A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of SU(2) connections

We establish a splitting formula for the spectral flow of the odd signature operator on a closed 3-manifold M coupled to a path of SU(2) connections, provided M = S cup X, where S is the solid torus. It describes the spectral flow on M in terms of the spectral flow on S, the spectral flow on X (with certain Atiyah-Patodi-Singer boundary conditions), and two correction terms which depend only on the endpoints. Our result improves on other splitting theorems by removing assumptions on the non-resonance level of the odd signature operator or the dimension of the kernel of the tangential operator, and allows progress towards a conjecture by Lisa Jeffrey in her work on Witten's 3-manifold invariants in the context of the asymptotic expansion conjecture.Comment: Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol9/paper52.abs.htm

Varied Signature Splitting Phenomena in Odd Proton Nuclei

Varied signature splitting phenomena in odd proton rare earth nuclei are investigated. Signature splitting as functions of $K$ and $j$ in the angular momentum projection theory is explicitly shown and compared with those of the particle rotor model. The observed deviations from these rules are due to the band mixings. The recently measured $^{169}$Ta high spin data are taken as a typical example where fruitful information about signature effects can be extracted. Six bands, two of which have not yet been observed, were calculated and discussed in detail in this paper. The experimentally unknown band head energies are given

Dispelling the antihydrogen myth

While achiral Bohr atom theory cannot generate Hbar signatures, achiral Heitler-London bond theory can but its Hbar signatures must be detected. We show that the largest spectral signature to probe Hbar is the singlet-triplet splitting of 9,5 eV at r(0)=0,74 Angstrom, observed in the dihydrogen band spectrum. This large Hbar-signature, overlooked for nearly a century, is confirmed with the observed HH potential energy curve. Hbar claims by CERN-based collaborations, seemingly important for the fate and future of Hbar, are premature and must be examined critically

On collective Rabi splitting in nanolasers and nano-LEDs

We analytically calculate the optical emission spectrum of nanolasers and nano-LEDs based on a model of many incoherently pumped two-level emitters in a cavity. At low pump rates we find two peaks in the spectrum for large coupling strengths and numbers of emitters. We interpret the double-peaked spectrum as a signature of collective Rabi splitting, and discuss the difference between the splitting of the spectrum and the existence of two eigenmodes. We show that an LED will never exhibit a split spectrum, even though it can have distinct eigenmodes. For systems where the splitting is possible we show that the two peaks merge into a single one when the pump rate is increased. Finally, we compute the linewidth of the systems, and discuss the influence of inter-emitter correlations on the lineshape

Quadrupole Pairing Interaction and Signature Inversion

The signature inversion in the \pi h11/2 \otimes \nu h11/2 rotational bands of odd-odd Cs and La isotopes and the \pi h11/2 \otimes \nu i13/2 bands of odd-odd Tb, Ho and Tm nuclei is investigated using pairing and deformation self consistent mean field calculations. The model can rather satisfactorily account for the anomalous signature splitting, provided that spin assignments in som of the bands are revised. Our calculations show that signature inversioncan appear already at axially symmetric shapes. It is found that this is due to the contribution of the \lambda\mu=22 component of the quadrupole pairing interaction to the mean field potential.Comment: 17 pages, 14 figures, Nuclear Physics A in prin

Normal--mode splitting in a weakly coupled optomechanical system

Normal--mode splitting is the most evident signature of strong coupling between two interacting subsystems. It occurs when two subsystems exchange energy between themselves faster than they dissipate it to the environment. Here we experimentally show that a weakly coupled optomechanical system at room temperature can manifest normal--mode splitting when the pump field fluctuations are anti-squashed by a phase-sensitive feedback loop operating close to its instability threshold. Under these conditions the optical cavity exhibits an effectively reduced decay rate, so that the system is effectively promoted to the strong coupling regime

Triaxiality in the interacting boson model

The signature splitting of the $\gamma$-vibrational band of several Ru, Pd, Xe, Ba, Os and Pt isotopes is analyzed in the framework of the interacting boson model (IBM). The nuclei studied are close to the $\gamma$-unstable SO(6) limit of the IBM and have well-known $\gamma$ bands. It is shown that in most nuclei the signature splitting is better reproduced by the inclusion of a three-body interaction between the $d$ bosons. In none of the nuclei evidence for a stable, triaxial ground-state shape is found.Comment: Accepted for publication in Nuclear Physics