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We present an approximate scheme for analytical gradients and nonadiabatic couplings for calculating state-average density matrix renormalization group self-consistent-field wavefunction. Our formalism follows closely the state-average…
Variational wave function ansatze are an invaluable tool to study the properties of strongly correlated systems. We propose such a wave function, based on the theory of auxiliary fields and combining aspects of auxiliary-field quantum Monte…
Orbital-free density functional theory (OF-DFT) is a promising method for large-scale quantum mechanics simulation as it provides a good balance of accuracy and computational cost. Its applicability to large-scale simulations has been aided…
We employ Non-equilibrium Green's functions (NEGF) to describe the real-time dynamics of an adsorbate-surface model system exposed to ultrafast laser pulses. For a finite number of electronic orbitals, the system is solved exactly and…
This paper presents a novel physically consistent analytical model for two-dimensional (2D) waveguide-fed metasurface antennas that is based on the discrete dipole approximation. The proposed framework extends previous works deriving…
A matrix representation is introduced for stationary beam-like light fields that allows for simultaneous treatment of the orbital angular momentum (OAM) and the second-order state of spatial coherence. This Coherence-OAM matrix is a…
We study a first-order system formulation of the (acoustic) wave equation and prove that the operator of this system is an isomorphsim from an appropriately defined graph space to L^2. The results rely on well-posedness and stability of the…
We introduce an automatic variationally stable analysis (AVS) for finite element (FE) computations of scalar-valued convection-diffusion equations with non-constant and highly oscillatory coefficients. In the spirit of least squares FE…
Maintaining long-term wavefront stability is critical for the Habitable Worlds Observatory (HWO), which targets contrasts approaching $10^{-10}$ and therefore requires continuous dark-zone maintenance using high-order wavefront sensing and…
We describe an algorithm for the numerical solution of second order linear differential equations in the highly-oscillatory regime. It is founded on the recent observation that the solutions of equations of this type can be accurately…
A high-order combined interpolation/finite element technique is developed for solving the coupled groundwater-surface water system that governs flows in karst aquifers. In the proposed high-order scheme we approximate the time derivative…
In this paper, a novel $h$-adaptive isogeometric solver utilizing high-order hierarchical splines is proposed to solve the all-electron Kohn--Sham equation. In virtue of the smooth nature of Kohn--Sham wavefunctions across the domain,…
By introducing a set of auxiliary equations representing a many-body system, we have derived an extension of the Kohn-Sham scheme for the density functional theory. These equations consist of a Kohn-Sham-type equation determining…
The combination of density functional theory (DFT) with a multiconfigurational wave function is an efficient way to include dynamical correlation in calculations with multiconfiguration self-consistent field wave functions. These methods…
We have developed a new efficient and accurate impurity solver for the single impurity Anderson model (SIAM), which is based on a non-perturbative recursion technique in a space of operators and involves expanding the self-energy as a…
Domain decomposition methods are among the most efficient for solving sparse linear systems of equations. Their effectiveness relies on a judiciously chosen coarse space. Originally introduced and theoretically proved to be efficient for…
We introduce a self-consistent mean-field quantum optimization algorithm that approximates the ground state of classical Ising Hamiltonians. The algorithm decomposes the problem into independent subproblems and treats the interactions…
KSSOLV (Kohn-Sham Solver) is a MATLAB toolbox for performing Kohn-Sham density functional theory (DFT) calculations with a plane-wave basis set. KSSOLV 2.0 preserves the design features of the original KSSOLV software to allow users and…
The nearest-neighbor quantum-antiferromagnetic (AF) Heisenberg model for spin 1/2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a…
A second-order face-centred finite volume strategy on general meshes is proposed. The method uses a mixed formulation in which a constant approximation of the unknown is computed on the faces of the mesh. Such information is then used to…