Related papers: Koopmans spectral functionals in periodic-boundary…
We propose a fully data-driven, Koopman-based framework for statistically robust control of discrete-time nonlinear systems with linear embeddings. Establishing a connection between the Koopman operator and contraction theory, it offers…
This manuscript revisits theoretical assumptions concerning dynamic mode decomposition (DMD) of Koopman operators, including the existence of lattices of eigenfunctions, common eigenfunctions between Koopman operators, and boundedness and…
Dynamical systems provide a comprehensive way to study complex and changing behaviors across various sciences. Many modern systems are too complicated to analyze directly or we do not have access to models, driving significant interest in…
New density functional theory approach based on a complete active space self-consistent field (CASSCF) reference function in Extended Koopmans' approximation is discussed. Recently, the number of generalizations of density functional theory…
A new, very fast, implementation of the exact (Fock) exchange operator for electronic structure calculations within the plane-wave pseudopotential method is described in detail for both molecular and periodic systems, and carefully…
The spectral properties of one exciton trapped in a self-assembled multi-layered quantum dot is obtained using a high precision variational numerical method. The exciton Hamiltonian includes the effect of the polarization charges, induced…
The desired shifts of the boundaries of spectral allowed zones of periodical systems are demonstrated. In particular, the phenomenon of merging neighbor allowed zones is exhibited and its simple explanation is given. It is also shown how to…
A disordered system of interacting particles exhibits localized behavior when the disorder is large compared to the interaction strength. Studying this phenomenon on a quantum computer without error correction is challenging because even…
We derive semiclassical approximations for wavefunctions, Green's functions and expectation values for classically chaotic quantum systems. Our method consists of applying singular and regular perturbations to quantum Hamiltonians. The…
We present a method to obtain spectral functions at finite temperature and density from the Functional Renormalization Group. Our method is based on a thermodynamically consistent truncation of the flow equations for 2-point functions with…
This is a follow-up of our recently proposed work on pseudopotential calculation (Ref. [21]) of atoms and molecules within DFT framework, using cartesian coordinate grid. Detailed results are presented to demonstrate the usefulness,…
We introduce a new approach to the study of modulation of high-frequency periodic wave patterns, based on pseudodifferential analysis, multi-scale expansion, and Kreiss symmetrizer estimates like those in hyperbolic and hyperbolic-parabolic…
Recent deep learning extensions in Koopman theory have enabled compact, interpretable representations of nonlinear dynamical systems which are amenable to linear analysis. Deep Koopman networks attempt to learn the Koopman eigenfunctions…
This work is motivated by the frequent occurrence of boundary value problems with various boundary conditions in the modeling of some problems in engineering and physical science. Here we propose a new technique to force the positive…
The Koopman operator is a powerful approach to global stability analysis of nonlinear systems, which provides a systematic procedure for Lyapunov function design. In this framework, Lyapunov functions are obtained through the eigenfunctions…
The fluctuations or disordered motion of the electromagnetic fields are described by statistical properties rather than instantaneous values. This statistical description of the optical fields is underlying in the Stokes-Mueller formalism…
We present a new code to evaluate thermoelectric and electronic transport properties of extended systems with a maximally-localized Wannier function basis set. The semiclassical Boltzmann transport equations for the homogeneous infinite…
Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…
Externally driven dense packings of particles can exhibit nonlinear wave phenomena that are not described by effective medium theory or linearized approximate models. Such nontrivial wave responses can be exploited to design…
Density functional theory has become the workhorse of quantum physics, chemistry, and materials science. Within these fields, a broad range of applications needs to be covered. These applications range from solids to molecular systems, from…