Adiabatic Motion of a Quantum Particle in a Two-Dimensional Magnetic Field

The adiabatic motion of a charged, spinning, quantum particle in a two - dimensional magnetic field is studied. A suitable set of operators generalizing the cinematical momenta and the guiding center operators of a particle moving in a homogeneous magnetic field is constructed. This allows us to separate the two degrees of freedom of the system into a {\sl fast} and a {\sl slow} one, in the classical limit, the rapid rotation of the particle around the guiding center and the slow guiding center drift. In terms of these operators the Hamiltonian of the system rewrites as a power series in the magnetic length \lb=\sqrt{\hbar c\over eB} and the fast and slow dynamics separates. The effective guiding center Hamiltonian is obtained to the second order in the adiabatic parameter \lb and reproduces correctly the classical limit.Comment: 17 pages, LaTe

Quantum Charged Spinning Particles in a Strong Magnetic Field (a Quantal Guiding Center Theory)

A quantal guiding center theory allowing to systematically study the separation of the different time scale behaviours of a quantum charged spinning particle moving in an external inhomogeneous magnetic filed is presented. A suitable set of operators adapting to the canonical structure of the problem and generalizing the kinematical momenta and guiding center operators of a particle coupled to a homogenous magnetic filed is constructed. The Pauli Hamiltonian rewrites in this way as a power series in the magnetic length $l_B= \sqrt{\hbar c/eB}$ making the problem amenable to a perturbative analysis. The first two terms of the series are explicitly constructed. The effective adiabatic dynamics turns to be in coupling with a gauge filed and a scalar potential. The mechanism producing such magnetic-induced geometric-magnetism is investigated in some detail.Comment: LaTeX (epsfig macros), 27 pages, 2 figures include

Boundary Conditions on Internal Three-Body Wave Functions

For a three-body system, a quantum wave function $\Psi^\ell_m$ with definite $\ell$ and $m$ quantum numbers may be expressed in terms of an internal wave function $\chi^\ell_k$ which is a function of three internal coordinates. This article provides necessary and sufficient constraints on $\chi^\ell_k$ to ensure that the external wave function $\Psi^\ell_m$ is analytic. These constraints effectively amount to boundary conditions on $\chi^\ell_k$ and its derivatives at the boundary of the internal space. Such conditions find similarities in the (planar) two-body problem where the wave function (to lowest order) has the form $r^{|m|}$ at the origin. We expect the boundary conditions to prove useful for constructing singularity free three-body basis sets for the case of nonvanishing angular momentum.Comment: 41 pages, submitted to Phys. Rev.

Maternal and infant food insecurity in the UK: a problem hiding in plain sight?

Lone parents with children under five are amongst the most food insecure in the UK (Cheong et al, 2021; Tobi et al, 2022). Yet maternal and infant food insecurity experience remains poorly understood in the UK. Drawing on findings from qualitative research conducted with parents of infants and young children, and early years health professionals, this paper highlights the hidden nature of poverty and food insecurity amongst young mothers and asks questions about the extent to which this problem is recognised and understood within health care. Two interview studies were conducted during 2020 and 2021 with 22 participants in north-east Scotland, including pregnant women and mothers with at least one child under five. One study included interviews with 18 midwives, health visitors and family nurses (HCP). The studies investigated experiences of parenting on a low income, and health professional support related to financial hardship challenges during pregnancy and early infancy. health professionals' perceptions of poverty within caseloads and experiences of raising financial issues during practice were also investigated. Data were thematically analysed using Grounded Theory principles. Key parent themes included: inadequate social security income co-existing with restricted access to paid employment; anxieties around food and other resource provision for their children; going without food themselves; and relying on charity or extended family for help with feeding. Fear of raising child protection concerns, shame and embarrassment, and exacerbating partner abuse prevented parents disclosing financial hardship and food insecurity to health professionals. Health professionals themselves were aware of poverty within some households, but not universally confident they could recognise the problem. They were also inhibited from raising the issue both because of poverty stigma, and further because of a lack of time and knowledge regarding how to do so effectively. Our findings point to the economic, nutritional and social vulnerability of lone parents that existed before the current cost-of-living crisis. As mothers continue to remain responsible for infant feeding - either as food producers themselves or through infant formula procurement from commercial sources (Frank, 2018; Doonan, 2018) - there is an urgent need to develop a better understanding of the nature and extent of maternal and infant food security in the UK, to develop more effective public policy and health care practice

Standing in a Garden of Forking Paths

According to the Path Principle, it is permissible to expand your set of beliefs iff (and because) the evidence you possess provides adequate support for such beliefs. If there is no path from here to there, you cannot add a belief to your belief set. If some thinker with the same type of evidential support has a path that they can take, so do you. The paths exist because of the evidence you possess and the support it provides. Evidential support grounds propositional justification. The principle is mistaken. There are permissible steps you may take that others may not even if you have the very same evidence. There are permissible steps that you cannot take that others can even if your beliefs receive the same type of evidential support. Because we have to assume almost nothing about the nature of evidential support to establish these results, we should reject evidentialism

Kinematic Orbits and the Structure of the Internal Space for Systems of Five or More Bodies

The internal space for a molecule, atom, or other n-body system can be conveniently parameterised by 3n-9 kinematic angles and three kinematic invariants. For a fixed set of kinematic invariants, the kinematic angles parameterise a subspace, called a kinematic orbit, of the n-body internal space. Building on an earlier analysis of the three- and four-body problems, we derive the form of these kinematic orbits (that is, their topology) for the general n-body problem. The case n=5 is studied in detail, along with the previously studied cases n=3,4.Comment: 38 pages, submitted to J. Phys.

Product rule for gauge invariant Weyl symbols and its application to the semiclassical description of guiding center motion

We derive a product rule for gauge invariant Weyl symbols which provides a generalization of the well-known Moyal formula to the case of non-vanishing electromagnetic fields. Applying our result to the guiding center problem we expand the guiding center Hamiltonian into an asymptotic power series with respect to both Planck's constant $\hbar$ and an adiabaticity parameter already present in the classical theory. This expansion is used to determine the influence of quantum mechanical effects on guiding center motion.Comment: 24 pages, RevTeX, no figures; shortened version will be published in J.Phys.