulting expression of minimal…

We propose to analyse the statistical properties of a sequence of vectors using the spectrum of the associated Gram matrix. Such sequences arise e.g. by the repeated action of a deterministic kicked quantum dynamics on an initial condition…

In the process of work it has been found that space-time quantum fluctuations are naturally described in terms of the deformation parameter introduced on going from the well-known quantum mechanics to that at Planck scales and put forward…

We characterize the quantum gate fidelity in a state-independent manner by giving an explicit expression for its variance. The method we provide can be extended to calculate all higher order moments of the gate fidelity. Using these results…

We investigate the small scale equidistribution properties of random waves in $\mathbb{R}^{n}$. Numerical evidence suggests that such objects display a fine scale filament structure. We show that the X-ray along any line segment is…