552 research outputs found
Alternative sampling for variational quantum Monte Carlo
Expectation values of physical quantities may accurately be obtained by the
evaluation of integrals within Many-Body Quantum mechanics, and these
multi-dimensional integrals may be estimated using Monte Carlo methods. In a
previous publication it has been shown that for the simplest, most commonly
applied strategy in continuum Quantum Monte Carlo, the random error in the
resulting estimates is not well controlled. At best the Central Limit theorem
is valid in its weakest form, and at worst it is invalid and replaced by an
alternative Generalised Central Limit theorem and non-Normal random error. In
both cases the random error is not controlled. Here we consider a new `residual
sampling strategy' that reintroduces the Central Limit Theorem in its strongest
form, and provides full control of the random error in estimates. Estimates of
the total energy and the variance of the local energy within Variational Monte
Carlo are considered in detail, and the approach presented may be generalised
to expectation values of other operators, and to other variants of the Quantum
Monte Carlo method.Comment: 14 pages, 9 figure
On the Extended Hensel Construction and its Application to the Computation of Real Limit Points
The Extended Hensel Construction (EHC) is a procedure which, for an input bivariate polyno- mial with complex coefficients, can serve the same purpose as the Newton-Puiseux algorithm. We show that the EHC requires only linear algebra and univariate polynomial arithmetic. We deduce complexity estimates and report on a software implementation together with experimental results. This work is motivated and illustrated by two applications. The first one is the computation of real branches of space curves. The second one is the computation of limits of real multivariate rational function. For the latter, we present an algorithm for determining the existence of the limit of a real multivariate rational function q at a given point p which is an isolated zero of the denominator of q. When the limit exists, the algorithm computes it, without making any assumptions on the number of variables
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