Related papers: Spectral and Parametric Averaging for Integrable S…
We evaluate the correlation function of the spectral staircase and use it to evaluate the mesoscopic particle number fluctuations in integrable systems.
The methods of obtaining the average spectral shape in a low statistics regime are presented. Different approaches to averaging are extensively tested with simulated spectra, based on the ASCA responses. The issue of binning up the spectrum…
Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…
Numerical calculus algorithms which estimate derivatives and integrals from data series acquired either via measurements or by sampling functions are essential in scientific computing. To date, a few quantum algorithms have been developed…
A key conjecture about the evolution of complex quantum systems towards an ergodic steady state, known as scrambling, is that this process acquires universal features when it is most efficient. We develop a single-parameter scaling theory…
Due to significant manufacturing process variations, the performance of integrated circuits (ICs) has become increasingly uncertain. Such uncertainties must be carefully quantified with efficient stochastic circuit simulators. This paper…
Spectral analysis plays a crucial role in high-dimensional statistics, where determining the asymptotic distribution of various spectral statistics remains a challenging task. Due to the difficulties of deriving the analytic form, recent…
In this work we analyze the spectral level statistics of the one-dimensional ionic Hubbard model, the Hubbard model with an alternating on-site potential. In particular, we focus on the statistics of the gap ratios between consecutive…
The averaging method is a classical powerful tool in perturbation theory of dynamical systems. There are two major obstacles to applying the averaging method, resonances and separatrices. In this paper we obtain realistic asymptotic…
In this paper we address the problem of uncertainty management for robust design, and verification of large dynamic networks whose performance is affected by an equally large number of uncertain parameters. Many such networks (e.g. power,…
During the last years quantum graphs have become a paradigm of quantum chaos with applications from spectral statistics to chaotic scattering and wave function statistics. In the first part of this review we give a detailed introduction to…
Computational spectrometers are at the forefront of spectroscopy, promising portable, on-chip, or in-situ spectrum analysis through the integration of advanced computational techniques into optical systems. However, existing computational…
We address the question as to why, in the semiclassical limit, classically chaotic systems generically exhibit universal quantum spectral statistics coincident with those of Random Matrix Theory. To do so, we use a semiclassical resummation…
We introduce a new strategy for coupling the parallel in time (parareal) iterative methodology with multiscale integrators. Following the parareal framework, the algorithm computes a low-cost approximation of all slow variables in the…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
We describe a proof-of-concept development and application of a phase averaging technique to the nonlinear rotating shallow water equations on the sphere, discretised using compatible finite element methods. Phase averaging consists of…
Permutation synchronization is an important problem in computer science that constitutes the key step of many computer vision tasks. The goal is to recover $n$ latent permutations from their noisy and incomplete pairwise measurements. In…
Theoretical expressions for the distribution of the ratio of consecutive level spacings for quantum systems with transiting dynamics remain unknown. We propose a family of one-parameter distributions $P(r)\equiv P(r;\beta)$, where…
We consider nearest neighbor spacing distributions of composite ensembles of levels. These are obtained by combining independently unfolded sequences of levels containing only few levels each. Two problems arise in the spectral analysis of…
Starting from a semiclassical approach recently developed for spectral correlation functions of quantum systems whose classical dynamics is chaotic, we focus on the case of broken time-reversal symmetry, the so-called unitary class. We…