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The existence of a positive linear functional acting on the space of (differences between) conformal blocks has been shown to rule out regions in the parameter space of conformal field theories (CFTs). We argue that at the boundary of the…

The Koopman operator framework offers a way to represent a nonlinear system as a linear one. The key to this simplification lies in the identification of eigenfunctions. While various data-driven algorithms have been developed for this…

We construct a stationary density functional for the partition function from a chosen set of one (boson) line irreducible Feynman diagrams. The construction does not proceed by the inversion of a Legendre transform. It is formulated for…

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…

We showcase the advantages of orbital-free density-potential functional theory (DPFT), a more flexible variant of Hohenberg-Kohn density functional theory. DPFT resolves the usual trouble with the gradient-expanded kinetic energy functional…

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…

In this work we give a comprehensive derivation of an exact and numerically feasible method to perform ab-initio calculations of quantum particles interacting with a quantized electromagnetic field. We present a hierachy of…

Probing optical excitations with nanometer resolution is important for understanding their dynamics and interactions down to the atomic scale. Electron microscopes currently offer the unparalleled ability of rendering spatially-resolved…

This work presents the general form solution of Koopman Partial Differential Equation and shows that its functional dimensionality is finite. The dimensionality is as the dimensionality of the dynamics. Thus, the representation of nonlinear…

Plant reflectance spectra - the profile of light reflected by leaves across different wavelengths - supply the spectral signature for a species at a spatial location to enable estimation of functional and taxonomic diversity for plants. We…

We calculate correlation functions of exactly-solvable one-dimensional flat-band models by utilizing the "molecular-orbital" representation. The models considered in this paper have a gapped ground state with flat-band being fully occupied,…

We introduce a spectral density functional theory which can be used to compute energetics and spectra of real strongly--correlated materials using methods, algorithms and computer programs of the electronic structure theory of solids. The…

Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…

We present a substantial extension of our constraint-based approach for development of orbital-free (OF) kinetic-energy (KE) density functionals intended for the calculation of quantum-mechanical forces in multi-scale molecular dynamics…

Measurable spectra are theoretically very often derived from complicated many-body Green's functions. In this way, one calculates much more information than actually needed. Here we present an in principle exact approach to construct…

We introduce a method that allows the evaluation of general expressions for the spectral functions of the one-dimensional Hubbard model for all values of the on-site electronic repulsion U. The spectral weights are expressed in terms of…

Functionals that strive to correct for such self-interaction errors, such as those obtained by imposing the Perdew-Zunger self-interaction correction or the generalized Koopmans' condition, become orbital dependent or orbital-density…

For certain correlated electron-photon systems we construct the exact density-to-potential maps, which are the basic ingredients of a density-functional reformulation of coupled matter-photon problems. We do so for numerically exactly…

We introduce an efficient first-principles framework for simulating angle-resolved photoemission spectroscopy (ARPES) based on the direct computation of photoelectron states as solutions of the Kohn-Sham equation with scattering boundary…

Koopman operator theory enables linear analysis of nonlinear dynamical systems by lifting their evolution to infinite-dimensional function spaces. However, finite-dimensional approximations of Koopman and transfer (Frobenius--Perron)…