Quantum spectrum as a time series : Fluctuation measures

The fluctuations in the quantum spectrum could be treated like a time series. In this framework, we explore the statistical self-similarity in the quantum spectrum using the detrended fluctuation analysis (DFA) and random matrix theory (RMT). We calculate the Hausdorff measure for the spectra of atoms and Gaussian ensembles and study their self-affine properties. We show that DFA is equivalent to $\Delta_3$ statistics of RMT, unifying two different approaches.We exploit this connection to obtain theoretical estimates for the Hausdorff measure.Comment: 4+ pages. 2 figure

Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions

The Kardar-Parisi-Zhang (KPZ) equation with infinitesimal surface tension, dynamically develops sharply connected valley structures within which the height derivative is not continuous. We discuss the intermittency issue in the problem of stationary state forced KPZ equation in 1+1--dimensions. It is proved that the moments of height increments $C_a =$ behave as $|x_1 -x_2|^{\xi_a}$ with $\xi_a = a$ for length scales $|x_1-x_2| << \sigma$. The length scale $\sigma$ is the characteristic length of the forcing term. We have checked the analytical results by direct numerical simulation.Comment: 13 pages, 9 figure

Bunching Transitions on Vicinal Surfaces and Quantum N-mers

We study vicinal crystal surfaces with the terrace-step-kink model on a discrete lattice. Including both a short-ranged attractive interaction and a long-ranged repulsive interaction arising from elastic forces, we discover a series of phases in which steps coalesce into bunches of n steps each. The value of n varies with temperature and the ratio of short to long range interaction strengths. We propose that the bunch phases have been observed in very recent experiments on Si surfaces. Within the context of a mapping of the model to a system of bosons on a 1D lattice, the bunch phases appear as quantum n-mers.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let

Depinning in a Random Medium

We develop a renormalized continuum field theory for a directed polymer interacting with a random medium and a single extended defect. The renormalization group is based on the operator algebra of the pinning potential; it has novel features due to the breakdown of hyperscaling in a random system. There is a second-order transition between a localized and a delocalized phase of the polymer; we obtain analytic results on its critical pinning strength and scaling exponents. Our results are directly related to spatially inhomogeneous Kardar-Parisi-Zhang surface growth.Comment: 11 pages (latex) with one figure (now printable, no other changes

Effect of a columnar defect on the shape of slow-combustion fronts

We report experimental results for the behavior of slow-combustion fronts in the presence of a columnar defect with excess or reduced driving, and compare them with those of mean-field theory. We also compare them with simulation results for an analogous problem of driven flow of particles with hard-core repulsion (ASEP) and a single defect bond with a different hopping probability. The difference in the shape of the front profiles for excess vs. reduced driving in the defect, clearly demonstrates the existence of a KPZ-type of nonlinear term in the effective evolution equation for the slow-combustion fronts. We also find that slow-combustion fronts display a faceted form for large enough excess driving, and that there is a corresponding increase then in the average front speed. This increase in the average front speed disappears at a non-zero excess driving in agreement with the simulated behavior of the ASEP model.Comment: 7 pages, 7 figure

Vicinal Surfaces, Fractional Statistics and Universality

We propose that the phases of all vicinal surfaces can be characterized by four fixed lines, in the renormalization group sense, in a three-dimensional space of coupling constants. The observed configurations of several Si surfaces are consistent with this picture. One of these fixed lines also describes one-dimensional quantum particles with fractional exclusion statistics. The featureless steps of a vicinal surface can therefore be thought of as a realization of fractional-statistics particles, possibly with additional short-range interactions.Comment: 6 pages, revtex, 3 eps figures. To appear in Physical Review Letters. Reference list properly arranged. Caption of Fig. 1 slightly reworded. Fig 3 (in color) is not part of the paper. It complements Fig.

Universal Ratios in the 2-D Tricritical Ising Model

We consider the universality class of the two-dimensional Tricritical Ising Model. The scaling form of the free-energy naturally leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We compute these universal ratios by a combined use of results coming from Perturbed Conformal Field Theory, Integrable Quantum Field Theory and numerical methods.Comment: 4 pages, LATEX fil

Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics

We use renormalization group to calculate the reunion and survival exponents of a set of random walkers interacting with a long range $1/r^2$ and a short range interaction. These exponents are used to study the binding-unbinding transition of polymers and the behavior of several quantum problems.Comment: Revtex 3.1, 9 pages (two-column format), 3 figures. Published version (PRE 63, 051103 (2001)). Reference corrections incorporated (PRE 64, 059902 (2001) (E