Two-Body Random Ensembles: From Nuclear Spectra to Random Polynomials

The two-body random ensemble (TBRE) for a many-body bosonic theory is mapped to a problem of random polynomials on the unit interval. In this way one can understand the predominance of 0+ ground states, and analytic expressions can be derived for distributions of lowest eigenvalues, energy gaps, density of states and so forth. Recently studied nuclear spectroscopic properties are addressed.Comment: 8 pages, 4 figures. To appear in Physical Review Letter

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

Remarks on NonHamiltonian Statistical Mechanics: Lyapunov Exponents and Phase-Space Dimensionality Loss

The dissipation associated with nonequilibrium flow processes is reflected by the formation of strange attractor distributions in phase space. The information dimension of these attractors is less than that of the equilibrium phase space, corresponding to the extreme rarity of nonequilibrium states. Here we take advantage of a simple model for heat conduction to demonstrate that the nonequilibrium dimensionality loss can definitely exceed the number of phase-space dimensions required to thermostat an otherwise Hamiltonian system.Comment: 5 pages, 2 figures, minor typos correcte

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

Generic Rotation in a Collective SD Nucleon-Pair Subspace

Low-lying collective states involving many nucleons interacting by a random ensemble of two-body interactions (TBRE) are investigated in a collective SD-pair subspace, with the collective pairs defined dynamically from the two-nucleon system. It is found that in this truncated pair subspace collective vibrations arise naturally for a general TBRE hamiltonian whereas collective rotations do not. A hamiltonian restricted to include only a few randomly generated separable terms is able to produce collective rotational behavior, as long as it includes a reasonably strong quadrupole-quadrupole component. Similar results arise in the full shell model space. These results suggest that the structure of the hamiltonian is key to producing generic collective rotation.Comment: 11 pages, 5 figure

Fractional Langevin equation

We investigate fractional Brownian motion with a microscopic random-matrix model and introduce a fractional Langevin equation. We use the latter to study both sub- and superdiffusion of a free particle coupled to a fractal heat bath. We further compare fractional Brownian motion with the fractal time process. The respective mean-square displacements of these two forms of anomalous diffusion exhibit the same power-law behavior. Here we show that their lowest moments are actually all identical, except the second moment of the velocity. This provides a simple criterion which enables to distinguish these two non-Markovian processes.Comment: 4 page

Global stabilization of feedforward systems under perturbations in sampling schedule

For nonlinear systems that are known to be globally asymptotically stabilizable, control over networks introduces a major challenge because of the asynchrony in the transmission schedule. Maintaining global asymptotic stabilization in sampled-data implementations with zero-order hold and with perturbations in the sampling schedule is not achievable in general but we show in this paper that it is achievable for the class of feedforward systems. We develop sampled-data feedback stabilizers which are not approximations of continuous-time designs but are discontinuous feedback laws that are specifically developed for maintaining global asymptotic stabilizability under any sequence of sampling periods that is uniformly bounded by a certain "maximum allowable sampling period".Comment: 27 pages, 5 figures, submitted for possible publication to SIAM Journal Control and Optimization. Second version with added remark

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

Boundary and Coulomb Effects on Boson Systems in High-Energy Heavy-Ion Collisions

The boundary of a boson system plays an important role in determining the momentum distribution of the bosons. For a boson system with a cylindrical boundary, the momentum distribution is enhanced at high transverse momenta but suppressed at low transverse momenta, relative to a Bose-Einstein distribution. The boundary effects on systems of massless gluons and massive pions are studied. For gluons in a quark-gluon plasma, the presence of the boundary may modify the signals for the quark-gluon plasma. For pions in a pion system in heavy-ion collisions, Coulomb final-state interactions with the nuclear participants in the vicinity of the central rapidity region further modify the momentum distribution at low transverse momenta. By including both the boundary effect and the Coulomb final-state interactions we are able to account for the behavior of the $\pi^{-}$ transverse momentum spectrum observed in many heavy-ion experiments, notably at low transverse momenta.Comment: 15 pages Postscript uuencoded tar-comprssed file, 9 Postscript figures uuencoded tar-compressed fil