Manifestation of quantum chaos on scattering techniques: application to low-energy and photo-electron diffraction intensities

Intensities of LEED and PED are analyzed from a statistical point of view. The probability distribution is compared with a Porter-Thomas law, characteristic of a chaotic quantum system. The agreement obtained is understood in terms of analogies between simple models and Berry's conjecture for a typical wavefunction of a chaotic system. The consequences of this behaviour on surface structural analysis are qualitatively discussed by looking at the behaviour of standard correlation factors.Comment: 5 pages, 4 postscript figures, Latex, APS, http://www.icmm.csic.es/Pandres/pedro.ht

Impediments to mixing classical and quantum dynamics

The dynamics of systems composed of a classical sector plus a quantum sector is studied. We show that, even in the simplest cases, (i) the existence of a consistent canonical description for such mixed systems is incompatible with very basic requirements related to the time evolution of the two sectors when they are decoupled. (ii) The classical sector cannot inherit quantum fluctuations from the quantum sector. And, (iii) a coupling among the two sectors is incompatible with the requirement of physical positivity of the theory, i.e., there would be positive observables with a non positive expectation value.Comment: RevTex, 21 pages. Title slightly modified and summary section adde

Dirac versus Reduced Quantization of the Poincar\'{e} Symmetry in Scalar Electrodynamics

The generators of the Poincar\'{e} symmetry of scalar electrodynamics are quantized in the functional Schr\"{o}dinger representation. We show that the factor ordering which corresponds to (minimal) Dirac quantization preserves the Poincar\'{e} algebra, but (minimal) reduced quantization does not. In the latter, there is a van Hove anomaly in the boost-boost commutator, which we evaluate explicitly to lowest order in a heat kernel expansion using zeta function regularization. We illuminate the crucial role played by the gauge orbit volume element in the analysis. Our results demonstrate that preservation of extra symmetries at the quantum level is sometimes a useful criterion to select between inequivalent, but nevertheless self-consistent, quantization schemes.Comment: 24 page

Van der Waals loops and the melting transition in two dimensions

Evidence for the existence of van der Waals loops in pressure p versus volume v plots has for some time supported the belief that melting in two dimensions is a first order phase transition. We report rather accurate equilibrium p(v) curves for systems of hard disks obtained from long Monte Carlo simulations. These curves, obtained in the constant volume ensemble, using periodic boundary conditions, exhibit well defined van der Waals loops. We illustrate their existence for finite systems that are known to undergo a continuous transition in the thermodynamic limit. To this end, we obtain magnetization m versus applied field curves from Monte Carlo simulations of the 2D Ising model, in the constant m ensemble, at the critical point. Whether van der Waals loops for disk systems behave in the thermodynamic limit as they do for the 2D Ising model at the critical point cannot be ruled out. Thus, the often made claim that melting in 2D is a first order phase transition, based on the evidence that van der Waals loops exist, is not sound.Comment: 10 pages, 6 Postscript figures (submitted to Phys.Rev.E). For related work, see http://pipe.unizar.es/~jf

LEED Holography applied to a complex superstructure: a direct view of the adatom cluster on SiC(111)-(3x3)

For the example of the SiC(111)-(3x3) reconstruction we show that a holographic interpretation of discrete Low Energy Electron Diffraction (LEED) spot intensities arising from ordered, large unit cell superstructures can give direct access to the local geometry of a cluster around an elevated atom, provided there is only one such prominent atom per surface unit cell. By comparing the holographic images obtained from experimental and calculated data we illuminate validity, current limits and possible shortcomings of the method. In particular, we show that periodic vacancies such as cornerholes may inhibit the correct detection of the atomic positions. By contrast, the extra diffraction intensity due to slight substrate reconstructions, as for example buckling, seems to have negligible influence on the images. Due to the spatial information depth of the method the stacking of the cluster can be imaged down to the fourth layer. Finally, it is demonstrated how this structural knowledge of the adcluster geometry can be used to guide the dynamical intensity analysis subsequent to the holographic reconstruction and necessary to retrieve the full unit cell structure.Comment: 11 pages RevTex, 6 figures, Phys. Rev. B in pres

Scalar density fluctuation at critical end point in NJL model

Soft mode near the critical end point in the phase diagram of two-flavor Nambu--Jona-Lasinio (NJL) model is investigated within the leading 1/N_c approximation with N_c being the number of the colors. It is explicitly shown by studying the spectral function of the scalar channel that the relevant soft mode is the scalar density fluctuation, which is coupled with the quark number density, while the sigma meson mode stays massive.Comment: 9 pages, 4 figure

Renormalization: the observable-state model

The usual mathematical formalism of quantum field theory is non-rigorous because it contains divergences that can only be renormalized by non-rigorous mathematical methods. The purpose of this paper is to present a method of subtraction of this divergences using the formalism of decoherence. This is achieved by replacing the standard renormalization method by a projector on a well defined Hilbert subspace. In this way a list of problems of the standard formalism disappears while the physical results of QFT remains valid. From it own nature, this formalism can be used in non-renormalizable theories.Comment: 23 page

Transition from a quark-gluon plasma in the presence of a sharp front

The effect of a sharp front separating the quark-gluon plasma phase from the hadronic phase is investigated. Energy-momentum conservation and baryon number conservation constrain the possible temperature jump across the front. If one assumes that the temperature in the hadronic phase is $T\simeq$ 200 MeV , as has been suggested by numerous results from relativistic ion collisions, one can determine the corresponding temperature in the quark phase with the help of continuity equations across the front. The calculations reveal that the quark phase must be in a strongly supercooled state. The stability of this solution with respect to minor modifications is investigated. In particular the effect of an admixture of hadronic matter in the quark phase (e.g. in the form of bubbles) is considered in detail. In the absence of admixture the transition proceeds via a detonation transition and is accompanied by a substantial super-cooling of the quark-gluon plasma phase. The detonation is accompanied by less supercooling if a small fraction of bubbles is allowed. By increasing the fraction of bubbles the supercooling becomes weaker and eventually the transition proceeds via a smoother deflagration wave.Comment: 10 pages, manuscript in TeX, 9 figures available as Postscript files, CERN-TH 6923/9

The Static and Dynamic Lattice Changes Induced by Hydrogen Adsorption on NiAl(110)

Static and dynamic changes induced by adsorption of atomic hydrogen on the NiAl(110) lattice at 130 K have been examined as a function of adsorbate coverage. Adsorbed hydrogen exists in three distinct phases. At low coverages the hydrogen is itinerant because of quantum tunneling between sites and exhibits no observable vibrational modes. Between 0.4 ML and 0.6 ML, substrate mediated interactions produce an ordered superstructure with c(2x2) symmetry, and at higher coverages, hydrogen exists as a disordered lattice gas. This picture of how hydrogen interacts with NiAl(110) is developed from our data and compared to current theoretical predictions.Comment: 36 pages, including 12 figures, 2 tables and 58 reference

Exponential behavior of a quantum system in a macroscopic medium

An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling, macroscopic limit. Some implications for the quantum measurement problem are discussed, in particular in connection with dissipation.Comment: 8 pages, report BA-TH/94-17