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A phenomenological Hamiltonian of a closed (i.e., unitary) quantum system is assumed to have an $N$ by $N$ real-matrix form composed of a unperturbed diagonal-matrix part $H^{(N)}_0$ and of a tridiagonal-matrix perturbation…
Quantum Hamiltonian identification is important for characterizing the dynamics of quantum systems, calibrating quantum devices and achieving precise quantum control. In this paper, an effective two-step optimization (TSO) quantum…
Understanding the linear response of any system is the first step towards analyzing its linear and nonlinear dynamics, stability properties, as well as its behavior in the presence of noise. In non-Hermitian Hamiltonian systems, calculating…
We study a class of time-dependent (TD) non-Hermitian Hamiltonians $H(t)$ that can be transformed into a time-independent pseudo-Hermitian Hamiltonian $\mathcal{H}_{0}^{PH}$ using a suitable TD unitary transformation $F(t)$. The latter can…
This note is devoted to inverse spectral problems for canonical Hamiltonian systems on the half-line. An approach to inverse spectral problems based on the use of truncated Toeplitz operators has been especially effective in the case when…
We discuss a general and systematic method for obtaining effective Hamiltonians that describe different nonlinear optical processes. The method exploits the existence of a nonlinear deformation of the usual su(2) algebra that arises as the…
This paper is concerned with the Taylor-reduced basis method (Taylor-RBM) for the efficient approximation of eigenspaces of large scale parametric Hermitian matrices. The Taylor-RBM is a local model order reduction method, which constructs…
This paper introduces an efficient algorithm for finding the dominant generalized eigenvectors of a pair of symmetric matrices. Combining tools from approximation theory and convex optimization, we develop a simple scalable algorithm with…
The reduction of Hamiltonian systems aims to build smaller reduced models, valid over a certain range of time and parameters, in order to reduce computing time. By maintaining the Hamiltonian structure in the reduced model, certain…
We present an extensive numerical study of ground-state properties of confined repulsively interacting fermions on one-dimensional optical lattices. Detailed predictions for the atom-density profiles are obtained from parallel Kohn-Sham…
Estimating the eigenvalues of non-normal matrices is a foundational problem with far-reaching implications, from modeling non-Hermitian quantum systems to analyzing complex fluid dynamics. Yet, this task remains beyond the reach of standard…
Adaptive Molecular Resolution approaches in Molecular Dynamics are becoming relevant tools for the analysis of molecular liquids characterized by the interplay of different physical scales. The essential difference among these methods is in…
A Bose-Hubbard Hamiltonian, modeling cold bosons in an optical lattice, is used to simulate the dynamics of interacting open quantum systems as subsystems a larger closed system, avoiding complications like the introduction of baths,…
We report an efficient program for computing the eigenvalues and symmetry-adapted eigenvectors of very large quaternionic (or Hermitian skew-Hamiltonian) matrices, using which structure-preserving diagonalization of matrices of dimension N…
We develop an accelerated gradient descent algorithm on the Grassmann manifold to compute the subspace spanned by a number of leading eigenvectors of a symmetric positive semi-definite matrix. This has a constant cost per iteration and a…
Many natural phenomena involve processes that happen simultaneously at different characteristic length- and timescales. Typically, the region where the process of interest happens is affected by fluctuations in its surroundings. Modeling…
The problem of the reconstruction of the large scale density and velocity fields from peculiar velocities surveys is addressed here within a Bayesian framework by means of Hamiltonian Monte Carlo (HMC) sampling. The HAmiltonian Monte carlo…
Solving eigenproblem of the Laplacian matrix of a fully connected weighted graph has wide applications in data science, machine learning, and image processing, etc. However, this is very challenging because it involves expensive matrix…
Studying the optoelectronic structure of materials can require the computation of several thousands of the smallest positive eigenpairs of a pseudo-hermitian Hamiltonian. Iterative eigensolvers may be preferred over direct methods for this…
Quantum physics can be extended into the complex domain by considering non-Hermitian Hamiltonians that are $\mathcal{PT}$-symmetric. These exhibit exceptional points (EPs) where the eigenspectrum changes from purely real to purely imaginary…