Related papers: Koopmans spectral functionals in periodic-boundary…
The self consistent version of the density functional theory is presented, which allows to calculate the ground state and dynamic properties of finite multi-electron systems. An exact functional equation for the effective interaction, from…
Koopman spectral theory has provided a new perspective in the field of dynamical systems in recent years. Modern dynamical systems are becoming increasingly non-linear and complex, and there is a need for a framework to model these systems…
Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…
This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to…
Spectral density functions quantify how environmental modes couple to quantum systems and govern their open dynamics. Inferring such frequency-dependent functions from time-domain measurements is an ill-conditioned inverse problem. Here, we…
Koopman operators and transfer operators represent dynamical systems through their induced linear action on vector spaces of observables, enabling the use of operator-theoretic techniques to analyze nonlinear dynamics in state space. The…
We calculate the spectral functions of model systems describing 5f-compounds adopting Cluster Perturbation Theory. The method allows for an accurate treatment of the short-range correlations. The calculated excitation spectra exhibit…
In this paper, we consider band-structure calculations governed by the Helmholtz or Maxwell equations in piecewise homogeneous periodic materials. Methods based on boundary integral equations are natural in this context, since they…
This paper presents a novel Koopman composition operator representation framework for control systems in reproducing kernel Hilbert spaces (RKHSs) that is free of explicit dictionary or input parametrizations. By establishing fundamental…
Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems -- the plane-wave method -- is a spectral method based on eigenfunction expansion, we formulate a spectral method…
Quantum dots with conduction electrons or holes originating from several bands are considered. We assume the particles are confined in a harmonic potential and assume the electrons (or holes) belonging to different bands to be different…
The density of states for a particle moving in a random potential with a Gaussian correlator is calculated exactly using the functional integral technique. It is achieved by expressing the functional degrees of freedom in terms of the…
The Koopman operator induced by a dynamical system is inherently linear and provides an alternate method of studying many properties of the system, including attractor reconstruction and forecasting. Koopman eigenfunctions represent the…
Spectral decomposition of the Koopman operator is attracting attention as a tool for the analysis of nonlinear dynamical systems. Dynamic mode decomposition is a popular numerical algorithm for Koopman spectral analysis; however, we often…
Wannier functions provide a localized representation of spectral subspaces of periodic Hamiltonians, and play an important role for interpreting and accelerating Hartree-Fock and Kohn-Sham density functional theory calculations in quantum…
We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal…
We develop a new generalization of Koopman operator theory that incorporates the effects of inputs and control. Koopman spectral analysis is a theoretical tool for the analysis of nonlinear dynamical systems. Moreover, Koopman is intimately…
We develop a semiclassical density functional theory in the context of quantum dots. Coulomb blockade conductance oscillations have been measured in several experiments using nanostructured quantum dots. The statistical properties of these…
Representing nonlinear dynamical systems using the Koopman Operator and its spectrum has distinct advantages in terms of linear interpretability of the model as well as in analysis and control synthesis through the use of well-studied…
We present a data-driven method for spectral analysis of the Koopman operator based on direct construction of the pseudo-resolvent from time-series data. Finite-dimensional approximation of the Koopman operator, such as those obtained from…