Regularities with random interactions in energy centroids defined by group symmetries

Regular structures generated by random interactions in energy centroids defined over irreducible representations (irreps) of some of the group symmetries of the interacting boson models $sd$IBM, $sdg$IBM, $sd$IBM-$T$ and $sd$IBM-$ST$ are studied by deriving trace propagations equations for the centroids. It is found that, with random interactions, the lowest and highest group irreps in general carry most of the probability for the corresponding centroids to be lowest in energy. This generalizes the result known earlier, via numerical diagonalization, for the more complicated fixed spin ($J$) centroids where simple trace propagation is not possible.Comment: 18 pages, 3 figure

Duality Between the Weak and Strong Interaction Limits for Randomly Interacting Fermions

We establish the existence of a duality transformation for generic models of interacting fermions with two-body interactions. The eigenstates at weak and strong interaction U possess similar statistical properties when expressed in the U=0 and U=infinity eigenstates bases respectively. This implies the existence of a duality point U_d where the eigenstates have the same spreading in both bases. U_d is surrounded by an interval of finite width which is characterized by a non Lorentzian spreading of the strength function in both bases. Scaling arguments predict the survival of this intermediate regime as the number of particles is increased.Comment: RevTex4, 4 pages, 4 figures. Accepted for publication at Phys. Rev. Let

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

Dynamics of Perfectly Wetting Drops under Gravity

We study the dynamics of small droplets of polydimethylsiloxane (PDMS) silicone oil on a vertical, perfectly-wetting, silicon wafer. Interference videomicroscopy allows us to capture the dynamics of these droplets. We use droplets with a volumes typically ranging from 100 to 500 nanolitres (viscosities from 10 to 1000 centistokes) to understand long time derivations from classical solutions. Past researchers used one dimensional theory to understand the typical $t^{1/3}$ scaling for the position of the tip of the droplet in time $t$. We observe this regime in experiment for intermediate times and discover a two-dimensional, similarity solution of the shape of the droplet. However, at long times our droplets start to move more slowly down the plane than the $t^{1/3}$ scaling suggests and we observe deviations in droplet shape from the similarity solution. We match experimental data with simulations to show these deviations are consistent with retarded van der Waals forcing which should become significant at the small heights observed

Chaos Thresholds in finite Fermi systems

The development of Quantum Chaos in finite interacting Fermi systems is considered. At sufficiently high excitation energy the direct two-particle interaction may mix into an eigen-state the exponentially large number of simple Slater-determinant states. Nevertheless, the transition from Poisson to Wigner-Dyson statistics of energy levels is governed by the effective high order interaction between states very distant in the Fock space. The concrete form of the transition depends on the way one chooses to work out the problem of factorial divergency of the number of Feynman diagrams. In the proposed scheme the change of statistics has a form of narrow phase transition and may happen even below the direct interaction threshold.Comment: 9 pages, REVTEX, 2 eps figures. Enlarged versio

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

Decay of Quasi-Particle in a Quantum Dot: the role of Energy Resolution

The disintegration of quasiparticle in a quantum dot due to the electron interaction is considered. It was predicted recently that above the energy \eps^{*} = \Delta(g/\ln g)^{1/2} each one particle peak in the spectrum is split into many components ($\Delta$ and $g$ are the one particle level spacing and conductance). We show that the observed value of \eps^{*} should depend on the experimental resolution \delta \eps. In the broad region of variation of \delta \eps the $\ln g$ should be replaced by \ln(\Delta/ g\delta \eps). We also give the arguments against the delocalization transition in the Fock space. Most likely the number of satellite peaks grows continuously with energy, being $\sim 1$ at \eps \sim \eps^{*}, but remains finite at \eps > \eps^{*}. The predicted logarithmic distribution of inter-peak spacings may be used for experimental confirmation of the below-Golden-Rule decay.Comment: 5 pages, REVTEX, 2 eps figures, version accepted for publication in Phys. Rev. Let

Half-lives and pre-supernova weak interaction rates for nuclei away from the stability line

A detailed model for the calculation of beta decay rates of the $fp$ shell nuclei for situations prevailing in pre-supernova and collapse phases of evolution of the core of massive stars leading to supernova explosion has been extended for electron-capture rates. It can also be used to determine the half-lives of neutron-rich nuclei in the $fp/fpg$ shell. The model uses an averaged Gamow-Teller (GT) strength function. But it can also use the experimental log ft values and GT strength function from $(n,p)$ reaction studies wherever available. The calculated rate includes contributions from each of the low-lying excited states of the mother including some specific resonant states ("back resonance") having large GT matrix elements.Comment: 11 pages; Latex; no figs; version to appear in J. Phys.

Cissus sicyoides C. Linnaeus (Vitaceae), a Potential Exotic Pest in the Lower Rio Grande Valley, Texas

English:Cissus sicyoides C. Linnaeus, a perennial vine native to tropical Mexico, Central America, and the Caribbean, has recently been rediscovered in the Lower Rio Grande Valley,Texas. A dense population of this exotic species has been located in a brushy area along a canal network and in two adjacent citrus groves near Weslaco. This species produces a dense mantle that covers other vegetation, appears to be invasive, and may pose a potential weed problem in citrus in the Lower Rio Grande Valley. Spanish: Cissus sicyoides C. Linnaeus, una enredadera perene nativa de los trópicos de México, América Central y el Caribe, se ha redescubierto recientemente en el Bajo Valle del Río Grande,Texas. Una población densa de esta especie exótica ha sido localizada en una área de matorral a lo largo de una red de canales y en dos huertas adyacentes de cítricos cercanas a Weslaco. Esta especie produce un manto denso que cubre otra vegetación, es invasiva y puede tener el potencial de convertirse en una maleza problemática para el cultivo de cítricos en el Bajo Valle del Río Grande en Texas

Statistical Theory of Finite Fermi-Systems Based on the Structure of Chaotic Eigenstates

The approach is developed for the description of isolated Fermi-systems with finite number of particles, such as complex atoms, nuclei, atomic clusters etc. It is based on statistical properties of chaotic excited states which are formed by the interaction between particles. New type of ``microcanonical'' partition function is introduced and expressed in terms of the average shape of eigenstates $F(E_k,E)$ where $E$ is the total energy of the system. This partition function plays the same role as the canonical expression $exp(-E^{(i)}/T)$ for open systems in thermal bath. The approach allows to calculate mean values and non-diagonal matrix elements of different operators. In particular, the following problems have been considered: distribution of occupation numbers and its relevance to the canonical and Fermi-Dirac distributions; criteria of equilibrium and thermalization; thermodynamical equation of state and the meaning of temperature, entropy and heat capacity, increase of effective temperature due to the interaction. The problems of spreading widths and shape of the eigenstates are also studied.Comment: 17 pages in RevTex and 5 Postscript figures. Changes are RevTex format (instead of plain LaTeX), minor misprint corrections plus additional references. To appear in Phys. Rev.