Related papers: Fundamental limitations of the eigenvalue continua…
Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to…
A common challenge faced in quantum physics is finding the extremal eigenvalues and eigenvectors of a Hamiltonian matrix in a vector space so large that linear algebra operations on general vectors are not possible. There are numerous…
Quantum many-body theory has witnessed tremendous progress in various fields, ranging from atomic and solid-state physics to quantum chemistry and nuclear structure. Due to the inherent computational burden linked to the ab initio treatment…
Eigenvector continuation is a computational method for parametric eigenvalue problems that uses subspace projection with a basis derived from eigenvector snapshots from different parameter sets. It is part of a broader class of…
Kernel methods are successful approaches for different machine learning problems. This success is mainly rooted in using feature maps and kernel matrices. Some methods rely on the eigenvalues/eigenvectors of the kernel matrix, while for…
We consider the phenomenon of eigenvalue absorption for a many body Hamiltonian, which depends on a parameter. The conditions on pair potentials, which guarantee that the eigenvalues approaching the bottom of the continuous spectrum become…
We consider the eigenvalue problem for the case where the input matrix is symmetric and its entries perturb in some given intervals. We present a characterization of some of the exact boundary points, which allows us to introduce an inner…
Entanglement detection is essential in quantum information science and quantum many-body physics. It has been proved that entanglement exists almost surely for a random quantum state, while the realizations of effective entanglement…
The paper focuses on the problem of tracking eigenvalue trajectories in large-scale power system models as system parameters vary. A continuation-based formulation is presented for tracing any single eigenvalue of interest, which supports…
In this work, we discuss a new method for calculation of extremal eigenvectors and eigenvalues in systems or regions of parameter space where direct calculation is problematic. This technique relies on the analytic continuation of the power…
Large-scale eigenvalue problems arise in various fields of science and engineering and demand computationally efficient solutions. In this study, we investigate the subspace approximation for parametric linear eigenvalue problems, aiming to…
The eigensolutions of many-body quantum systems are always difficult to compute. The envelope theory is a method to easily obtain approximate, but reliable, solutions in the case of identical particles. It is extended here to treat systems…
Parameterizing mathematical models of biological systems often requires fitting to stable periodic data. In cardiac electrophysiology this typically requires converging to a stable action potential through long simulations. We explore this…
A unitarily invariant projective framework is introduced to analyze the complexity of path-following methods for the eigenvalue problem. A condition number, and its relation to the distance to ill-posedness, is given. A Newton map…
The envelope theory is an easy-to-use approximation method to obtain eigensolutions for some quantum many-body systems, in particular in the domain of hadronic physics. Even if the solutions are reliable and an improvement procedure exists,…
Equilibrium sampling of biomolecules remains an unmet challenge after more than 30 years of atomistic simulation. Efforts to enhance sampling capability, which are reviewed here, range from the development of new algorithms to…
In this article, we establish a limiting distribution for eigenvalues of a class of auto-covariance matrices. The same distribution has been found in the literature for a regularized version of these auto-covariance matrices. The original…
We investigate the passivity constraints on the relations between transmission, reflection, and absorption eigenvalues in linear time-invariant systems. Using techniques from matrix analysis, we derive necessary and sufficient conditions…
It has been known for some years that entanglement entropy obtained from partial trace does not provide the correct entanglement measure when applied to systems of identical particles. Several criteria have been proposed that have the…
Reliable and efficient computation of the pseudospectral abscissa in the large-scale setting is still not settled. Unlike the small-scale setting where there are globally convergent criss-cross algorithms, all algorithms in the large-scale…