Related papers: Local Relativistic Exact Decoupling
We propose a scheme to construct predictive models for Hamiltonian matrices in atomic orbital representation from ab initio data as a function of atomic and bond environments. The scheme goes beyond conventional tight binding descriptions…
The paper gives full details of the computation within the canonical formalism of Arnowitt, Deser, and Misner of the local-in-time part of the fourth post-Newtonian, i.e. of power eight in one over speed of light, conservative Hamiltonian…
We apply a number of atomic decomposition schemes across the standard QM7 dataset -- a small model set of organic molecules at equilibrium geometry -- to inspect the possible emergence of trends among contributions to atomization energies…
We propose a method to manipulate, possibly faster than adiabatically, four-level systems with time-dependent couplings and constant energy shifts (detunings in quantum-optical realizations). We inversely engineer the Hamiltonian, in…
We develop a method to compute $H^2$-conforming finite element approximations in both two and three space dimensions using readily available finite element spaces. This is accomplished by deriving a novel, equivalent mixed variational…
Commuting Hamiltonians lie at the boundary between classical constraint satisfaction and quantum many-body physics, exhibiting rich quantum structure while remaining more tractable than general noncommuting models. In contrast, physical…
The variational method and the Hamiltonian formalism of QCD are used to derive relativistic, momentum space integral equations for a quark-antiquark system with an arbitrary number of gluons present. As a first step, the resulting infinite…
In this paper we study decomposition methods based on separable approximations for minimizing the augmented Lagrangian. In particular, we study and compare the Diagonal Quadratic Approximation Method (DQAM) of Mulvey and Ruszczy\'{n}ski and…
We defend the Fock-space Hamiltonian truncation method, which allows to calculate numerically the spectrum of strongly coupled quantum field theories, by putting them in a finite volume and imposing a UV cutoff. The accuracy of the method…
A general procedure of local reduction for the Dirac equation is introduced to study one- and n-body interacting systems. In the one-body case we show that the reduction allows for an approximate solution of the Dirac equation, correlating…
Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is a numerical technique for solving strongly coupled QFTs, in which the full Hilbert space is truncated to a finite-dimensional low-energy subspace. The accuracy of the method is…
A relativistic version of the coupled-cluster single-double (CCSD) method is developed for atoms with a single valence electron. In earlier work, a linearized version of the CCSD method (with extensions to include a dominant class of triple…
We consider a numerical scheme for Hamilton-Jacobi equations based on a direct discretization of the Lax-Oleinik semi-group. We prove that this method is convergent with respect to the time and space stepsizes provided the solution is…
The adaptive perturbation chooses a non-standard decomposition. The Hamiltonian becomes a sum of solvable and perturbation parts. We calculate the spectrum using the adaptive perturbation method at the leading-order to compare to numerical…
Based on self-consistent field (SCF) atomic mean-field (amf) quantities, we present two simple, yet computationally efficient and numerically accurate matrix-algebraic approaches to correct both scalar-relativistic \textit{and} spin-orbit…
We demonstrate that a tight-binding Hamiltonian with nearest- and next-nearest-neighbor hopping integrals can be decomposed into bulk and boundary parts in a general lattice system. The Hamiltonian decomposition reveals that next…
We show how to apply the quantum adiabatic algorithm directly to the quantum computation of molecular properties. We describe a procedure to map electronic structure Hamiltonians to 2-local qubit Hamiltonians with a small set of physically…
In this paper, a unified nonlocal rational continuum enrichment technique is presented for improving the dispersive characteristics of some well known classical continuum equations on the basis of atomistic dispersion relations. This type…
One of the qualitatively distinct and robust implication of Loop Quantum Gravity (LQG) is the underlying discrete structure. In the cosmological context elucidated by Loop Quantum Cosmology (LQC), this is manifested by the Hamiltonian…
This paper addresses the approximation of fractional harmonic maps. Besides a unit-length constraint, one has to tackle the difficulty of nonlocality. We establish weak compactness results for critical points of the fractional Dirichlet…