108 research outputs found
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
The decline of macrofauna in the deeper parts of the Baltic proper and the Gulf of Finland
An attempt is made to describe the large-scale changes in the benthic soft bottom macrofauna in the deep parts of the Bornholm Basin, the Gulf of Gdansk, the Central Basin and the Gulf of Finland, from the beginning of Baltic zoobenthos research to the present day. The authors also try to correlate these changes with fluctuations in the oxygen content and salinity in near-bottom water layers. The paper surveys the literature and presents recent, earlier unpublished results. During the later part of last century and the first decades of the twentieth century no area of the Baltic Sea seems to have been total ly devoid of macrofauna. Unfortunately there are considerable gaps in our knowledge of the time before the middle of this century. The most striking decline has taken place, generally speaking, after the exceptionally great inflow in 1951-1952, and the subsequent prolonged stagnation. The first records of "dead" bottoms in the Bornholm Basin are from 1948, when no macrofauna was recorded below 80 m. Records from 1954 show that the deepest parts of the Eastern Gotland Basin and the deep area between Öland and Gotland were devoid of macrofauna at that time, but that the deep areas of the northernmost Baltic proper and the Gulf of Finland were still populated. The change continued, and during the 1960s the communities dominated by lamellibranchs in the Bornholm and Gdansk Deeps disappeared, and were subsequently replaced by polychaete cummunities. These have been wiped out during periods of bad oxygen conditions, but quickly re-established when conditions had improved. The lamellibranch community has not been restored. In the Northern Central Basin and the Gulf of Finland the depopulation of the deep bottoms probably began later, in the late 50s. In the 70s practically no macrofauna has been recorded below the permanent halocline in the Central Basin (except the southernmost parts of it) and the Gulf of Finland. During the 60s and 70s the area with periodically unfavourable oxygen conditions has covered about 100000 km2, which is c. 25 % of the total area of the Baltic Sea
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.
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 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
Alternative Technique for "Complex" Spectra Analysis
. The choice of a suitable random matrix model of a complex system is very
sensitive to the nature of its complexity. The statistical spectral analysis of
various complex systems requires, therefore, a thorough probing of a wide range
of random matrix ensembles which is not an easy task. It is highly desirable,
if possible, to identify a common mathematcal structure among all the ensembles
and analyze it to gain information about the ensemble- properties. Our
successful search in this direction leads to Calogero Hamiltonian, a
one-dimensional quantum hamiltonian with inverse-square interaction, as the
common base. This is because both, the eigenvalues of the ensembles, and, a
general state of Calogero Hamiltonian, evolve in an analogous way for arbitrary
initial conditions. The varying nature of the complexity is reflected in the
different form of the evolution parameter in each case. A complete
investigation of Calogero Hamiltonian can then help us in the spectral analysis
of complex systems.Comment: 20 pages, No figures, Revised Version (Minor Changes
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 (). 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
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 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 and . 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 are also obtained.Comment: 50 Pages, 5 figure
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
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