Parity-Time Symmetry Breaking beyond One Dimension: The Role of Degeneracy
We consider the role of degeneracy in Parity-Time (PT) symmetry breaking for non-hermitian wave equations beyond one dimension. We show that if the spectrum is degenerate in the absence of T-breaking, and T is broken in a generic manner (without preserving other discrete symmetries), then the standard PT-symmetry breaking transition does not occur, meaning that the spectrum is complex even for infinitesimal strength of gain and loss. However the realness of the entire spectrum can be preserved over a finite interval if additional discrete symmetries X are imposed when T is broken, if X decouple all degenerate modes. When this is true only for a subset of the degenerate spectrum, there can be a partial PT transition in which this subset remains real over a finite interval of T-breaking. If the spectrum has odd-degeneracy, a fraction of the degenerate spectrum can remain in the symmetric phase even without imposing additional discrete symmetries, and they are analogous to dark states in atomic physics. These results are illustrated by the example of different T-breaking perturbations of a uniform dielectric disk and sphere, and a group theoretical analysis is given in the disk case. Finally, we show that multimode coupling is capable of restoring the T-symmetric phase at finite T-breaking. We also analyze these questions when the parity operator is replaced by another spatial symmetry operator and find that the behavior can be qualitatively different.

title: Weak localization and integrability in ballistic cavities.
abstract: We demonstrate the existence of an interference contribution to the average magnetoconductance, G(B), of ballistic cavities and use it to test the semiclassical theory of quantum billiards. G(B) is qualitatively different for chaotic and regular cavities (saturation versus linear increase) which is explained semiclassically by the differing classical distribution of areas. The magnitude of G(B) is poorly explained by the semiclassical theory of coherent backscattering (elastic enhancement factor); interference between trajectories which are not exactly time reversed must be included

title: Universal conductance fluctuations in metals: Effects of finite temperature, interactions, and magnetic field.

title: Measurement of semileptonic branching fractions of B mesons to narrow D** states.
abstract: Using the data accumulated in 2002-2004 with the D0 detector in proton-antiproton collisions at the Fermilab Tevatron collider with a center-of-mass energy of 1.96 TeV, the branching fractions of the decays B --> D0(1)(2420)mu+ vmuX and B --> D2(*0)(2460)mu+ vmuX and their ratio have been measured: B(b --> B) x B(B --> D0(1)mu+ vmuX) x B(D0(*0) --> D*- pi+) = [0.087 +/- 0.007(stat) +/- 0.014(syst)]%; B(b --> B) x B(B --> D2(*0) mu+ vmuX) x B(D2(*0) --> D*- pi+) = [0.035 +/- 0.007(stat) +/- 0.008(syst)]% and [B(B --> D2(*0)mu+ vmuX) x B(D2(*0) --> D*- pi+)]/[B(B --> D0(1)mu+ vmuX) x B(D0(1) --> D*- pi+)] = 0.39 +/- 0.09(stat) +/- 0.12 (syst), where the charge conjugated states are always implied.

title: Measurement of the Probability of Gluon Splitting into Charmed Quarks in Hadronic Z Decays
abstract: We have measured the probability, $\overline{n}_{\rm{g} \rightarrow c\overline{c}}$, of a gluon splitting into a charm-quark pair using 1.7 million hadronic Z decays collected by the L3 detector. Two independent methods have been applied to events with a three-jet topology. One method relies on tagging charmed hadrons by identifying a lepton in the lowest energy jet. The other method uses a neural network based on global event shape parameters. Combining both methods, we measure $\overline{n}_{\rm{g} \rightarrow c\overline{c} } = [2.45 \pm 0.29 \pm