I. Harczuk — Atomic decomposition of molecular
... which has led to a wide window of physical phenomena being understood at larger scales 1 . However, at the most fundamental level of computational chemistry, there is an inherent bottleneck which makes the computational time of quantum mechanical methods scale non-linearly with respect to the proble ...
... which has led to a wide window of physical phenomena being understood at larger scales 1 . However, at the most fundamental level of computational chemistry, there is an inherent bottleneck which makes the computational time of quantum mechanical methods scale non-linearly with respect to the proble ...
QUANTUM COMPUTATION: THE TOPOLOGICAL APPROACH
... What is actually observed is a frequency, say a flash of light, corresponding to an eigenvalue of the observable. Which eigenvalue is observed depends probabilistically on the rotated state vector. ...
... What is actually observed is a frequency, say a flash of light, corresponding to an eigenvalue of the observable. Which eigenvalue is observed depends probabilistically on the rotated state vector. ...
Smoothed Particle Hydrodynamics (SPH)
... Note: If the magnitude of ni is small we can get numerical problem in the division above. To avoid this we only calculate ni / ni if the magnitude of ni exceeds a certain threshold. ...
... Note: If the magnitude of ni is small we can get numerical problem in the division above. To avoid this we only calculate ni / ni if the magnitude of ni exceeds a certain threshold. ...
Renormalization
In quantum field theory, the statistical mechanics of fields, and the theory of self-similar geometric structures, renormalization is any of a collection of techniques used to treat infinities arising in calculated quantities.Renormalization specifies relationships between parameters in the theory when the parameters describing large distance scales differ from the parameters describing small distances. Physically, the pileup of contributions from an infinity of scales involved in a problem may then result in infinities. When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. To define them, this continuum limit, the removal of the ""construction scaffolding"" of lattices at various scales, has to be taken carefully, as detailed below.Renormalization was first developed in quantum electrodynamics (QED) to make sense of infinite integrals in perturbation theory. Initially viewed as a suspect provisional procedure even by some of its originators, renormalization eventually was embraced as an important and self-consistent actual mechanism of scale physics in several fields of physics and mathematics. Today, the point of view has shifted: on the basis of the breakthrough renormalization group insights of Kenneth Wilson, the focus is on variation of physical quantities across contiguous scales, while distant scales are related to each other through ""effective"" descriptions. All scales are linked in a broadly systematic way, and the actual physics pertinent to each is extracted with the suitable specific computational techniques appropriate for each.