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

Misleading signatures of quantum chaos

The main signature of chaos in a quantum system is provided by spectral statistical analysis of the nearest neighbor spacing distribution and the spectral rigidity given by $\Delta_3(L)$. It is shown that some standard unfolding procedures, like local unfolding and Gaussian broadening, lead to a spurious increase of the spectral rigidity that spoils the $\Delta_3(L)$ relationship with the regular or chaotic motion of the system. This effect can also be misinterpreted as Berry's saturation.Comment: 4 pages, 5 figures, submitted to Physical Review

Collectivity Embedded in Complex Spectra of Finite Interacting Fermi Systems: Nuclear Example

The mechanism of collectivity coexisting with chaos in a finite system of strongly interacting fermions is investigated. The complex spectra are represented in the basis of two-particle two-hole states describing the nuclear double-charge exchange modes in $^{48}$Ca. An example of $J^{\pi}=0^-$ excitations shows that the residual interaction, which generically implies chaotic behavior, under certain specific and well identified conditions may create strong transitions, even much stronger than those corresponding to a pure mean-field picture. Such an effect results from correlations among the off-diagonal matrix elements, is connected with locally reduced density of states and a local minimum in the information entropy.Comment: 16 pages, LaTeX2e, REVTeX, 8 PostScript figures, to appear in Physical Review

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

Wigner--Dyson statistics for a class of integrable models

We construct an ensemble of second--quantized Hamiltonians with two bosonic degrees of freedom, whose members display with probability one GOE or GUE statistics. Nevertheless, these Hamiltonians have a second integral of motion, namely the boson number, and thus are integrable. To construct this ensemble we use some ``reverse engineering'' starting from the fact that $n$--bosons in a two--level system with random interactions have an integrable classical limit by the old Heisenberg association of boson operators to actions and angles. By choosing an $n$--body random interaction and degenerate levels we end up with GOE or GUE Hamiltonians. Ergodicity of these ensembles completes the example.Comment: 3 pages, 1 figur

Enhanced mesoscopic fluctuations in the crossover between random matrix ensembles

In random-matrix ensembles that interpolate between the three basic ensembles (orthogonal, unitary, and symplectic), there exist correlations between elements of the same eigenvector and between different eigenvectors. We study such correlations, using a remarkable correspondence between the interpolating ensembles late in the crossover and a basic ensemble of finite size. In small metal grains or semiconductor quantum dots, the correlations between different eigenvectors lead to enhanced fluctuations of the electron-electron interaction matrix elements which become parametrically larger than the non-universal fluctuations.Comment: 4 pages, RevTeX; 3 figure

Wavefunction statistics in open chaotic billiards

We study the statistical properties of wavefunctions in a chaotic billiard that is opened up to the outside world. Upon increasing the openings, the billiard wavefunctions cross over from real to complex. Each wavefunction is characterized by a phase rigidity, which is itself a fluctuating quantity. We calculate the probability distribution of the phase rigidity and discuss how phase rigidity fluctuations cause long-range correlations of intensity and current density. We also find that phase rigidities for wavefunctions with different incoming wave boundary conditions are statistically correlated.Comment: 4 pages, RevTeX; 1 figur

Alternative Technique for "Complex" Spectra Analysis

. The choice of a suitable random matrix model of a complex system is very sensitive to the nature of its complexity. The statistical spectral analysis of various complex systems requires, therefore, a thorough probing of a wide range of random matrix ensembles which is not an easy task. It is highly desirable, if possible, to identify a common mathematcal structure among all the ensembles and analyze it to gain information about the ensemble- properties. Our successful search in this direction leads to Calogero Hamiltonian, a one-dimensional quantum hamiltonian with inverse-square interaction, as the common base. This is because both, the eigenvalues of the ensembles, and, a general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary initial conditions. The varying nature of the complexity is reflected in the different form of the evolution parameter in each case. A complete investigation of Calogero Hamiltonian can then help us in the spectral analysis of complex systems.Comment: 20 pages, No figures, Revised Version (Minor Changes

Full 0ℏω0\hbar\omega shell model calculation of the binding energies of the 1f7/21f_{7/2} nuclei

Binding energies and other global properties of nuclei in the middle of the $pf$ shell, such as M1, E2 and Gamow-Teller sum rules, have been obtained using a new Shell Model code (NATHAN) written in quasi-spin formalism and using a $j-j$-coupled basis. An extensive comparison is made with the recently available Shell Model Monte Carlo results using the effective interaction KB3. The binding energies for -nearly- all the $1f_{7/2}$ nuclei are compared with the measured (and extrapolated) results.Comment: 7 page

Induced Parity Nonconserving Interaction and Enhancement of Two-Nucleon Parity Nonconserving Forces

Two-nucleon parity nonconserving (PNC) interaction induced by the single-particle PNC weak potential and the two-nucleon residual strong interaction is considered. An approximate analytical formula for this Induced PNC Interaction (IPNCI) between proton and neutron is derived ($Q({\bf r} {\bf \sigma}_{p} \times {\bf \sigma}_{n}) \delta({\bf r}_{p}-{\bf r}_{n})$), and the interaction constant is estimated. As a result of coherent contributions from the nucleons to the PNC potential, IPNCI is an order of magnitude stronger ($\sim A^{1/3}$) than the residual weak two-nucleon interaction and has a different coordinate and isotopic structure (e.g., the strongest part of IPNCI does not contribute to the PNC mean field). IPNCI plays an important role in the formation of PNC effects, e.g., in neutron-nucleus reactions. In that case, it is a technical way to take into account the contribution of the distant (small) components of a compound state which dominates the result. The absence of such enhancement ($\sim A^{1/3}$) in the case of T- and P-odd interaction completes the picture.Comment: Phys. Rev. C, to appear; 17 pages, revtex 3, no figure