Generalized seniority from random Hamiltonians

We investigate the generic pairing properties of shell-model many-body Hamiltonians drawn from ensembles of random two-body matrix elements. Many features of pairing that are commonly attributed to the interaction are in fact seen in a large part of the ensemble space. Not only do the spectra show evidence of pairing with favored J=0 ground states and an energy gap, but the relationship between ground state wave functions of neighboring nuclei show signatures of pairing as well. Matrix elements of pair creation/annihilation operators between ground states tend to be strongly enhanced. Furthermore, the same or similar pair operators connect several ground states along an isotopic chain. This algebraic structure is reminiscent of the generalized seniority model. Thus pairing may be encoded to a certain extent in the Fock space connectivity of the interacting shell model even without specific features of the interaction required.Comment: 10 pages, 7 figure

Statistical Theory of Parity Nonconservation in Compound Nuclei

We present the first application of statistical spectroscopy to study the root-mean-square value of the parity nonconserving (PNC) interaction matrix element M determined experimentally by scattering longitudinally polarized neutrons from compound nuclei. Our effective PNC interaction consists of a standard two-body meson-exchange piece and a doorway term to account for spin-flip excitations. Strength functions are calculated using realistic single-particle energies and a residual strong interaction adjusted to fit the experimental density of states for the targets, ^{238} U for A\sim 230 and ^{104,105,106,108} Pd for A\sim 100. Using the standard Desplanques, Donoghue, and Holstein estimates of the weak PNC meson-nucleon coupling constants, we find that M is about a factor of 3 smaller than the experimental value for ^{238} U and about a factor of 1.7 smaller for Pd. The significance of this result for refining the empirical determination of the weak coupling constants is discussed.Comment: Latex file, no Fig

Suppression of Ground-State Magnetization in Finite-Sized Systems Due to Off-Diagonal Interaction Fluctuations

We study a generic model of interacting fermions in a finite-sized disordered system. We show that the off-diagonal interaction matrix elements induce density of states fluctuations which generically favor a minimum spin ground state at large interaction amplitude, $U$. This effect competes with the exchange effect which favors large magnetization at large $U$, and it suppresses this exchange magnetization in a large parameter range. When off-diagonal fluctuations dominate, the model predicts a spin gap which is larger for odd-spin ground states as for even-spin, suggesting a simple experimental signature of this off-diagonal effect in Coulomb blockade transport measurements.Comment: Final, substantially modified version of the article. Accepted for publication in Physical Review Letter

Photograph of Abraham Lincoln Statue at Lincoln Memorial

The black and white photograph features an image of the statue Abraham Lincoln (1920 Statue) located at the Lincoln Memorial in Washington, D. C. .https://scholarsjunction.msstate.edu/fvw-photographs/1553/thumbnail.jp

Photograph of Abraham Lincoln Statue at Lincoln Memorial

The black and white photograph features an image of the statue Abraham Lincoln (1920 Statue) located at the Lincoln Memorial in Washington, D. C. .https://scholarsjunction.msstate.edu/fvw-artifacts/2179/thumbnail.jp

Spectral Statistics of the Two-Body Random Ensemble Revisited

Using longer spectra we re-analyze spectral properties of the two-body random ensemble studied thirty years ago. At the center of the spectra the old results are largely confirmed, and we show that the non-ergodicity is essentially due to the variance of the lowest moments of the spectra. The longer spectra allow to test and reach the limits of validity of French's correction for the number variance. At the edge of the spectra we discuss the problems of unfolding in more detail. With a Gaussian unfolding of each spectrum the nearest neighbour spacing distribution between ground state and first exited state is shown to be stable. Using such an unfolding the distribution tends toward a semi-Poisson distribution for longer spectra. For comparison with the nuclear table ensemble we could use such unfolding obtaining similar results as in the early papers, but an ensemble with realistic splitting gives reasonable results if we just normalize the spacings in accordance with the procedure used for the data.Comment: 11 pages, 7 figure

Heart rate variability and direct current measurement characteristics in professional mixed martial arts athletes

This study’s purpose was to examine heart rate variability (HRV) and direct current potential (DC) measures’ sensitivity and correlations between changes in the acute recovery and stress scale (ARSS) and the previous day’s training load. Training load, HRV, DC and ARSS data were collected from fourteen professional mixed martial arts athletes (32.6 ± 5.3 years, 174.8 ± 8.8 cm, 79.2 ± 17.5 kg) the following morning after hard, easy and rest days. Sensitivity was expressed as a signal-to-noise ratio (SNR, inter-day typical error (TE) or coefficient of variation (%CV) divided by intra-day TE or %CV). Correlations between HRV, DC and ARSS with training load were also examined. The SNRs for the various HRV and DC measures were acceptable to good (1.02–2.85). There was a 23.1% CV average increase between measures taken between different locations versus the same location. Training load changes were not correlated with HRV/DC but were correlated with ARSS stress variables. Practitioners should be aware of HRV/DC variability; however the daily training signal was greater than the test-retest error in this investigation. Upon awakening, HRV/DC measures appear superior for standardization and planning. HRV and DC measures were less sensitive to the previous day’s training load than ARSS measures