396 research outputs found
Cat States and Single Runs for the Damped Harmonic Oscillator
We discuss the fate of initial states of the cat type for the damped harmonic
oscillator, mostly employing a linear version of the stochastic Schr\"odinger
equation. We also comment on how such cat states might be prepared and on the
relation of single realizations of the noise to single runs of experiments.Comment: 18, Revte
Predictability sieve, pointer states, and the classicality of quantum trajectories
We study various measures of classicality of the states of open quantum
systems subject to decoherence. Classical states are expected to be stable in
spite of decoherence, and are thought to leave conspicuous imprints on the
environment. Here these expected features of environment-induced superselection
(einselection) are quantified using four different criteria: predictability
sieve (which selects states that produce least entropy), purification time
(which looks for states that are the easiest to find out from the imprint they
leave on the environment), efficiency threshold (which finds states that can be
deduced from measurements on a smallest fraction of the environment), and
purity loss time (that looks for states for which it takes the longest to lose
a set fraction of their initial purity). We show that when pointer states --
the most predictable states of an open quantum system selected by the
predictability sieve -- are well defined, all four criteria agree that they are
indeed the most classical states. We illustrate this with two examples: an
underdamped harmonic oscillator, for which coherent states are unanimously
chosen by all criteria, and a free particle undergoing quantum Brownian motion,
for which most criteria select almost identical Gaussian states (although, in
this case, predictability sieve does not select well defined pointer states.)Comment: 10 pages, 13 figure
Optimization of water use for field crop production in the upper Midwest
This project investigated combinations of both irrigation and drainage treatments in order to determine the best water management practices
for field crop production in claypan soils in the upper Midwest. Four years of corn and one year of soybean yield data from forty field plots are presented. The irrigation treatments were sprinkler, furrow, and no irrigation; the drainage treatments were surface, subsurface, surface
plus subsurface, and no drainage. The plots were located on a claypan soil in south-central Illinois. Sprinkler irrigation was provided by a solid set system. Furrow irrigation was done with gated pipes. The plots with surface drainage had a slope of 0.5%; the others were graded level. Subsurface drainage was provided by plastic tubing on 20-ft centers. Drainage water from the plots and surrounding areas was stored in ponds and recycled as irrigation water. The data indicate average corn yield increases of 13 and 50 bu/acre due to drainage and irrigation, respectively. Together, they act synergistically to produce an average yield increase of 92 bu/acre. This synergistic yield increase provides economic impetus to combining irrigation and drainage systems and storing drainage water in ponds or lakes for later use in irrigation. This combination will have the added effect of conserving water resources, of improving water use efficiency and downstream water quality, and of lessening downstream flooding.U.S. Geological SurveyU.S. Department of the InteriorOpe
Conditional quantum dynamics with several observers
We consider several observers who monitor different parts of the environment
of a single quantum system and use their data to deduce its state. We derive a
set of conditional stochastic master equations that describe the evolution of
the density matrices each observer ascribes to the system under the Markov
approximation, and show that this problem can be reduced to the case of a
single "super-observer", who has access to all the acquired data. The key
problem - consistency of the sets of data acquired by different observers - is
then reduced to the probability that a given combination of data sets will be
ever detected by the "super-observer". The resulting conditional master
equations are applied to several physical examples: homodyne detection of
phonons in quantum Brownian motion, photo-detection and homodyne detection of
resonance fluorescence from a two-level atom. We introduce {\it relative
purity} to quantify the correlations between the information about the system
gathered by different observers from their measurements of the environment. We
find that observers gain the most information about the state of the system and
they agree the most about it when they measure the environment observables with
eigenstates most closely correlated with the optimally predictable {\it pointer
basis} of the system.Comment: Updated version: new title and contents. 22 pages, 8 figure
Optimal control of entanglement via quantum feedback
It has recently been shown that finding the optimal measurement on the
environment for stationary Linear Quadratic Gaussian control problems is a
semi-definite program. We apply this technique to the control of the
EPR-correlations between two bosonic modes interacting via a parametric
Hamiltonian at steady state. The optimal measurement turns out to be nonlocal
homodyne measurement -- the outputs of the two modes must be combined before
measurement. We also find the optimal local measurement and control technique.
This gives the same degree of entanglement but a higher degree of purity than
the local technique previously considered [S. Mancini, Phys. Rev. A {\bf 73},
010304(R) (2006)].Comment: 10 pages, 5 figure
Stochastic simulations of conditional states of partially observed systems, quantum and classical
In a partially observed quantum or classical system the information that we
cannot access results in our description of the system becoming mixed even if
we have perfect initial knowledge. That is, if the system is quantum the
conditional state will be given by a state matrix and if classical
the conditional state will be given by a probability distribution
where is the result of the measurement. Thus to determine the evolution of
this conditional state under continuous-in-time monitoring requires an
expensive numerical calculation. In this paper we demonstrating a numerical
technique based on linear measurement theory that allows us to determine the
conditional state using only pure states. That is, our technique reduces the
problem size by a factor of , the number of basis states for the system.
Furthermore we show that our method can be applied to joint classical and
quantum systems as arises in modeling realistic measurement.Comment: 16 pages, 11 figure
Linear stochastic wave-equations for continuously measured quantum systems
While the linearity of the Schr\"odinger equation and the superposition
principle are fundamental to quantum mechanics, so are the backaction of
measurements and the resulting nonlinearity. It is remarkable, therefore, that
the wave-equation of systems in continuous interaction with some reservoir,
which may be a measuring device, can be cast into a linear form, even after the
degrees of freedom of the reservoir have been eliminated. The superposition
principle still holds for the stochastic wave-function of the observed system,
and exact analytical solutions are possible in sufficiently simple cases. We
discuss here the coupling to Markovian reservoirs appropriate for homodyne,
heterodyne, and photon counting measurements. For these we present a derivation
of the linear stochastic wave-equation from first principles and analyze its
physical content.Comment: 34 pages, Revte
Human gene copy number spectra analysis in congenital heart malformations
The clinical significance of copy number variants (CNVs) in congenital heart disease (CHD) continues to be a challenge. Although CNVs including genes can confer disease risk, relationships between gene dosage and phenotype are still being defined. Our goal was to perform a quantitative analysis of CNVs involving 100 well-defined CHD risk genes identified through previously published human association studies in subjects with anatomically defined cardiac malformations. A novel analytical approach permitting CNV gene frequency “spectra” to be computed over prespecified regions to determine phenotype-gene dosage relationships was employed. CNVs in subjects with CHD (n = 945), subphenotyped into 40 groups and verified in accordance with the European Paediatric Cardiac Code, were compared with two control groups, a disease-free cohort (n = 2,026) and a population with coronary artery disease (n = 880). Gains (≥200 kb) and losses (≥100 kb) were determined over 100 CHD risk genes and compared using a Barnard exact test. Six subphenotypes showed significant enrichment (P ≤ 0.05), including aortic stenosis (valvar), atrioventricular canal (partial), atrioventricular septal defect with tetralogy of Fallot, subaortic stenosis, tetralogy of Fallot, and truncus arteriosus. Furthermore, CNV gene frequency spectra were enriched (P ≤ 0.05) for losses at: FKBP6, ELN, GTF2IRD1, GATA4, CRKL, TBX1, ATRX, GPC3, BCOR, ZIC3, FLNA and MID1; and gains at: PRKAB2, FMO5, CHD1L, BCL9, ACP6, GJA5, HRAS, GATA6 and RUNX1. Of CHD subjects, 14% had causal chromosomal abnormalities, and 4.3% had likely causal (significantly enriched), large, rare CNVs. CNV frequency spectra combined with precision phenotyping may lead to increased molecular understanding of etiologic pathways
Generalized stochastic Schroedinger equations for state vector collapse
A number of authors have proposed stochastic versions of the Schr\"odinger
equation, either as effective evolution equations for open quantum systems or
as alternative theories with an intrinsic collapse mechanism. We discuss here
two directions for generalization of these equations. First, we study a general
class of norm preserving stochastic evolution equations, and show that even
after making several specializations, there is an infinity of possible
stochastic Schr\"odinger equations for which state vector collapse is provable.
Second, we explore the problem of formulating a relativistic stochastic
Schr\"odinger equation, using a manifestly covariant equation for a quantum
field system based on the interaction picture of Tomonaga and Schwinger. The
stochastic noise term in this equation can couple to any local scalar density
that commutes with the interaction energy density, and leads to collapse onto
spatially localized eigenstates. However, as found in a similar model by
Pearle, the equation predicts an infinite rate of energy nonconservation
proportional to , arising from the local double commutator in
the drift term.Comment: 24 pages Plain TeX. Minor changes, some new references. To appear in
Journal of Physics
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