Challenges and opportunities surrounding Catholic education

Catholic education faces a number of serious challenges including cultural and political disrespect for, and hostility towards religion in general and Catholicism in particular, and lack of knowledge of, and commitment to, Catholic beliefs and values among Catholic educational administrators, school managers, teachers, and other staff, as well as the diminishing percentage of even nominally Catholic staff. I set these matters within the context of broader challenges surrounding Catholic education, deriving from three cultural movements: the reformation, the emergence of liberalism, and the scientific revolution, which undermined the synthesis of scripture, theology, and speculative and practical philosophy achieved in the high middle-ages. I propose in response a creative critique showing that what is of authentic value in modernity can be accommodated within the traditional synthesis. I also connect that tradition with strands of eastern philosophy suggesting that the movement of people, ideas, and traditions from Eastern cultures into historically Western societies provides an opportunity for further synthesis of a wisdom-based approach to education.Peer reviewe

Incompressible states of negatively charged magneto-excitons

We study the system of up to four negatively charged magneto-excitons (X-'s) in the spherical geometry, using the exact-diagonalization techniques. At low energies, X-'s are bound and behave like charged particles without internal dynamics. The pseudopotential describing X-:X- scattering is almost identical to that of electrons and the low-lying few X- states correspond to the few-electron states. The total angular momentum of the ground state depends on the effective filling factor nu and vanishes at its special values. The analogs to the Laughlin nu=1/3 state and the Jain nu=2/5 state of electrons are found. The X- system is predicted to exhibit the fractional quantum Hall effect.Comment: RevTeX + 2 EPS figures formatted in the text with epsf.sty; to appear in Physica

Reversed-Spin Quasiparticles in Fractional Quantum Hall Systems and Their Effect on Photoluminescence

The energy, interaction, and optical properties of reversed-spin quasielectrons (QE_R's) in fractional quantum Hall systems are studied. Based on the short range of the QE_R-QE_R repulsion, a partially unpolarized incompressible nu=4/11 state is postulated within Haldane hierarchy scheme. To describe photoluminescence, a reversed-spin fractionally charged exciton hQE_R (QE_R bound to a valence hole h) is predicted. In contrast to its spin-polarized analog, hQE_R is strongly bound and radiative.Comment: 4 pages, 2 figures, paper for EP2DS1

Residual interactions and correlations among Laughlin quasiparticles: Novel hierarchy states

The residual interactions between Laughlin quasiparticles can be obtained from exact numerical diagonalization studies of small systems. The pseudopotentials V_QP(R)$ describing the energy of interaction of QE's (or QH's) as a function of their "relative angular momentum" R cannot support Laughlin correlations at certain QP filling factors (e.g., nu_QE}=1/3 and nu_QH=1/5). Because of this the novel condensed quantum fluid states observed at nu=4/11, 4/13 and other filling fractions cannot possibly be spin polarized Laughlin correlated QP states of the composite Fermion hierarchy. Pairing of the QP's clearly must occur, but the exact nature of the incompressible ground states is not completely clear.Comment: 5 pages, 2 figures, accepted for Solid State Commu

Spin phase diagram of the nu_e=4/11 composite fermion liquid

Spin polarization of the "second generation" nu_e=4/11 fractional quantum Hall state (corresponding to an incompressible liquid in a one-third-filled composite fermion Landau level) is studied by exact diagonalization. Spin phase diagram is determined for GaAs structures of different width and electron concentration. Transition between the polarized and partially unpolarized states with distinct composite fermion correlations is predicted for realistic parameters.Comment: 5 pages, 3 figure

Transformation of Statistics in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a tube carrying a single quantum of flux oriented opposite to the applied magnetic field. When the mean field approximation is made in Haldane's spherical geometry, the Fermion angular momentum l_F is replaced by l_B=l_F-(N-1)/2. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical only if the pseudopotential V (interaction energy as a function of pair angular momentum L_12) increases as L_12(L_12+1). Similar bands of low energy states occur in the two spectra if V increases more quickly than this.Comment: 4 pages, 1 figure, poster at ARW in Queenstown, New Zealand (2001

Fractional quantum Hall effect and electron correlations in partially filled first excited Landau level

We present a quantitative study of most prominent incompressible quantum Hall states in the partially filled first excited Landau level (LL1) which have been recently studied experimentally by Choi et al. The pseudopotential describing the electron - electron interaction in LL1 is harmonic at short range. It produces a series of incompressible states which is different from its LL0 counterpart. The numerical data indicate that the most prominent states $\nu={5/2}$, 7/3, and 8/3 are not produced by Laughlin correlated electrons, but result from a tendency of electrons to form pairs or larger clusters which eventually become Laughlin correlated. States with smaller gaps at filling factors 14/5, 16/7, 11/5, 19/7 are Laughlin correlated electron or hole states and fit Jain's sequence of filled $\rm{CF}^4$ levels.Comment: 4 pages, 7 figure

The Fermion-Boson Transformation in Fractional Quantum Hall Systems

A Fermion to Boson transformation is accomplished by attaching to each Fermion a single flux quantum oriented opposite to the applied magnetic field. When the mean field approximation is made in the Haldane spherical geometry, the Fermion angular momentum $l_F$ is replaced by $l_B= l_F-{1\over2}(N-1)$. The set of allowed total angular momentum multiplets is identical in the two different pictures. The Fermion and Boson energy spectra in the presence of many body interactions are identical if and only if the pseudopotential is ``harmonic'' in form. However, similar low energy bands of states with Laughlin correlations occur in the two spectra if the interaction has short range. The transformation is used to clarify the relation between Boson and Fermion descriptions of the hierarchy of condensed fractional quantum Hall states.Comment: 5 pages, 4 figures, submitted to Physica

Energy spectra and photoluminescence of charged magneto-excitons

Charged magneto-excitons X- in a dilute 2D electron gas in narrow and symmetric quantum wells are studied using exact diagonalization techniques. An excited triplet X- state with a binding energy of about 1 meV is found. This state and the singlet are the two optically active states observed in photoluminescence (PL). The interaction of X-'s with electrons is shown to have short range, which effectively isolates bound X- states from a dilute e-h plasma. This results in the insensitivity of PL to the filling factor nu. For the "dark" triplet X- ground state, the oscillator strength decreases exponentially as a function of 1/nu which explains why it is not seen in PL.Comment: 3 pages, 4 figures, submitted to Physica