Sampling in a Quantum Population, and Applications

Siyuan Chen, Yiqi Yang, Miguel A. Morales +1 more

Correlated sampling has wide-ranging applications in Monte Carlo calculations. When branching random walks are involved, as commonly found in many algorithms in quantum physics and electronic structure, population control is typically not applied with correlated sampling due to technical difficulties. This hinders the stability and efficiency of correlated sampling. In this paper, we study schemes for allowing birth/death in correlated sampling and propose an algorithm for population control. The algorithm can be realized in several variants depending on the application. One variant is a static method that creates a reference run and allows other correlated calculations to be added a posteriori. Another optimizes the population control for a set of correlated, concurrent runs dynamically. These approaches are tested in different applications in quantum systems, including both the Hubbard model and electronic structure calculations in real materials.

Jonas Maziero

A. A. Bogdanov, А. И. Зайцев, Igor Viktorovich Ryzhov

The effect of the sample extent in the process of superradiance and superradiance without population inversion of a thin ( L ≤ λ) layer of three-level atoms (Λ-configuration of working transitions) is investigated. The limits of applicability of the spatially homogeneous approximation are determined. The consideration of the extent is shown to introduce new effects into the kinetics of populations and the field.

Faqir Chand Auluck

Luigi Accardi, Wilhelm von Waldenfels

Huw Price

Methods of selecting samples from larger populations may produce bias, in either direction: inducing correlations between variables independent in the full population, or masking correlations between variables dependent in the full population. Here we propose a surprising application of these familiar ideas. We argue that they are relevant to puzzling correlations uncovered in quantum theory by John Stewart Bell (Bell 1964). In the light of Bell's work and subsequent experiments it is widely believed that the quantum world is 'nonlocal', in apparent tension with relativity. Many hold that the only alternative is to abandon 'realism', the view that there is an objective world independent of measurement. We propose instead that Bell's correlations are selection artefacts, in tension neither with relativity nor realism. In standard two-particle Bell experiments the relevant selection is a preselection, achieved by the preparation of the initial state. Again, selection bias via preselection is familiar elsewhere in science, but it doesn't seem to have been noticed that it is applicable in this case.