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This paper revisits the error analysis of the Stochastic Lanczos Quadrature (SLQ) method for approximating the trace of matrix functions, with a specific focus on asymmetric Lanczos quadrature rules. We reexplain an existing theoretical…
We reformulate the Lanczos tau method for the discretization of time-delay systems in terms of a pencil of operators, allowing for new insights into this approach. As a first main result, we show that, for the choice of a shifted Legendre…
Using an operatorial formalism, we study the Kramers equation and its applications to numerical simulations. We obtain classes of algorithms which may be made precise at every desired order in the time step $\epsilon$ and with a set of free…
We study the universal properties of the Lanczos algorithm applied to finite-size many-body quantum systems. Focusing on autocorrelation functions of local operators and on their infinite-time behaviour at finite size, we conjecture that in…
This paper describes four methods for estimating autocorrelation time and evaluates these methods with a test set of seven series. Fitting an autoregressive process appears to be the most accurate method of the four. An R package is…
We investigate early-time equilibration rates of observables in closed many-body quantum systems and compare them to those of two correlation functions, first introduced by Kubo and Srednicki. We explore whether these different rates…
Isolated many-body quantum systems quenched far from equilibrium can eventually equilibrate, but it is not yet clear how long they take to do so. To answer this question, we use exact numerical methods and analyze the entire evolution, from…
In this paper we compare two methods for finding extremal eigenvalues and eigenvectors: the restarted Lanczos method and momentum accelerated power iterations. The convergence of both methods is based on ratios of Chebyshev polynomials…
We introduce structured random matrix ensembles, constructed to model many-body quantum systems with local interactions. These ensembles are employed to study equilibration of isolated many-body quantum systems, showing that rather complex…
Lanczos-type algorithms are efficient and easy to implement. Unfortunately they breakdown frequently and well before convergence has been achieved. These algorithms are typically based on recurrence relations which involve formal orthogonal…
This work introduces a method for determining the energy spectrum of lattice quantum chromodynamics (LQCD) by applying the Lanczos algorithm to the transfer matrix and using a bootstrap generalization of the Cullum-Willoughby method to…
The autonomous systems need to decide how to react to the changes at runtime efficiently. The ability to rigorously analyze the environment and the system together is theoretically possible by the model-driven approaches; however, the model…
We present a Lanczos tau method for the approximation and optimization of the $H^2$-norm of time-delay systems described by semi-explicit delay differential algebraic equations. The soundness of this approach is proven under the assumption…
Recovering properties of correlation functions is typically challenging. On one hand, experimentally, it requires measurements with a temporal resolution finer than the system's dynamics. On the other hand, analytical or numerical analysis…
We characterize the conditions under which a multi-time quantum process with a finite temporal resolution can be approximately described by an equilibrium one. By providing a generalization of the notion of equilibration on average, where a…
We present a method based on the Path Integral Monte Carlo formalism for the calculation of ground-state time correlation functions in quantum systems. The key point of the method is the consideration of time as a complex variable whose…
We propose efficient preconditioning algorithms for an eigenvalue problem arising in quantum physics, namely the computation of a few interior eigenvalues and their associated eigenvectors for the largest sparse real and symmetric…
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…
The time-ordered exponential is defined as the function that solves a system of coupled first-order linear differential equations with generally non-constant coefficients. In spite of being at the heart of much system dynamics, control…
Recent work introduced a new framework for analyzing correlation functions with improved convergence and signal-to-noise properties, as well as rigorous quantification of excited-state effects, based on the Lanczos algorithm and spurious…