Remarks on ``Coloring Random Triangulation''

We transform the two-matrix model, studied by P.Di Francesco and al., into a normal one-matrix model by identifying a ``formal'' integral used by these authors as a proper integral. We show also, using their method, that the results obtained for the resolvent and the density are not reliable.Comment: 6 pages, no figures, LaTe

On the critical behaviour of hermitean f-matrix models in the double scaling limit with f >= 3

An algorithm for the isolation of any singularity of f-matrix models in the double scaling limit is presented. In particular it is proved by construction that only those universality classes exist that are known from 2-matrix models.Comment: 24 pages, LaTex, correction of some notation errors and addition of four reference

The Continuous Series of Critical Points of the Two-Matrix Model at N -> infinity in the Double Scaling Limit

The critical points of the continuous series are characterized by two complex numbers l_1,l_2 (Re(l_1,l_2)=3) which enters the string susceptibility constant through gamma = -2/(n-1). The critical potentials are analytic functions with a convergence radius depending on l_1 or l_2. We use the orthogonal polynomial method and solve the Schwinger-Dyson equations with a technique borrowed from conformal field theory.Comment: 24 pages, LaTe

Widely-tunable mid-IR frequency comb source based on difference frequency generation

We report on a mid-infrared frequency comb source of unprecedented tunability covering the entire 3-10 {\mu}m molecular fingerprint region. The system is based on difference frequency generation in a GaSe crystal pumped by a 151 MHz Yb:fiber frequency comb. The process was seeded with Raman shifted solitons generated in a highly nonlinear suspended-core fiber with the same source. Average powers up to 1.5 mW were achieved at 4.7 {\mu}m wavelength.Comment: 3 pages, 3 figure

Full phase stabilization of a Yb:fiber femtosecond frequency comb via high-bandwidth transducers

We present full phase stabilization of an amplified Yb:fiber femtosecond frequency comb using an intra-cavity electro-optic modulator and an acousto-optic modulator. These transducers provide high servo bandwidths of 580 kHz and 250 kHz for frep and fceo, producing a robust and low phase noise fiber frequency comb. The comb was self-referenced with an f - 2f interferometer and phase locked to an ultra-stable optical reference used for the JILA Sr optical clock at 698 nm, exhibiting 0.21 rad and 0.47 rad of integrated phase errors (over 1 mHz - 1 MHz) respectively. Alternatively, the comb was locked to two optical references at 698 nm and 1064 nm, obtaining 0.43 rad and 0.14 rad of integrated phase errors respectively

Transverse and longitudinal characterization of electron beams using interaction with optical near-fields

We demonstrate an experimental technique for both transverse and longitudinal characterization of bunched femtosecond free electron beams. The operation principle is based on monitoring of the current of electrons that obtained an energy gain during the interaction with the synchronized optical near-field wave excited by femtosecond laser pulses. The synchronous accelerating/decelerating fields confined to the surface of a silicon nanostructure are characterized using a highly focused sub-relativistic electron beam. Here the transverse spatial resolution of 450 nm and femtosecond temporal resolution achievable by this technique are demonstrated

Causal trajectories description of atom diffraction by surfaces

9 pages, 7 figures -- PACS numbers: 79.20.Rf, 03.65.Sq, 03.65.BzThe method of quantum trajectories proposed by de Broglie and Bohm is applied to the study of atom diffraction by surfaces. As an example, a realistic model for the scattering of He off corrugated Cu is considered. In this way, the final angular distribution of trajectories is obtained by box-counting, which is in excellent agreement with the results calculated by standard S-matrix methods of scattering theory. More interestingly, the accumulation of quantum trajectories at the different diffraction peaks is explained in terms of the corresponding quantum potential. This non-local potential "guides" the trajectories causing a transition from a distribution near the surface, which reproduces its shape, to the final diffraction pattern observed in the asymptotic region, far from the diffracting object. These two regimes are homologous to the Fresnel and Fraunhofer regions described in undulatory optics. Finally, the turning points of the quantum trajectories provide a better description of the surface electronic density than the corresponding classical ones, usually employed for this task.This work was supported by DGES (Spain) under contracts No PB95-71, PB95-425 and PB96-76. A.S. Sanz also acknowledges the Universidad Autónoma de Madrid for a doctoral grant.Peer reviewe