EDM operator free from Schiff's theorem

We present generalized Schiff's transformation on electric dipole moments (EDM) in quantum field theory. By the unitary transformation, the time and parity violating interaction $i{ge\over 2} \bar \psi \sigma_{\mu \nu} \gamma_5 \psi F^{\mu \nu}$ is transformed into a new form, but its nonrelativistic reduction has a unique form, which is free from Schiff's theorem. The relativistic corrections to the new EDM operator turn out to be a small increase to the EDM as given by $b_2 (\alpha Z)^2$ with $b_2 \simeq 2$. Therefore, the calculation of the EDM with nonrelativistic Hartree-Fock wave functions presents the most conservative but reliable estimation for the enhancement factor of the EDM in atoms.Comment: 23 pages, Prog. Theor. Phys. in pres

Non-Ergodic Behaviour of the k-Body Embedded Gaussian Random Ensembles for Bosons

We investigate the shape of the spectrum and the spectral fluctuations of the $k$-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the number of Bosons $m \to \infty$ while both $k$, the rank of the interaction, and $l$, the number of single-particle states, are kept fixed. We show that the relative fluctuations of the low spectral moments do not vanish in this limit, proving that the ensemble is non-ergodic. Numerical simulations yield spectra which display a strong tendency towards picket-fence type. The wave functions also deviate from canonical random-matrix behaviourComment: 7 pages, 5 figures, uses epl.cls (included

g-factor of a tightly bound electron

We study the hyperfine splitting of an electron in hydrogen-like $^{209}Bi ^{82+}$. It is found that the hfs energy splitting can be explained well by considering the g-factor reduction due to the binding effect of a bound electron. We determine for the first time the experimental value of the magnetic moment of a tightly bound electron.Comment: 6 pages, Latex, Phys. Rev. A in pres

Spectral statistics of the k-body random-interaction model

We reconsider the question of the spectral statistics of the k-body random-interaction model, investigated recently by Benet, Rupp, and Weidenmueller, who concluded that the spectral statistics are Poissonian. The binary-correlation method that these authors used involves formal manipulations of divergent series. We argue that Borel summation does not suffice to define these divergent series without further (arbitrary) regularization, and that this constitutes a significant gap in the demonstration of Poissonian statistics. Our conclusion is that the spectral statistics of the k-body random-interaction model remains an open question.Comment: 17 pages, no figure

Hyperfine Anomaly of Be Isotopes and Anomalous Large Anomaly in 11^{11}Be

A new result of investigations of the hyperfine structure (hfs) anomaly in Be isotopes is presented. The hfs constant for $^{11}$Be is obtained by using the core plus neutron type wave function: $|2s_{1\over 2}>+|1d_{5\over2}\times 2^+ ; {1/2}^{+}>$. A large hfs anomaly of $^{11}$Be is found, which is mainly due to a large radius of the halo single particle state.Comment: 14 pages, Late

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

Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons

We consider $m$ spinless Bosons distributed over $l$ degenerate single-particle states and interacting through a $k$-body random interaction with Gaussian probability distribution (the Bosonic embedded $k$-body ensembles). We address the cases of orthogonal and unitary symmetry in the limit of infinite matrix dimension, attained either as $l \to \infty$ or as $m \to \infty$. We derive an eigenvalue expansion for the second moment of the many-body matrix elements of these ensembles. Using properties of this expansion, the supersymmetry technique, and the binary correlation method, we show that in the limit $l \to \infty$ the ensembles have nearly the same spectral properties as the corresponding Fermionic embedded ensembles. Novel features specific for Bosons arise in the dense limit defined as $m \to \infty$ with both $k$ and $l$ fixed. Here we show that the ensemble is not ergodic, and that the spectral fluctuations are not of Wigner-Dyson type. We present numerical results for the dense limit using both ensemble unfolding and spectral unfolding. These differ strongly, demonstrating the lack of ergodicity of the ensemble. Spectral unfolding shows a strong tendency towards picket-fence type spectra. Certain eigenfunctions of individual realizations of the ensemble display Fock-space localization.Comment: Minor corrections; figure 5 slightly modified (30 pages, 6 figs

Hyperfine Structure Constants for Eu Isotopes: Is The Empirical Formula of HFS Anomaly Universal ?

We calculate the hyperfine structure constant for the Eu isotopes with shell model wave functions. The calculated results are compared with those predicted by the Moskowitz-Lombardi (M-L) empirical formula. It turns out that the two approaches give the very different behaviors of the hfs constants in the isotope dependence. This should be easily measured by experiment, which may lead to the universality check of the M-L formula.Comment: 18 pages, Latex, two figure

Nucleon Edm from Atomic Systems and Constraints on Supersymmetry Parameters

The nucleon EDM is shown to be directly related to the EDM of atomic systems. From the observed EDM values of the atomic Hg system, the neutron EDM can be extracted, which gives a very stringent constraint on the supersymmetry parameters. It is also shown that the measurement of Nitrogen and Thallium atomic systems should provide important information on the flavor dependence of the quark EDM. We perform numerical analyses on the EDM of neutron, proton and electron in the minimal supersymmetric standard model with CP-violating phases. We demonstrate that the new limit on the neutron EDM extracted from atomic systems excludes a wide parameter region of supersymmetry breaking masses above 1 TeV, while the old limit excludes only a small mass region below 1 TeV.Comment: 10 pages, 7 figure file

Review of the k-Body Embedded Ensembles of Gaussian Random Matrices

The embedded ensembles were introduced by Mon and French as physically more plausible stochastic models of many--body systems governed by one--and two--body interactions than provided by standard random--matrix theory. We review several approaches aimed at determining the spectral density, the spectral fluctuation properties, and the ergodic properties of these ensembles: moments methods, numerical simulations, the replica trick, the eigenvector decomposition of the matrix of second moments and supersymmetry, the binary correlation approximation, and the study of correlations between matrix elements.Comment: Final version. 29 pages, 4 ps figures, uses iopart.st