On the refined 3-enumeration of alternating sign matrices

AbstractAn explicit expression for the numbers A(n,r;3) describing the refined 3-enumeration of alternating sign matrices is given. The derivation is based on the recent results of Stroganov for the corresponding generating function. As a result, A(n,r;3)'s are represented as 1-fold sums which can also be written in terms of terminating F34 series of argument 1/4

The arctic curve of the domain-wall six-vertex model in its anti-ferroelectric regime

An explicit expression for the spatial curve separating the region of ferroelectric order (`frozen' zone) from the disordered one (`temperate' zone) in the six-vertex model with domain wall boundary conditions in its anti-ferroelectric regime is obtained.Comment: 12 pages, 1 figur

Arctic curves of the four-vertex model

We consider the four-vertex model with a particular choice of fixed boundary conditions, closely related to scalar products of off-shell Bethe states. In the scaling limit, the model exhibits the limit shape phenomenon, with the emergence of an arctic curve separating a central disordered region from six frozen `corners' of ferroelectric or anti-ferroelectric type. We determine the analytic expression of the interface by means of the Tangent Method. We extend the method to situations in which the curve separates disorder from anti-ferroelectric order. We supplement this heuristic method with an alternative, rigorous derivation of the arctic curve. This is based on the exact evaluation of suitable correlation functions, discriminating spatial transition from order to disorder, in terms of the partition function of some discrete log-gas associated to Hahn polynomials. As a by-product, we also deduce that the arctic curve's fluctuations are governed by the Tracy-Widom distribution.Comment: 35 pages, 21 figure

Laser deposition of diamondlike carbon films at high intensities

Unhydrogenated diamondlike carbon (DLC) thin films have been deposited by laser ablation of graphite, using a high power Ti: sapphire solid state laser system. DLC films were deposited onto silicon substrates at room temperature with subpicosecond laser pulses, at peak intensities in the 4×1014–5×1015 W/cm2 range. A variety of techniques, including scanning and transmission electron microscopy (SEM and TEM), Raman spectroscopy, spectroscopic ellipsometry (SE), and electron energy loss spectroscopy (EELS) have been used to analyze the film quality. Smooth, partially transparent films were produced, distinct from the graphite target. Sp3 volume fractions were found to be in the 50%–60% range, with Tauc band gaps ranging from 0.6 to 1.2 eV, depending on laser intensity. Kinetic energies carried by the carbon ions in the laser induced plasma were measured through time‐of‐flight (TOF) spectroscopy. Their most probable kinetic energies were found to be in the 700–1000 eV range, increasing with laser intensity. © 1995 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70135/2/APPLAB-67-21-3120-1.pd

Exotic solutions in string theory

Solutions of classical string theory, correspondent to the world sheets, mapped in Minkowsky space with a fold, are considered. Typical processes for them are creation of strings from vacuum, their recombination and annihilation. These solutions violate positiveness of square of mass and Regge condition. In quantum string theory these solutions correspond to physical states |DDF>+|sp> with non-zero spurious component.Comment: accepted in Il Nuovo Cimento A for publication in 199

Algebraic arctic curves in the domain-wall six-vertex model

The arctic curve, i.e. the spatial curve separating ordered (or `frozen') and disordered (or `temperate) regions, of the six-vertex model with domain wall boundary conditions is discussed for the root-of-unity vertex weights. In these cases the curve is described by algebraic equations which can be worked out explicitly from the parametric solution for this curve. Some interesting examples are discussed in detail. The upper bound on the maximal degree of the equation in a generic root-of-unity case is obtained.Comment: 15 pages, no figures; v2: metadata correcte

The Finite Size SU(3) Perk-Schultz Model with Deformation Parameter q=exp(i 2 pi/3)

From extensive numeric diagonalizations of the SU(3) Perk-Schultz Hamiltonian with a special value of the anisotropy and different boundary conditions, we have observed simple regularities for a significant part of its eigenspectrum. In particular the ground state energy and nearby excitations belong to this part of the spectrum. Our simple formulae describing these regularities remind, apart from some selection rules, the eigenspectrum of the free fermion model. Based on the numerical observations we formulate several conjectures. Using explicit solutions of the associated nested Bethe-ansatz equations, guessed from an analysis of the functional equations of the model, we provide evidence for a part of them.Comment: 19 pages, no figure

High intensity femtosecond laser deposition of diamond-like carbon thin films

Hydrogen-free diamond-like carbon (DLC) films have been deposited with a 100 fs (FWHM) Ti:sapphire laser beam at intensities I in the 1014–1015 W/cm21014–1015W/cm2 range. The films were studied with scanning probe microscopy, variable angle spectroscopic ellipsometry, Raman spectroscopy, and electron energy loss spectroscopy. DLC films with good scratch resistance, excellent chemical inertness, and high optical transparency in the visible and near infrared range were deposited at room temperature. As the laser intensity was increased from 3×10143×1014 to 6×1015 W/cm2,6×1015W/cm2, the films showed an increased surface particle density, a decreased optical transparency (85%→60%),(85%→60%), and Tauc band gap (1.4→0.8 eV),(1.4→0.8eV), as well as a lower sp3sp3 content (60%→50%).(60%→50%). The time-of-flight spectra recorded from the laser plume exhibited a double-peak distribution, with a high energy suprathermal ion peak preceding a slower thermal component. The most probable ion kinetic energy showed an I0.55I0.55 dependence, increasing from 300 to 2000 eV, when the laser intensity was varied from 3×10143×1014 to 6×1015 W/cm2,6×1015W/cm2, while the kinetic energy of suprathermal ions increased from 3 to over 20 keV and showed an I0.33I0.33 dependence. These high energy ions are believed to have originated from an electrostatic acceleration field established by suprathermal electrons which were formed by resonant absorption of the intense laser beams. © 1999 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70817/2/JAPIAU-86-4-2281-1.pd