25,031 research outputs found
Implementing the three-particle quantization condition including higher partial waves
We present an implementation of the relativistic three-particle quantization
condition including both - and -wave two-particle channels. For this, we
develop a systematic expansion about threshold of the three-particle
divergence-free K matrix, , which is a
generalization of the effective range expansion of the two-particle K matrix,
. Relativistic invariance plays an important role in this
expansion. We find that -wave two-particle channels enter first at quadratic
order. We explain how to implement the resulting multichannel quantization
condition, and present several examples of its application. We derive the
leading dependence of the threshold three-particle state on the two-particle
-wave scattering amplitude, and use this to test our implementation. We show
how strong two-particle -wave interactions can lead to significant effects
on the finite-volume three-particle spectrum, including the possibility of a
generalized three-particle Efimov-like bound state. We also explore the
application to the system, which is accessible to lattice QCD
simulations, where we study the sensitivity of the spectrum to the components
of . Finally, we investigate the circumstances
under which the quantization condition has unphysical solutions.Comment: 57 pages, 12 figures, 3 tables (v2: Made minor clarifications,
updated a reference, fixed typos
Continuum variational and diffusion quantum Monte Carlo calculations
This topical review describes the methodology of continuum variational and
diffusion quantum Monte Carlo calculations. These stochastic methods are based
on many-body wave functions and are capable of achieving very high accuracy.
The algorithms are intrinsically parallel and well-suited to petascale
computers, and the computational cost scales as a polynomial of the number of
particles. A guide to the systems and topics which have been investigated using
these methods is given. The bulk of the article is devoted to an overview of
the basic quantum Monte Carlo methods, the forms and optimisation of wave
functions, performing calculations within periodic boundary conditions, using
pseudopotentials, excited-state calculations, sources of calculational
inaccuracy, and calculating energy differences and forces
Quantum Monte Carlo study of a positron in an electron gas
Quantum Monte Carlo calculations of the relaxation energy, pair-correlation function, and annihilating-pair momentum density are presented for a positron immersed in a homogeneous electron gas. We find smaller relaxation energies and contact pair-correlation functions in the important low-density regime than predicted by earlier studies. Our annihilating-pair momentum densities have almost zero weight above the Fermi momentum due to the cancellation of electron-electron and electron-positron correlation effects
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