Functorial properties of Putnam's homology theory for Smale spaces

We investigate functorial properties of Putnam's homology theory for Smale spaces. Our analysis shows that the addition of a conjugacy condition is necessary to ensure functoriality. Several examples are discussed that elucidate the need for our additional hypotheses. Our second main result is a natural generalization of Putnam's Pullback Lemma from shifts of finite type to non-wandering Smale spaces.Comment: Updated to agree with published versio

Static and Dynamic Properties of Trapped Fermionic Tonks-Girardeau Gases

We investigate some exact static and dynamic properties of one-dimensional fermionic Tonks-Girardeau gases in tight de Broglie waveguides with attractive p-wave interactions induced by a Feshbach resonance. A closed form solution for the one-body density matrix for harmonic trapping is analyzed in terms of its natural orbitals, with the surprising result that for odd, but not for even, numbers of fermions the maximally occupied natural orbital coincides with the ground harmonic oscillator orbital and has the maximally allowed fermionic occupancy of unity. The exact dynamics of the trapped gas following turnoff of the p-wave interactions are explored.Comment: 4 pages, 2 figures, submitted to PR

Saddle Points and Stark Ladders: Exact Calculations of Exciton Spectra in Superlattices

A new, exact method for calculating excitonic absorption in superlattices is described. It is used to obtain high resolution spectra showing the saddle point exciton feature near the top of the miniband. The evolution of this feature is followed through a series of structures with increasing miniband width. The Stark ladder of peaks produced by an axial electric field is investigated, and it is shown that for weak fields the line shapes are strongly modified by coupling to continuum states, taking the form of Fano resonances. The calculated spectra, when suitably broadened, are found to be in good agreement with experimental results.Comment: 9 pages Revtex v3.0, followed by 4 uuencoded postscript figures, SISSA-CM-94-00

Theory of spinor Fermi and Bose gases in tight atom waveguides

Divergence-free pseudopotentials for spatially even and odd-wave interactions in spinor Fermi gases in tight atom waveguides are derived. The Fermi-Bose mapping method is used to relate the effectively one-dimensional fermionic many-body problem to that of a spinor Bose gas. Depending on the relative magnitudes of the even and odd-wave interactions, the N-atom ground state may have total spin S=0, S=N/2, and possibly also intermediate values, the case S=N/2 applying near a p-wave Feshbach resonance, where the N-fermion ground state is space-antisymmetric and spin-symmetric. In this case the fermionic ground state maps to the spinless bosonic Lieb-Liniger gas. An external magnetic field with a longitudinal gradient causes a Stern-Gerlach spatial separation of the corresponding trapped Fermi gas with respect to various values of $S_z$.Comment: 4+ pages, 1 figure, revtex4. Submitted to PRA. Minor corrections of typos and notatio

Coherence properties of the microcavity polariton condensate

A theoretical model is presented which explains the dominant decoherence process in a microcavity polariton condensate. The mechanism which is invoked is the effect of self-phase modulation, whereby interactions transform polariton number fluctuations into random energy variations. The model shows that the phase coherence decay, g1(t), has a Kubo form, which can be Gaussian or exponential, depending on whether the number fluctuations are slow or fast. This fluctuation rate also determines the decay time of the intensity correlation function, g2(t), so it can be directly determined experimentally. The model explains recent experimental measurements of a relatively fast Gaussian decay for g1(t), but also predicts a regime, further above threshold, where the decay is much slower.Comment: 5 pages, 1 figur

A direct proof of Kim's identities

As a by-product of a finite-size Bethe Ansatz calculation in statistical mechanics, Doochul Kim has established, by an indirect route, three mathematical identities rather similar to the conjugate modulus relations satisfied by the elliptic theta constants. However, they contain factors like $1 - q^{\sqrt{n}}$ and $1 - q^{n^2}$, instead of $1 - q^n$. We show here that there is a fourth relation that naturally completes the set, in much the same way that there are four relations for the four elliptic theta functions. We derive all of them directly by proving and using a specialization of Weierstrass' factorization theorem in complex variable theory.Comment: Latex, 6 pages, accepted by J. Physics

Media Coverage, Public Awareness and State Intervention in Child Abuse in China – An Analysis of High-Profile Cases

Abstract Key Practitioner Messages •Child abuse is a complex social problem that is often deeply rooted in the cultural, economic and social practices of the country in which it exists. •Child abuse in China is understood as deliberate and harmful acts, while many Western societies also include acts of omission such as neglect. •There is a complex relationship between public awareness, media coverage and state intervention

Evaluation of the Lewisham Trauma Informed Group Work Programme

This study is an evaluation of the Trauma Informed Group Work Programme developed by the Lewisham Youth Offending Service. It was commissioned by the London Borough of Lewisham with funding from the Youth Justice Board. The Lewisham Trauma Informed Group Work Programme is an intervention that aims to reduce morbidity and mortality in under-18s due to violent assaults