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

Parameter Symmetry of the Interacting Boson Model

We discuss the symmetry of the parameter space of the interacting boson model (IBM). It is shown that for any set of the IBM Hamiltonian parameters (with the only exception of the U(5) dynamical symmetry limit) one can always find another set that generates the equivalent spectrum. We discuss the origin of the symmetry and its relevance for physical applications.Comment: Minor changes; Revtex, 14 pages with 1 figur

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

Quantum open systems and turbulence

We show that the problem of non conservation of energy found in the spontaneous localization model developed by Ghirardi, Rimini and Weber is very similar to the inconsistency between the stochastic models for turbulence and the Navier-Stokes equation. This sort of analogy may be useful in the development of both areas.Comment: to appear in Physical Review

Incompleteness of Representation Theory: Hidden symmetries and Quantum Non-Integrability

Representation theory is shown to be incomplete in terms of enumerating all integrable limits of quantum systems. As a consequence, one can find exactly solvable Hamiltonians which have apparently strongly broken symmetry. The number of these hidden symmetries depends upon the realization of the Hamiltonian.Comment: 4 pages, Revtex, Phys. Rev. Lett. , July 27 (1997), in pres

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

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

Group Theory Approach to Band Structure: Scarf and Lame Hamiltonians

The group theoretical treatment of bound and scattering state problems is extended to include band structure. We show that one can realize Hamiltonians with periodic potentials as dynamical symmetries, where representation theory provides analytic solutions, or which can be treated with more general spectrum generating algebraic methods. We find dynamical symmetries for which we derive the transfer matrices and dispersion relations. Both compact and non-compact groups are found to play a role.Comment: 4 pages + 2 figs. Revtex/epsf. To appear: Phys Rev Lett, v.83 199

Universal Predictions for Statistical Nuclear Correlations

We explore the behavior of collective nuclear excitations under a multi-parameter deformation of the Hamiltonian. The Hamiltonian matrix elements have the form $P(|H_{ij}|)\propto 1/\sqrt{|H_{ij}|}\exp(-|H_{ij}|/V)$, with a parametric correlation of the type $\log \langle H(x)H(y)\rangle\propto -|x-y|$. The studies are done in both the regular and chaotic regimes of the Hamiltonian. Model independent predictions for a wide variety of correlation functions and distributions which depend on wavefunctions and energies are found from parametric random matrix theory and are compared to the nuclear excitations. We find that our universal predictions are observed in the nuclear states. Being a multi-parameter theory, we consider general paths in parameter space and find that universality can be effected by the topology of the parameter space. Specifically, Berry's phase can modify short distance correlations, breaking certain universal predictions.Comment: Latex file + 12 postscript 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