相关论文: An embedding scheme for the Dirac equation
A matricial Darboux operator intertwining two one-dimensional stationary Dirac Hamiltonians is constructed. This operator is such that the potential of the second Dirac Hamiltonian as well as the corresponding eigenfunctions are determined…
Following from a question of Wheeler, why does the Hamiltonian constraint ${\cal H}$ of GR have the particular form it does? A first answer, by Hojman, Kucha\v{r} and Teitelboim, is that using embeddability into spacetime as a principle…
Recent numerical advances in the field of strongly correlated electron systems allow the calculation of the entanglement spectrum and entropies for interacting fermionic systems. An explicit determination of the entanglement (modular)…
We present a general approach to solve the (1+1) and (2+1)-dimensional Dirac equation in the presence of static scalar, pseudoscalar and gauge potentials, for the case in which the potentials have the same functional form and thus the…
An explicit high-order noncanonical symplectic algorithm for ideal two-fluid systems is developed. The fluid is discretized as particles in the Lagrangian description, while the electromagnetic fields and internal energy are treated as…
By introducing multipe-site correlation functions, we propose a hierarchical Green function approach, and apply it to study the characteristic properties of a 2D square lattice Hubbard model by solving the equation of motions of a…
We consider a generalization of a functional equation that models the learning process in various animal species. The equation can be considered nonlocal, as it is built with a convex combination of the unknown function evaluated at mixed…
This paper advances theoretical understanding of infinite-dimensional geometrical properties associated with Bayesian inference. First, we introduce a novel class of infinite-dimensional Hamiltonian systems for saddle Hamiltonian functions…
Hamiltonian systems are known to conserve the Hamiltonian function, which describes the energy evolution over time. Obtaining a numerical spatio-temporal scheme that accurately preserves the discretized Hamiltonian function is often a…
The intertwining technique has been widely used to study the Schr\"odinger equation and to generate new Hamiltonians with known spectra. This technique can be adapted to find the bound states of certain Dirac Hamiltonians. In this paper the…
A new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is proposed. The method is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which…
A compact form for the static Green's function for symmetric loading of an elastic sphere is derived. The expression captures the singularity in closed form using standard functions and quickly convergent series. Applications to problems…
The Dirac equation for H$_2^+$ is solved numerically by expansion in a basis set of two-center exponential functions, using different kinetic balance schemes. Very high precision (27-32 digits) is achieved, either with the dual kinetic…
Applications of the H\"uckel (tight binding) model are ubiquitous in quantum chemistry and solid state physics. The matrix representation of this model is isomorphic to an unoriented vertex adjacency matrix of a bipartite graph, which is…
We prove tunneling estimates for two-dimensional Dirac systems which are localized in space due to the presence of a magnetic field. The Hamiltonian driving the motion admits the decomposition $H = H_0 + W$, where $H_0 $ is a rotationally…
Some arguments are considered in favor of the idea that the canonical anticommutation relations for fermions should be modified in curved spacetime near the event horizon of a black hole. Such a modification is expected to lead to a change…
We report tests and results from a new approach to the spectral density and the mode number distribution of the Dirac operator in lattice gauge theories. The algorithm generates the spectral density of the lattice Dirac operator as a…
Analytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree-Fock and density functional…
We construct a boundary integral formula for harmonic functions on open, smoothly-bordered subdomains of Riemann surfaces embeddable into $\C\P^2$. The formula may be considered as an analogue of the Green's formula for domains in $\C$.
We apply a recently proposed Green Function Monte Carlo to the study of Hamiltonian lattice gauge theories. This class of algorithms computes quantum vacuum expectation values by averaging over a set of suitable weighted random walkers. By…