相关论文: Derivatives of the fixed-node energy

We derive formulas which connect cumulants of particle numbers observed with efficiency losses with the original ones based on the binomial model. These formulas can describe the case with multiple efficiencies in a compact form. Compared…

We show how several important classical problems, with positive definite potential energy, can be solved by starting from the factorization of the total mechanical energy using complex numbers. In particular, we derive in a new way exact…

In these lecture notes we discuss recent progress in the rigorous derivation of effective evolution equations for the description of the dynamics of quantum mechanical many-body systems.

We study several aspects of the recently introduced fixed-phase spin-orbit diffusion Monte Carlo (FPSODMC) method, in particular, its relation to the fixed-node method and its potential use as a general approach for electronic structure…

Properties that are necessarily formulated within pure (symmetric) expectation values are difficult to calculate for projector quantum Monte Carlo approaches, but are critical in order to compute many of the important observable properties…

New techniques for evaluating the closed time path action for non-equilibrium quantum fields are presented. A derivative expansion is performed using a proper time kernel. Applications relevant to the scalar field theory of warm inflation…

Perturbative coefficients for Wilson loops and the static quark self-energy are extracted from Monte Carlo simulations at large beta on finite volumes, where all the lattice momenta are large. The Monte Carlo results are in excellent…

Monte-Carlo simulations are routinely used for estimating the scaling exponents of complex systems. However, due to finite-size effects, determining the exponent values is often difficult and not reliable. Here we present a novel technique…

Variational Monte Carlo and Green's function Monte Carlo are powerful tools for calculations of properties of light nuclei using realistic two-nucleon and three-nucleon potentials. Recently the GFMC method has been extended to multiple…

We analyse a multilevel Monte Carlo method for the approximation of distribution functions of univariate random variables. Since, by assumption, the target distribution is not known explicitly, approximations have to be used. We provide an…

In this note, we prove or re-prove several important results regarding one dimensional time fractional ODEs following our previous work \cite{fllx17}. Here we use the definition of Caputo derivative proposed in \cite{liliu17frac1,liliu2017}…

We prove a priori bounds for all derivatives of non-relativistic Coulombic eigenfunctions, involving negative powers of the distance to the singularities of the many-body potential. We use these to derive bounds for all derivatives of the…

The quasiparticle effective mass is a key quantity in the physics of electron gases, describing the renormalization of the electron mass due to electron-electron interactions. Two-dimensional electron gases are of fundamental importance in…

The total energy and electron addition and removal spectra can in principle be obtained exactly from the one-body Green's function. In practice, the Green's function is obtained from an approximate self-energy. In the framework of many-body…

This paper presents an in-depth mathematical analysis of the Monte Carlo replica method, commonly used in global fitting studies within the high-energy physics theory field. For the first time, we offer a rigorous derivation of the…

Nowadays, there is pressing demand for sustainable energy sources, or clean and 'green' fuel and hydrogen is a perfect candidate. It can be made by dissociating methane with the energy input compensated by metal-hydrogen bond formation.…

Simulating nonadiabatic effects with many-body wave function approaches is an open field with many challenges. Recent interest has been driven by new algorithmic developments and improved theoretical understanding of properties unique to…

We present a new numerical tool to solve partial differential equations involving Caputo derivatives of fractional variable order. Three Caputo-type fractional operators are considered, and for each one of them an approximation formula is…

We investigate the use of different variational principles in quantum Monte Carlo, namely energy and variance minimization, prompted by the interest in the robust and accurate estimate of electronic excited states. For two prototypical,…

Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation…