Dimer Coverings on the Sierpinski Gasket

We present the number of dimer coverings N _d (n) on the Sierpinski gasket SG _d (n) at stage n with dimension d equal to two, three, four or five. When the number of vertices, denoted as v(n), of the Sierpinski gasket is an even number, N _d (n) is the number of close-packed dimers. When the number of vertices is an odd number, no close-packed configurations are possible and we allow one of the outmost vertices uncovered. The entropy of absorption of diatomic molecules per site, defined as , is calculated to be ln (2)/3 exactly for SG ₂. The numbers of dimers on the generalized Sierpinski gasket SG _d,b (n) with d=2 and b=3,4,5 are also obtained exactly with entropies equal to ln (6)/7, ln (28)/12, ln (200)/18, respectively. The number of dimer coverings for SG ₃ is given by an exact product expression, such that its entropy is given by an exact summation expression. The upper and lower bounds for the entropy are derived in terms of the results at a certain stage for SG _d (n) with d=3,4,5. As the difference between these bounds converges quickly to zero as the calculated stage increases, the numerical value of with d=3,4,5 can be evaluated with more than a hundred significant figures accurate. This paper is written during the Lung-Chi Chen visit to PIMS, University of British Columbia. The author thanks the institute for the hospitality.     

Threshold effects on renormalization group running of neutrino parameters in the low-scale seesaw model

We show that, in the low-scale type-I seesaw model, renormalization group running of neutrino parameters may lead to significant modifications of the leptonic mixing angles in view of so-called seesaw threshold effects. Especially, we derive analytical formulas for radiative corrections to neutrino parameters in crossing the different seesaw thresholds, and show that there may exist enhancement factors efficiently boosting the renormalization group running of the leptonic mixing angles. We find that, as a result of the seesaw threshold corrections to the leptonic mixing angles, various flavor symmetric mixing patterns (e.g., bi-maximal and tri-bimaximal mixing patterns) can be easily accommodated at relatively low energy scales, which is well within the reach of running and forthcoming experiments (e.g., the LHC).     

Asynchronous sampling for ultrafast experiments with low momentum compaction at the ANKA ring

A high‐repetition‐rate pump–probe experiment is presented, based on the asynchronous sampling approach. The low‐α mode at the synchrotron ANKA can be used for a time resolution down to the picosecond limit for the time‐domain sampling of the coherent THz emission as well as for hard X‐ray pump–probe experiments, which probe structural dynamics in the condensed phase. It is shown that a synchronization of better than 1 ps is achieved, and examples of phonon dynamics of semiconductors are presented.     

Entangling different degrees of freedom by quadrature squeezing cylindrically polarized modes

Quantum systems such as, for example, photons, atoms, or Bose-Einstein condensates, prepared in complex states where entanglement between distinct degrees of freedom is present, may display several intriguing features. In this Letter we introduce the concept of such complex quantum states for intense beams of light by exploiting the properties of cylindrically polarized modes. We show that already in a classical picture the spatial and polarization field variables of these modes cannot be factorized. Theoretically it is proven that by quadrature squeezing cylindrically polarized modes one generates entanglement between these two different degrees of freedom. Experimentally we demonstrate amplitude squeezing of an azimuthally polarized mode by exploiting the nonlinear Kerr effect in a specially tailored photonic crystal fiber. These results display that such novel continuous-variable entangled systems can, in principle, be realized.     

Diode-pumped single-frequency-Nd:YGG-MOPA for water–vapor DIAL measurements: design, setup and performance

A diode-pumped Q-switched and injection-seeded single-frequency laser, generating tunable laser radiation at 935 nm, is presented. Using Nd:YGG (Y₃Ga₅O₁₂) as the active medium, the laser that was developed to serve as a transmitter for water–vapor lidar measurements. The configuration consists of a stable resonator in rod geometry that is injection seeded by a narrowband diode laser and stabilized by the ramp-and-fire technique. Energy scaling was done in a power amplifier in slab geometry. Both oscillator and amplifier crystal were diode pumped at 806 nm. More than 30 mJ pulse energy at 100 Hz repetition rate with a beam propagation factor of M²<1.4 and pulse duration of 52 ns in single-frequency mode were generated. To our knowledge this is the first direct generation of 935 nm Q-switched pulses from Nd:YGG suitable for water–vapor measurements. The reported results show great promise of this laser in applications where high efficiency and reduced complexity is indispensable, such as for spaceborne or airborne water–vapor lidar instruments.     

Probing angular correlations in sequential double ionization

We study electron correlation in sequential double ionization of noble gas atoms and HCl in intense, femtosecond laser pulses. We measure the photoelectron angular distributions of Ne+ relative to the first electron in a pump-probe experiment with 8 fs, 800 nm, circularly polarized laser pulses at a peak intensity of a few 10(15) W/cm2. Using a linear-linear pump-probe setup, we further study He, Ar, and HCl. We find a clear angular correlation between the two ionization steps in the sequential double ionization intensity regime.     

Probing shear-band initiation in metallic glasses

In?situ acoustic emission monitoring is shown to capture the initiation of shear bands in metallic glasses. A model picture is inferred from stick-slip flow in granular media such that the origin of acoustic emission is attributed to a mechanism of structural dilatation. By employing a quantitative approach, the critical volume change associated with shear-band initiation in a metallic glass is estimated to be a few percent only. This result agrees with typical values of excess free volume found in the supercooled liquid regime near the glass transition temperature.     

Time-humidity-superposition principle in electrical conductivity spectra of ion-conducting polymers

We analyze the scaling properties of the ac conductivity spectra of ion-conducting polyelectrolyte complexes of different compositions. Spectra were taken at ambient temperature but at different relative humidities. For the first time, we report on a scaling principle for conductivity spectra termed "time-humidity-superposition principle" in analogy with the well-known time-temperature-superposition principle. This model-free scaling holds for different materials over several decades in frequency. It implies that the hydration is activating ion motion over short and long distances in a similar general way, a concept so far only established for thermal energy.     

A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence

We study the two-dimensional gauge theory of the symmetric group S_n describing the statistics of branched n-coverings of Riemann surfaces. We consider the theory defined on the disc and on the sphere in the large-n limit. A non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that any gauge theory on a two-dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold: in the case of S_n, one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk. A connection with the theory of phase transitions in random graphs is also pointed out. Finally we discuss how our results may be related to the known phase transitions in Yang-Mills theory. We discover that a cutoff transition occurs also in two dimensional Yang-Mills theory on a sphere, in a large N limit where the coupling constant is scaled with N with an extra logN compared to the standard t Hooft scaling.