176 research outputs found
Transport and Dissipation in Quantum Pumps
This paper is about adiabatic transport in quantum pumps. The notion of
``energy shift'', a self-adjoint operator dual to the Wigner time delay, plays
a role in our approach: It determines the current, the dissipation, the noise
and the entropy currents in quantum pumps. We discuss the geometric and
topological content of adiabatic transport and show that the mechanism of
Thouless and Niu for quantized transport via Chern numbers cannot be realized
in quantum pumps where Chern numbers necessarily vanish.Comment: 31 pages, 10 figure
Dynamics of a classical Hall system driven by a time-dependent Aharonov--Bohm flux
We study the dynamics of a classical particle moving in a punctured plane
under the influence of a strong homogeneous magnetic field, an electrical
background, and driven by a time-dependent singular flux tube through the hole.
We exhibit a striking classical (de)localization effect: in the far past the
trajectories are spirals around a bound center; the particle moves inward
towards the flux tube loosing kinetic energy. After hitting the puncture it
becomes ``conducting'': the motion is a cycloid around a center whose drift is
outgoing, orthogonal to the electric field, diffusive, and without energy loss
Connecting protein and mRNA burst distributions for stochastic models of gene expression
The intrinsic stochasticity of gene expression can lead to large variability
in protein levels for genetically identical cells. Such variability in protein
levels can arise from infrequent synthesis of mRNAs which in turn give rise to
bursts of protein expression. Protein expression occurring in bursts has indeed
been observed experimentally and recent studies have also found evidence for
transcriptional bursting, i.e. production of mRNAs in bursts. Given that there
are distinct experimental techniques for quantifying the noise at different
stages of gene expression, it is of interest to derive analytical results
connecting experimental observations at different levels. In this work, we
consider stochastic models of gene expression for which mRNA and protein
production occurs in independent bursts. For such models, we derive analytical
expressions connecting protein and mRNA burst distributions which show how the
functional form of the mRNA burst distribution can be inferred from the protein
burst distribution. Additionally, if gene expression is repressed such that
observed protein bursts arise only from single mRNAs, we show how observations
of protein burst distributions (repressed and unrepressed) can be used to
completely determine the mRNA burst distribution. Assuming independent
contributions from individual bursts, we derive analytical expressions
connecting means and variances for burst and steady-state protein
distributions. Finally, we validate our general analytical results by
considering a specific reaction scheme involving regulation of protein bursts
by small RNAs. For a range of parameters, we derive analytical expressions for
regulated protein distributions that are validated using stochastic
simulations. The analytical results obtained in this work can thus serve as
useful inputs for a broad range of studies focusing on stochasticity in gene
expression
Extinction Rates for Fluctuation-Induced Metastabilities : A Real-Space WKB Approach
The extinction of a single species due to demographic stochasticity is
analyzed. The discrete nature of the individual agents and the Poissonian noise
related to the birth-death processes result in local extinction of a metastable
population, as the system hits the absorbing state. The Fokker-Planck
formulation of that problem fails to capture the statistics of large deviations
from the metastable state, while approximations appropriate close to the
absorbing state become, in general, invalid as the population becomes large. To
connect these two regimes, a master equation based on a real space WKB method
is presented, and is shown to yield an excellent approximation for the decay
rate and the extreme events statistics all the way down to the absorbing state.
The details of the underlying microscopic process, smeared out in a mean field
treatment, are shown to be crucial for an exact determination of the extinction
exponent. This general scheme is shown to reproduce the known results in the
field, to yield new corollaries and to fit quite precisely the numerical
solutions. Moreover it allows for systematic improvement via a series expansion
where the small parameter is the inverse of the number of individuals in the
metastable state
Estimación del rendimiento de trigo en el departamento capital - La Pampa- basado en variables climáticas
El presente trabajo se realizó con el objeto de estimar el rendimiento de trigo, con anterioridad a la cosecha, en el Departamento Capital - La Pampa, República Argentina- a través de ciertas variables climáticas. Se analizó un periodo de catorce años (campaña 77/78-90/91), utilizando un análisis de correlación simple para seleccionar las variables más ligadas al rendimiento y posteriormente una regresión múltiple. Se encontraron como variables climáticas significativas la precipitación acumulada de octubre (pa 1), la tensión de vapor promedio de julio (tv2) y el viento máximo promedio de setiembre (vi3). La ecuación que liga dichas variables con el rendimiento de trigo (Y) es: Y=2576,732 + 7,022 pal - 104,614 tv2 - 38,992 vi3 (r2=0,91746), la cual permite estimar el rendimiento a corto plazo, si nos movemos dentro del rango de las variables independientes. Palabras claves: trigo, rendimiento, variables climáticas, regresión múltiple.Director: Lic. Laura Antón de Ferramola. Cátedra de Estadística
Anderson localization for a class of models with a sign-indefinite single-site potential via fractional moment method
A technically convenient signature of Anderson localization is exponential
decay of the fractional moments of the Green function within appropriate energy
ranges. We consider a random Hamiltonian on a lattice whose randomness is
generated by the sign-indefinite single-site potential, which is however
sign-definite at the boundary of its support. For this class of Anderson
operators we establish a finite-volume criterion which implies that above
mentioned the fractional moment decay property holds. This constructive
criterion is satisfied at typical perturbative regimes, e. g. at spectral
boundaries which satisfy 'Lifshitz tail estimates' on the density of states and
for sufficiently strong disorder. We also show how the fractional moment method
facilitates the proof of exponential (spectral) localization for such random
potentials.Comment: 29 pages, 1 figure, to appear in AH
Time-Energy coherent states and adiabatic scattering
Coherent states in the time-energy plane provide a natural basis to study
adiabatic scattering. We relate the (diagonal) matrix elements of the
scattering matrix in this basis with the frozen on-shell scattering data. We
describe an exactly solvable model, and show that the error in the frozen data
cannot be estimated by the Wigner time delay alone. We introduce the notion of
energy shift, a conjugate of Wigner time delay, and show that for incoming
state the energy shift determines the outgoing state.Comment: 11 pages, 1 figur
Smooth adiabatic evolutions with leaky power tails
Adiabatic evolutions with a gap condition have, under a range of
circumstances, exponentially small tails that describe the leaking out of the
spectral subspace. Adiabatic evolutions without a gap condition do not seem to
have this feature in general. This is a known fact for eigenvalue crossing. We
show that this is also the case for eigenvalues at the threshold of the
continuous spectrum by considering the Friedrichs model.Comment: Final form, to appear in J. Phys. A; 11 pages, no figure
Localization via fractional moments for models on with single-site potentials of finite support
One of the fundamental results in the theory of localization for discrete
Schr\"odinger operators with random potentials is the exponential decay of
Green's function and the absence of continuous spectrum. In this paper we
provide a new variant of these results for one-dimensional alloy-type
potentials with finitely supported sign-changing single-site potentials using
the fractional moment method.Comment: LaTeX-file, 26 pages with 2 LaTeX figure
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