164 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
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
The weak localization for the alloy-type Anderson model on a cubic lattice
We consider alloy type random Schr\"odinger operators on a cubic lattice
whose randomness is generated by the sign-indefinite single-site potential. We
derive Anderson localization for this class of models in the Lifshitz tails
regime, i.e. when the coupling parameter is small, for the energies
.Comment: 45 pages, 2 figures. To appear in J. Stat. Phy
Rate of Convergence Towards Hartree Dynamics
We consider a system of N bosons interacting through a two-body potential
with, possibly, Coulomb-type singularities. We show that the difference between
the many-body Schr\"odinger evolution in the mean-field regime and the
effective nonlinear Hartree dynamics is at most of the order 1/N, for any fixed
time. The N-dependence of the bound is optimal.Comment: 26 page
Mean-Field Dynamics: Singular Potentials and Rate of Convergence
We consider the time evolution of a system of identical bosons whose
interaction potential is rescaled by . We choose the initial wave
function to describe a condensate in which all particles are in the same
one-particle state. It is well known that in the mean-field limit the quantum -body dynamics is governed by the nonlinear Hartree
equation. Using a nonperturbative method, we extend previous results on the
mean-field limit in two directions. First, we allow a large class of singular
interaction potentials as well as strong, possibly time-dependent external
potentials. Second, we derive bounds on the rate of convergence of the quantum
-body dynamics to the Hartree dynamics.Comment: Typos correcte
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
Dynamical Collapse of Boson Stars
We study the time evolution in system of bosons with a relativistic
dispersion law interacting through an attractive Coulomb potential with
coupling constant . We consider the mean field scaling where tends to
infinity, tends to zero and remains fixed. We investigate
the relation between the many body quantum dynamics governed by the
Schr\"odinger equation and the effective evolution described by a
(semi-relativistic) Hartree equation. In particular, we are interested in the
super-critical regime of large (the sub-critical case has been
studied in \cite{ES,KP}), where the nonlinear Hartree equation is known to have
solutions which blow up in finite time. To inspect this regime, we need to
regularize the Coulomb interaction in the many body Hamiltonian with an
dependent cutoff that vanishes in the limit . We show, first, that
if the solution of the nonlinear equation does not blow up in the time interval
, then the many body Schr\"odinger dynamics (on the level of the
reduced density matrices) can be approximated by the nonlinear Hartree
dynamics, just as in the sub-critical regime. Moreover, we prove that if the
solution of the nonlinear Hartree equation blows up at time (in the sense
that the norm of the solution diverges as time approaches ), then
also the solution of the linear Schr\"odinger equation collapses (in the sense
that the kinetic energy per particle diverges) if and,
simultaneously, sufficiently fast. This gives the first
dynamical description of the phenomenon of gravitational collapse as observed
directly on the many body level.Comment: 40 page
Radiation Exposure and Mortality from Cardiovascular Disease and Cancer in Early NASA Astronauts: Space for Exploration
Of the many possible health challenges posed during extended exploratory missions to space, the effects of space radiation on cardiovascular disease and cancer are of particular concern. There are unique challenges to estimating those radiation risks; care and appropriate and rigorous methodology should be applied when considering small cohorts such as the NASA astronaut population. The objective of this work was to establish whether there is evidence for excess cardiovascular disease or cancer mortality in an early NASA astronaut cohort and determine if a correlation exists between space radiation exposure and mortality
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