arXiv subjects

Mark Everitt

Publications and source records attributed to Mark Everitt.

3 recordsLinked to original sources

arXiv2026

Spinor Structure from Relativistic Mass-Shell Factorisation in Phase Space

Spin is usually regarded as one of the most intrinsically quantum phenomena, while its lack of a natural analogue in classical physics presents an obstacle to phase-space deformation-quantisation accounts of its origin. We show that this difficulty may arise from imposing an overly restrictive scalar Hamiltonian structure on relativistic phase space. Requiring the complete massive mass-shell constraint to be represented by a single finite-dimensional expression that is linear in all four components of momentum forces its coefficient matrices to satisfy a Clifford algebra. The minimal complex representation of this algebra is four-dimensional. Requiring statistical completeness within the rank-two subspace selected by the mass-shell factor then leads to a four-by-four matrix-valued ensemble distribution. At each on-shell momentum, the linear mass-shell operator selects a two-dimensional subspace, so a general classical ensemble is described by a $2 \times 2$ matrix before quantisation. Projecting the Weyl-ordered Liouville equation into this subspace gives relativistic transport while preserving arbitrary populations and coherences and the remaining projector components determine the first deformation correction. Expansion of the matrix Moyal star commutator yields the symmetrised classical matrix Liouvillian at leading order. If the stronger two-sided star constraints are imposed, they reproduce the left and right Dirac-Wigner equations and introduce $\hbar$ as the scale converting the dimensionless internal algebra into physical angular momentum. These results suggest a non-quantum origin for spinor structure and a route to reconciling relativistic covariance, classical phase-space transport, and quantum spin.

quant-ph↗

arXiv2019

Errors, chaos and the collisionless limit

We simultaneously study the dynamics of the growth of errors and the question of the faithfulness of simulations of $N$-body systems. The errors are quantified through the numerical reversibility of small-$N$ spherical systems, and by comparing fixed-timestep runs with different stepsizes. The errors add randomly, before exponential divergence sets in, with exponentiation rate virtually independent of $N$, but scale saturating as $\sim 1/\sqrt{N}$, in line with theoretical estimates presented. In a third phase, the growth rate is initially driven by multiplicative enhancement of errors, as in the exponential stage. It is then qualitatively different for the phase space variables and mean field conserved quantities (energy and momentum); for the former, the errors grow systematically through phase mixing, for the latter they grow diffusively. For energy, the $N$-variation of the `relaxation time' of error growth follows the $N$-scaling of two-body relaxation. This is also true for angular momentum in the fixed stepsize runs, although the associated error threshold is higher and the relaxation time smaller. Due to shrinking saturation scales, the information loss associated with the exponential instability decreases with $N$ and the dynamical entropy vanishes at any finite resolution as $N \rightarrow \infty$. A distribution function depending on the integrals of motion in the smooth potential is decreasingly affected. In this sense there is convergence to the collisionless limit, despite the persistence of exponential instability on infinitesimal scales. Nevertheless, the slow $N$-variation in its saturation points to the slowness of the convergence.

astro-ph.IM↗

arXiv2013

A new introductory quantum mechanics curriculum

The Institute of Physics New Quantum Curriculum consists of freely available online learning and teaching materials (quantumphysics.iop.org) for a first course in university quantum mechanics starting from two-level systems. This approach immediately immerses students in inherently quantum mechanical aspects by focusing on experiments that have no classical explanation. It allows from the start a discussion of interpretive aspects of quantum mechanics and quantum information theory. This article gives an overview of the resources available at the IOP website. The core text is presented as around 80 articles co-authored by leading experts that are arranged in themes and can be used flexibly to provide a range of alternative approaches. Many of the articles include interactive simulations with accompanying activities and problem sets that can be explored by students to enhance their understanding. Much of the linear algebra needed for this approach is part of the resource. Solutions to activities are available to instructors. The resources can be used in a variety of ways from supplements to existing courses to a complete programme.

physics.ed-ph↗