2,413 research outputs found
Two interacting Hofstadter butterflies
The problem of two interacting particles in a quasiperiodic potential is
addressed. Using analytical and numerical methods, we explore the spectral
properties and eigenstates structure from the weak to the strong interaction
case. More precisely, a semiclassical approach based on non commutative
geometry techniques permits to understand the intricate structure of such a
spectrum. An interaction induced localization effect is furthermore emphasized.
We discuss the application of our results on a two-dimensional model of two
particles in a uniform magnetic field with on-site interaction.Comment: revtex, 12 pages, 11 figure
Quantum Group, Bethe Ansatz and Bloch Electrons in a Magnetic Field
The wave functions for two dimensional Bloch electrons in a uniform magnetic
field at the mid-band points are studied with the help of the algebraic
structure of the quantum group . A linear combination of its
generators gives the Hamiltonian. We obtain analytical and numerical solutions
for the wave functions by solving the Bethe Ansatz equations, proposed by
Wiegmann and Zabrodin on the basis of above observation. The semi-classical
case with the flux per plaquette is analyzed in detail, by exploring
a structure of the Bethe Ansatz equations. We also reveal the multifractal
structure of the Bethe Ansatz solutions and corresponding wave functions when
is irrational, such as the golden or silver mean.Comment: 30 pages, 11 GIF figures(use xv, or WWW browser
What determines the spreading of a wave packet?
The multifractal dimensions D2^mu and D2^psi of the energy spectrum and
eigenfunctions, resp., are shown to determine the asymptotic scaling of the
width of a spreading wave packet. For systems where the shape of the wave
packet is preserved the k-th moment increases as t^(k*beta) with
beta=D2^mu/D2^psi, while in general t^(k*beta) is an optimal lower bound.
Furthermore, we show that in d dimensions asymptotically in time the center of
any wave packet decreases spatially as a power law with exponent D_2^psi - d
and present numerical support for these results.Comment: Physical Review Letters to appear, 4 pages postscript with figure
Bloch Electrons in a Magnetic Field - Why Does Chaos Send Electrons the Hard Way?
We find that a 2D periodic potential with different modulation amplitudes in
x- and y-direction and a perpendicular magnetic field may lead to a transition
to electron transport along the direction of stronger modulation and to
localization in the direction of weaker modulation. In the experimentally
accessible regime we relate this new quantum transport phenomenon to avoided
band crossing due to classical chaos.Comment: 4 pages, 3 figures, minor modifications, PRL to appea
Double butterfly spectrum for two interacting particles in the Harper model
We study the effect of interparticle interaction on the spectrum of the
Harper model and show that it leads to a pure-point component arising from the
multifractal spectrum of non interacting problem. Our numerical studies allow
to understand the global structure of the spectrum. Analytical approach
developed permits to understand the origin of localized states in the limit of
strong interaction and fine spectral structure for small .Comment: revtex, 4 pages, 5 figure
Bayesian inference of biochemical kinetic parameters using the linear noise approximation
Background
Fluorescent and luminescent gene reporters allow us to dynamically quantify changes in molecular species concentration over time on the single cell level. The mathematical modeling of their interaction through multivariate dynamical models requires the deveopment of effective statistical methods to calibrate such models against available data. Given the prevalence of stochasticity and noise in biochemical systems inference for stochastic models is of special interest. In this paper we present a simple and computationally efficient algorithm for the estimation of biochemical kinetic parameters from gene reporter data.
Results
We use the linear noise approximation to model biochemical reactions through a stochastic dynamic model which essentially approximates a diffusion model by an ordinary differential equation model with an appropriately defined noise process. An explicit formula for the likelihood function can be derived allowing for computationally efficient parameter estimation. The proposed algorithm is embedded in a Bayesian framework and inference is performed using Markov chain Monte Carlo.
Conclusion
The major advantage of the method is that in contrast to the more established diffusion approximation based methods the computationally costly methods of data augmentation are not necessary. Our approach also allows for unobserved variables and measurement error. The application of the method to both simulated and experimental data shows that the proposed methodology provides a useful alternative to diffusion approximation based methods
An SU(2) Analog of the Azbel--Hofstadter Hamiltonian
Motivated by recent findings due to Wiegmann and Zabrodin, Faddeev and
Kashaev concerning the appearence of the quantum U_q(sl(2)) symmetry in the
problem of a Bloch electron on a two-dimensional magnetic lattice, we introduce
a modification of the tight binding Azbel--Hofstadter Hamiltonian that is a
specific spin-S Euler top and can be considered as its ``classical'' analog.
The eigenvalue problem for the proposed model, in the coherent state
representation, is described by the S-gap Lam\'e equation and, thus, is
completely solvable. We observe a striking similarity between the shapes of the
spectra of the two models for various values of the spin S.Comment: 19 pages, LaTeX, 4 PostScript figures. Relation between Cartan and
Cartesian deformation of SU(2) and numerical results added. Final version as
will appear in J. Phys. A: Math. Ge
Coupled evolution of temperature and carbonate chemistry during the Paleocene–Eocene; new trace element records from the low latitude Indian Ocean
This is the final version. Available on open access from Elsevier via the DOI in this recordThe early Paleogene represents the most recent interval in Earth’s history characterized by global
greenhouse warmth on multi-million year timescales, yet our understanding of long-term climate and
carbon cycle evolution in the low latitudes, and in particular the Indian Ocean, remains very poorly
constrained. Here we present the first long-term sub-eccentricity-resolution stable isotope (δ13 30 C and
δ
18 O) and trace element (Mg/Ca and B/Ca) records spanning the late Paleocene–early Eocene (~58–
53 Ma) across a surface–deep hydrographic reconstruction of the northern Indian Ocean, resolving
late Paleocene 405-kyr paced cyclicity and a portion of the PETM recovery. Our new records reveal a
long-term warming of ~4–5°C at all depths in the water column, with absolute surface ocean
temperatures and magnitudes of warming comparable to the low latitude Pacific. As a result of
warming, we observe a long-term increase in δ
18 Osw of the mixed layer, implying an increase in net
evaporation. We also observe a collapse in the temperature gradient between mixed layer- and
thermocline-dwelling species from ~57–54 Ma, potentially due to either the development of a more
homogeneous water column with a thicker mixed layer, or depth migration of the Morozovella in
response to warming. Synchronous warming at both low and high latitudes, along with decreasing
B/Ca ratios in planktic foraminifera indicating a decrease in ocean pH and/or increasing dissolved
inorganic carbon, suggest that global climate was forced by rising atmospheric CO2 concentrations
during this time.European Consortium for Ocean Research Drilling (ECORD)International Association of Sedimentologists (IAS)NSFNatural Environment Research Council (NERC
Prioritizing Risks and Uncertainties from Intentional Release of Selected Category A Pathogens
This paper synthesizes available information on five Category A pathogens (Bacillus anthracis, Yersinia pestis, Francisella tularensis, Variola major and Lassa) to develop quantitative guidelines for how environmental pathogen concentrations may be related to human health risk in an indoor environment. An integrated model of environmental transport and human health exposure to biological pathogens is constructed which 1) includes the effects of environmental attenuation, 2) considers fomite contact exposure as well as inhalational exposure, and 3) includes an uncertainty analysis to identify key input uncertainties, which may inform future research directions. The findings provide a framework for developing the many different environmental standards that are needed for making risk-informed response decisions, such as when prophylactic antibiotics should be distributed, and whether or not a contaminated area should be cleaned up. The approach is based on the assumption of uniform mixing in environmental compartments and is thus applicable to areas sufficiently removed in time and space from the initial release that mixing has produced relatively uniform concentrations. Results indicate that when pathogens are released into the air, risk from inhalation is the main component of the overall risk, while risk from ingestion (dermal contact for B. anthracis) is the main component of the overall risk when pathogens are present on surfaces. Concentrations sampled from untracked floor, walls and the filter of heating ventilation and air conditioning (HVAC) system are proposed as indicators of previous exposure risk, while samples taken from touched surfaces are proposed as indicators of future risk if the building is reoccupied. A Monte Carlo uncertainty analysis is conducted and input-output correlations used to identify important parameter uncertainties. An approach is proposed for integrating these quantitative assessments of parameter uncertainty with broader, qualitative considerations to identify future research priorities
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