394 research outputs found
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 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 with .
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
-body Embedded Gaussian Ensemble for Bosons in the dense limit, where the
number of Bosons while both , the rank of the interaction,
and , 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
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
g-factor of a tightly bound electron
We study the hyperfine splitting of an electron in hydrogen-like . 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
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 --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 --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
Hyperfine Anomaly of Be Isotopes and Anomalous Large Anomaly in Be
A new result of investigations of the hyperfine structure (hfs) anomaly in Be
isotopes is presented. The hfs constant for Be is obtained by using the
core plus neutron type wave function: . A large hfs anomaly of Be is found, which is mainly due
to a large radius of the halo single particle state.Comment: 14 pages, Late
Spectral Properties of the k-Body Embedded Gaussian Ensembles of Random Matrices for Bosons
We consider spinless Bosons distributed over degenerate
single-particle states and interacting through a -body random interaction
with Gaussian probability distribution (the Bosonic embedded -body
ensembles). We address the cases of orthogonal and unitary symmetry in the
limit of infinite matrix dimension, attained either as or as . 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 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
with both and 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
- …