Related papers: A Time-Dependent Random State Approach for Large-s…
Phase shifts for single-channel elastic electron-atom scattering are derived from time-dependent density functional theory. The H$^-$ ion is placed in a spherical box, its discrete spectrum found, and phase shifts deduced. Exact-exchange…
Using the Runge-Gross theorem that establishes the foundation of Time-dependent Density Functional Theory (TDDFT) we prove that for a given electronic Hamiltonian, choice of initial state, and choice of fragmentation, there is a unique…
While the variational principle for excited-state energies leads to a route to obtaining excited-state densities from time-dependent density functional theory, relatively little attention has been paid to the quality of the resulting…
The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by…
In this paper we propose a method to estimate the density matrix \rho of a d-level quantum system by measurements on the N-fold system. The scheme is based on covariant observables and representation theory of unitary groups and it extends…
Time-dependent density functional theory (TDDFT) is presently enjoying enormous popularity in quantum chemistry, as a useful tool for extracting electronic excited state energies. This article discusses how TDDFT is much broader in scope,…
We develop a first-principle approach to compute the counting statistics in the ground-state of $N$ noninteracting spinless fermions in a general potential in arbitrary dimensions $d$ (central for $d>1$). In a confining potential, the Fermi…
We develop a method in which the electronic densities of small fragments determined by Kohn-Sham density functional theory (DFT) are embedded using stochastic DFT to form the exact density of the full system. The new method preserves the…
The density of states for the Schroedinger equation with a Gaussian random potential is calculated in a space of dimension d=4-epsilon in the entire energy range including the vicinity of a mobility edge. Leading terms in 1/epsilon are…
A numerical approach to ground-state dynamical correlation functions from Density Matrix Renormalization Group (DMRG) is developed. Using sum rules, moments of a dynamic correlation function can be calculated with DMRG, and with the moments…
We consider interacting Fermi systems close to the unitary regime and compute the corrections to the energy density that are due to a large scattering length and a small effective range. Our approach exploits the universality of the density…
We use a meta-learning neural-network approach to analyse data from a measured quantum state. Once our neural network has been trained it can be used to efficiently sample measurements of the state in measurement bases not contained in the…
The electron density $n(\rb,t)$, which is the central tool of time-dependent density functional theory, is presently considered to be derivable from a one-body time-dependent potential $V(\rb,t)$, via one-electron wave functions satisfying…
The question of how best to estimate a continuous probability density from finite data is an intriguing open problem at the interface of statistics and physics. Previous work has argued that this problem can be addressed in a natural way…
We provide a new formulation of Time-Dependent Density Functional Theory (TDDFT) based on the geometric structure of the set of states constrained to have a fixed density. Orbital-free TDDFT is formulated using a hydrodynamics equation…
Using a finite-size scaling method, we calculate the localization properties of a disordered two-dimensional electron system in the presence of a random magnetic field. Below a critical energy $E_c$ all states are localized and the…
Machine learning is used to approximate density functionals. For the model problem of the kinetic energy of non-interacting fermions in 1d, mean absolute errors below 1 kcal/mol on test densities similar to the training set are reached with…
A generalization of the Kohn--Sham approach is derived where the correlation-energy functional depends on the one-particle density matrix of noninteracting states and on the external potential from the interacting target-state. The…
A generalized approach to Wang-Landau simulations, macroscopically constrained Wang-Landau, is proposed to simulate the density of states of a system with multiple macroscopic order parameters. The method breaks a multidimensional…
Simulating time evolution is one of the most natural applications of quantum computers and is thus one of the most promising prospects for achieving practical quantum advantage. Here, we develop quantum algorithms to extract thermodynamic…