Ground state spin 0+^+ dominance of many-body systems with random interactions and related topics

In this talk we shall show our recent results in understanding the spin$^{\rm parity}$ 0$^+$ ground state (0 g.s.) dominance of many-body systems. We propose a simple approach to predict the spin $I$ g.s. probabilities which does not require the diagonalization of a Hamiltonian with random interactions. Some findings related to the 0 g.s. dominance will also be discussed.Comment: 11 pages and 4 figure

Angular momentum I ground state probabilities of boson systems interacting by random interactions

In this paper we report our systematic calculations of angular momentum $I$ ground state probabilities ($P(I)$) of boson systems with spin $l$ in the presence of random two-body interactions. It is found that the P(0) dominance is usually not true for a system with an odd number of bosons, while it is valid for an even number of bosons, which indicates that the P(0) dominance is partly connected to the even number of identical particles. It is also noticed that the $P(I_{max})$'s of bosons with spin $l$ do not follow the 1/N ($N=l+1$, referring to the number of independent two-body matrix elements) relation. The properties of the $P(I)$'s obtained in boson systems with spin $l$ are discussed.Comment: 8 pages and 3 figure

Many-body Systems Interacting via a Two-body Random Ensemble (I): Angular Momentum distribution in the ground states

In this paper, we discuss the angular momentum distribution in the ground states of many-body systems interacting via a two-body random ensemble. Beginning with a few simple examples, a simple approach to predict P(I)'s, angular momenta I ground state (g.s.) probabilities, of a few solvable cases, such as fermions in a small single-j shell and d boson systems, is given. This method is generalized to predict P(I)'s of more complicated cases, such as even or odd number of fermions in a large single-j shell or a many-j shell, d-boson, sd-boson or sdg-boson systems, etc. By this method we are able to tell which interactions are essential to produce a sizable P(I) in a many-body system. The g.s. probability of maximum angular momentum $I_{max}$ is discussed. An argument on the microscopic foundation of our approach, and certain matrix elements which are useful to understand the observed regularities, are also given or addressed in detail. The low seniority chain of 0 g.s. by using the same set of two-body interactions is confirmed but it is noted that contribution to the total 0 g.s. probability beyond this chain may be more important for even fermions in a single-j shell. Preliminary results by taking a displaced two-body random ensemble are presented for the I g.s. probabilities.Comment: 39 pages and 8 figure

FPU β\beta model: Boundary Jumps, Fourier's Law and Scaling

We examine the interplay of surface and volume effects in systems undergoing heat flow. In particular, we compute the thermal conductivity in the FPU $\beta$ model as a function of temperature and lattice size, and scaling arguments are used to provide analytic guidance. From this we show that boundary temperature jumps can be quantitatively understood, and that they play an important role in determining the dynamics of the system, relating soliton dynamics, kinetic theory and Fourier transport.Comment: 5pages, 5 figure

Group Theoretical Properties and Band Structure of the Lame Hamiltonian

We study the group theoretical properties of the Lame equation and its relation to su(1,1) and su(2). We compute the band structure, dispersion relation and transfer matrix and discuss the dynamical symmetry limits.Comment: 21 pages Revtex + 6 eps + 2 jpg figure

Giant-dipole Resonance and the Deformation of Hot, Rotating Nuclei

The development of nuclear shapes under the extreme conditions of high spin and/or temperature is examined. Scaling properties are used to demonstrate universal properties of both thermal expectation values of nuclear shapes as well as the minima of the free energy, which can be used to understand the Jacobi transition. A universal correlation between the width of the giant dipole resonance and quadrupole deformation is found, providing a novel probe to measure the nuclear deformation in hot nuclei.Comment: 6 pages including 6 figures. To appear in Phys. Rev. Lett. Revtex

Phase Transitions in Finite Nuclei and the Integer Nucleon Number Problem

The study of spherical-deformed ground--state phase transitions in finite nuclei as a function of N and Z is hindered by the discrete values of the nucleon number. A resolution of the integer nucleon number problem, and evidence relating to phase transitions in finite nuclei, are discussed from the experimental point of view and interpreted within the framework of the interacting boson model.Comment: 8 pages Latex + 8 figs (postscript). In Phys Rev Lett, June 199

Environmental Determinants of the Distribution and Abundance of the Ants, Lasiophanes picinus and L. valdiviensis, in Argentina

The distribution and abundance variation of the terrestrial ants, Lasiophanes picinus and Lasiophanes valdiviensis Emery (Formicinae: Lasiini), which are endemic in Patagonia (Argentina and Chile), are described and a set of environmental factors are examined to explain the observed patterns. Ants were collected using 450 pitfall traps arranged in 50, 100 m2 grid plots each with nine traps within a roughly 150 × 150 km area representative of the subantartic-patagonian transition of Argentina. Five sampling periods each 8-days long were carried out between November 2004 and March 2006. To understand the distributional patterns and their link to environmental variables discriminant analysis was used. Path analysis was performed to test for direct and indirect effects of a set of environmental variables on species abundance variation. L. picinus was more frequently captured and attained higher abundance in the forests, while L. valdiviensis was more frequently captured and more abundant in the scrubs. The maximum daily temperature and mean annual precipitation explained L. picinus distribution (i.e. presence or absence) with an accuracy of 90%. L. valdiviensis distribution was predicted with almost 70% accuracy, taking into account herbal richness. The maximum daily temperature was the only climatic variable that affected ant abundance directly; an increase in temperature led to an increase of L. picinus abundance and a decrease of L. valdiviensis abundance. The amount of resources, as indicated by the percent plant cover, explained the variation of the abundance of both species better than the variety of resources as indicated by plant richness (i.e. models including plant richness had low fit or no fit at all). A direct effect of habitat use by cattle was found, as indicated by the amount of feces in the plots, only when variables related to the amount of resources were replaced by variables with less explanatory power related to the variety of resources. This study provides new data on the ecology of Lasiophanes species in relation to existing hypotheses proposed to explain patterns of abundance variation. Evidence is provided that changes in temperature (i.e. global climate change) may have important consequences on populations of these species

Dynamics of a Simple Quantum System in a Complex Environment

We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective stochastic models which emerge from random matrix theory. Using the Feynman-Vernon path integral formalism, we derive the influence functional and obtain either analytical or numerical solutions for the time evolution of the entire quantum system. We discuss thoroughly the structure of the solutions for some representative cases and make connections to well known limiting results, particularly to Brownian motion, Kramers classical limit and the Caldeira-Leggett approach.Comment: 41 pages and 12 figures in revte