Related papers: Comment on "Self-Averaging Stochastic Kohn-Sham De…
Many approximations within density-functional theory spuriously predict that a many-electron system can dissociate into fractionally charged fragments. Here, we revisit the case of dissociated diatomic molecules, known to exhibit this…
In the density functional (DF) theory of Kohn and Sham, the kinetic energy of the ground state of a system of noninteracting electrons in a general external field is calculated using a set of orbitals. Orbital free methods attempt to…
Quite unexpectedly, kinetic theory is found to specify the correct definition of average value to be employed in nonextensive statistical mechanics. It is shown that the normal average is consistent with the generalized Stosszahlansatz…
Cosmological observables rely heavily on summary statistics such as two-point correlation functions. In many practical cases (e.g. the weak-lensing cosmic shear), those correlation functions are estimated from a finite, discrete sample of…
A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale…
The eigenvalue statistics of quantum ideal gases with single particle energies $e_n=n^\alpha$ are studied. A recursion relation for the partition function allows to calculate the mean density of states from the asymptotic expansion for the…
The exact interaction energy of a many-electron system is determined by the electron pair density, which is not well-approximated in standard Kohn-Sham density functional models. Here we study the (complicated but well-defined) exact…
A finite dimensional abstract approximation and convergence theory is developed for estimation of the distribution of random parameters in infinite dimensional discrete time linear systems with dynamics described by regularly dissipative…
An efficient mixed deterministic/sparse-stochastic plane-wave approach is developed for bandstructure calculations of large supercell periodic generalized-Kohn-Sham density functional theory, for any hybrid-exchange density functional. The…
Synchrotron emissivities, absorptivities, and Faraday rotation and conversion coefficients are needed in modeling a variety of astrophysical sources, including Event Horizon Telescope (EHT) sources. We develop a method for estimating…
The standard assumption for the equilibrium microcanonical state in quantum mechanics, that the system must be in one of the energy eigenstates, is weakened so as to allow superpositions of states. The weakened form of the microcanonical…
We present SPARC-atomSFE, a spectral finite-element package for accurate and efficient atomic structure calculations within the framework of Kohn-Sham density functional theory. The package supports both all-electron and norm conserving…
The Hohenberg-Kohn theorem of the density functional theory is extended by modifying the Levy constrained-search formulation. The new theorem allows us to choose arbitrary physical quantities as the basic variables which determine the…
We present an explicit method for simulating stochastic differential equations (SDEs) that have variable diffusion coefficients and satisfy the detailed balance condition with respect to a known equilibrium density. In Tupper and Yang…
The Boltzmann distribution of an ideal gas is determined by the Hamiltonian function generating single particle dynamics. Systems with higher complexity often exhibit topological constraints, which are independent of the Hamiltonian and may…
Self-assembly kinetics is usually described by approaches which assume that the shape of the aggregates has a definite form (e.g., spherical, cylindrical, cubic, etc), however that is unlikely to be the case in many finite-sized…
The grand canonical density functional theory for inhomogeneous systems of interacting bosons is developed in the effective action approach. The Legendre transform of the generating functional for Green's functions is used to define the…
Particle theorists typically use expectation values to study the quantum back-reaction on inflation, whereas many cosmologists stress the stochastic nature of the process. While expectation values certainly give misleading results for some…
The frequency-dependent exchange-correlation potential, which appears in the usual Kohn-Sham formulation of a time-dependent linear response problem, is a strongly nonlocal functional of the density, so that a consistent local density…
The capabilities of a new approach towards the foundations of Statistical Mechanics are explored. The approach is genuine quantum in the sense that statistical behavior is a consequence of objective quantum uncertainties due to entanglement…