Related papers: Rigorous Formalization of Orbital Functionals: Add…
We study periodic orbits in a time-dependent two-center Stark-Zeeman system, which models the motion of a charged particle attracted by two fixed Coulomb centers and subject to external magnetic and time-dependent electric fields. A…
Traditional geometry employs idealized concepts like that of a point or a curve, the operational definition of which relies on the availability of classical point particles as probes. Real, physical objects are quantum in nature though,…
Coulomb integrals, i.e., matrix elements of bare or screened Coulomb interaction between one-electron orbitals, are fundamental objects in many approaches developed to tackle the challenging problem of calculating the electronic structure…
Orbital-free density functional theory promises to deliver linear-scaling electronic structure calculations. This requires the knowledge of the non-interacting kinetic-energy density functional (KEDF), which should be accurate and must…
Functional geometry is a framework using concepts from geometry to understand the invariance of amplitudes in quantum field theory under a large class of field redefinitions, including those involving derivatives. It is inspired by…
In this effort, a novel operator theoretic framework is developed for data-driven solution of optimal control problems. The developed methods focus on the use of trajectories (i.e., time-series) as the fundamental unit of data for the…
The issue of orbital relaxation in computational core-hole spectroscopy, specifically x-ray absorption, has been a major problem for methods such as equation-of-motion coupled cluster with singles and doubles (EOM-CCSD). The…
We present a new theory for partitioning simulations of periodic and solid-state systems into physically sound atomic contributions at the level of Kohn-Sham density functional theory. Our theory is based on spatially localized linear…
Nonrelativistic conformal groups, indexed by l=N/2, are analyzed. Under the assumption that the "mass" parametrizing the central extension is nonvanishing the coadjoint orbits are classified and described in terms of convenient variables.…
Using principles of asymptotic analysis, we derive the exact leading corrections to the Thomas-Fermi kinetic energy approximation for Kohn-Sham electrons for slabs. This asymptotic expansion approximation includes crucial quantum…
Million-atom quantum simulations are in principle feasible with Orbital-Free Density Functional Theory (OF-DFT) because the algorithms only require simple functional minimizations with respect to the electron density function. In this…
Local density approximation (LDA) to the density functional theory (DFT) has continuous derivative of total energy as a number of electrons function and continuous exchange-correlation potential, while in exact DFT both should be…
We present a hierarchical viewpoint on the operator-algebraic formulation of quantum systems, in which $C^{*}$-algebras are responsible for the universal and intrinsic description, whereas von Neumann algebras provide the detailed account…
We describe stabilizer states and Clifford group operations using linear operations and quadratic forms over binary vector spaces. We show how the n-qubit Clifford group is isomorphic to a group with an operation that is defined in terms of…
We report the first wholly non-empirical generalized gradient approximation, non-interacting free energy functional for orbital-free density functional theory and use that new functional to provide forces for finite-temperature molecular…
To any action of a compact quantum group on a von Neumann algebra which is a direct sum of factors we associate an equivalence relation corresponding to the partition of a space into orbits of the action. We show that in case all factors…
We re-examine three issues, the Hopf term, fractional spin and the soliton operators, in the 2+1 dimensional O(3) nonlinear sigma model based on the adjoint orbit parameterization (AOP) introduced earlier. It is shown that the Hopf Term is…
Kohn-Sham density functional theory (DFT) has long struggled with the accurate description of strongly correlated and open shell systems and improvements have been minor even in the newest hybrid functionals. In this Letter we treat the…
An axiomatic approach is herein used to determine the physically acceptable forms for general $D$-dimensional kinetic energy density functionals (KEDF). The resulted expansion captures most of the known forms of one-point KEDFs. By…
The Grover search algorithm is one of the two key algorithms in the field of quantum computing, and hence it is of significant interest to describe it in the most efficient mathematical formalism. We show firstly, that Clifford's formalism…