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

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

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

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

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

Quantum critical lines in holographic phases with (un)broken symmetry

All possible scaling IR asymptotics in homogeneous, translation invariant holographic phases preserving or breaking a U(1) symmetry in the IR are classified. Scale invariant geometries where the scalar extremizes its effective potential are distinguished from hyperscaling violating geometries where the scalar runs logarithmically. It is shown that the general critical saddle-point solutions are characterized by three critical exponents ($\theta, z, \zeta$). Both exact solutions as well as leading behaviors are exhibited. Using them, neutral or charged geometries realizing both fractionalized or cohesive phases are found. The generic global IR picture emerging is that of quantum critical lines, separated by quantum critical points which correspond to the scale invariant solutions with a constant scalar.Comment: v3: 32+29 pages, 2 figures. Matches version published in JHEP. Important addition of an exponent characterizing the IR scaling of the electric potentia

Some remarks on PM2.5

Since 1970, the General Physics Department of «Università degli Studi di Torino» has carried out a project research, on inorganic solid particulate matter. The special issue of Annals of Geophysics, published for Professor Giorgio Fiocco’s 70th birthday, gives us the possibility to make some important remarks on this topic, focusing on PM2.5. This has been possible using all the old and new experimental data of the measures made by the authors of this paper since 1970

Statistical Theory for the Kardar-Parisi-Zhang Equation in 1+1 Dimension

The Kardar-Parisi-Zhang (KPZ) equation in 1+1 dimension dynamically develops sharply connected valley structures within which the height derivative {\it is not} continuous. There are two different regimes before and after creation of the sharp valleys. We develop a statistical theory for the KPZ equation in 1+1 dimension driven with a random forcing which is white in time and Gaussian correlated in space. A master equation is derived for the joint probability density function of height difference and height gradient $P(h-\bar h,\partial_{x}h,t)$ when the forcing correlation length is much smaller than the system size and much bigger than the typical sharp valley width. In the time scales before the creation of the sharp valleys we find the exact generating function of $h-\bar h$ and $\partial_x h$. Then we express the time scale when the sharp valleys develop, in terms of the forcing characteristics. In the stationary state, when the sharp valleys are fully developed, finite size corrections to the scaling laws of the structure functions $<(h-\bar h)^n (\partial_x h)^m>$ are also obtained.Comment: 50 Pages, 5 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.

The Quantum Dynamics of Two Coupled Qubits

We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the initial state. The difference appears as non positive-definite diffusion terms in the quantum evolution equation of an appropriate positive phase-space probability density. Thus, it is not possible to express the dynamics in terms of a convolution of a positive transition probability function and the initial condition as can be done in the classical case. We conclude that the dynamics is a quantum element of NMR quantum information processing. There are two limits where our quantum evolution coincide with the classical one: the short time limit before spin-spin interaction sets in and the long time limit when phase diffusion is incorporated