18,020 research outputs found
Conditions for the Quantum to Classical Transition: Trajectories vs. Phase Space Distributions
We contrast two sets of conditions that govern the transition in which
classical dynamics emerges from the evolution of a quantum system. The first
was derived by considering the trajectories seen by an observer (dubbed the
``strong'' transition) [Bhattacharya, et al., Phys. Rev. Lett. 85: 4852
(2000)], and the second by considering phase-space densities (the ``weak''
transition) [Greenbaum, et al., Chaos 15, 033302 (2005)]. On the face of it
these conditions appear rather different. We show, however, that in the
semiclassical regime, in which the action of the system is large compared to
, and the measurement noise is small, they both offer an essentially
equivalent local picture. Within this regime, the weak conditions dominate
while in the opposite regime where the action is not much larger than Planck's
constant, the strong conditions dominate.Comment: 8 pages, 2 eps figure
The Quantum Emergence of Chaos
The dynamical status of isolated quantum systems, partly due to the linearity
of the Schrodinger equation is unclear: Conventional measures fail to detect
chaos in such systems. However, when quantum systems are subjected to
observation -- as all experimental systems must be -- their dynamics is no
longer linear and, in the appropriate limit(s), the evolution of expectation
values, conditioned on the observations, closely approaches the behavior of
classical trajectories. Here we show, by analyzing a specific example, that
microscopic continuously observed quantum systems, even far from any classical
limit, can have a positive Lyapunov exponent, and thus be truly chaotic.Comment: 4 pages, 4 figure
Statics and dynamics of domain patterns in hexagonal-orthorhombic ferroelastics
We study the statics and the dynamics of domain patterns in proper
hexagonal-orthorhombic ferroelastics; these patterns are of particular interest
because they provide a rare physical realization of disclinations in crystals.
Both our static and dynamical theories are based entirely on classical,
nonlinear elasticity theory; we use the minimal theory consistent with
stability, symmetry and ability to explain qualitatively the observed patterns.
After scaling, the only parameters of the static theory are a temperature
variable and a stiffness variable. For moderate to large stiffness, our static
results show nested stars, unnested stars, fans and other nodes, triangular and
trapezoidal regions of trapped hexagonal phase, etc observed in electron
microscopy of Ta4N and Mg-Cd alloys, and also in lead orthovanadate (which is
trigonal-monoclinic); we even find imperfections in some nodes, like those
observed. For small stiffness, we find patterns like those observed in the
mineral Mg-cordierite. Our dynamical studies of growth and relaxation show the
formation of these static patterns, and also transitory structures such as
12-armed bursts, streamers and striations which are also seen experimentally.
The major aspects of the growth-relaxation process are quite unlike those in
systems with conventional order parameters, for it is inherently nonlocal; for
example, the changes from one snapshot to the next are not predictable by
inspection.Comment: 9 pages, 3 figures (1 b&w, 2 colour); animations may be viewed at
http://huron.physics.utoronto.ca/~curnoe/sim.htm
Rapid state purification protocols for a Cooper pair box
We propose techniques for implementing two different rapid state purification
schemes, within the constraints present in a superconducting charge qubit
system. Both schemes use a continuous measurement of charge (z) measurements,
and seek to minimize the time required to purify the conditional state. Our
methods are designed to make the purification process relatively insensitive to
rotations about the x-axis, due to the Josephson tunnelling Hamiltonian. The
first proposed method, based on the scheme of Jacobs [Phys. Rev. A 67,
030301(R) (2003)] uses the measurement results to control bias (z) pulses so as
to rotate the Bloch vector onto the x-axis of the Bloch sphere. The second
proposed method, based on the scheme of Wiseman and Ralph [New J. Phys. 8, 90
(2006)] uses a simple feedback protocol which tightly rotates the Bloch vector
about an axis almost parallel with the measurement axis. We compare the
performance of these and other techniques by a number of different measures.Comment: 14 pages, 14 figures. v2: Revised version after referee comments.
Accepted for publication by Physical Review
Standard Quantum Limits for broadband position measurement
I utilize the Caves-Milburn model for continuous position measurements to
formulate a broadband version of the Standard Quantum Limit (SQL) for
monitoring the position of a free mass, and illustrate the use of Kalman
filtering to recover the SQL for estimating a weak classical force that acts on
a quantum-mechanical test particle under continuous observation. These
derivations are intended to clarify the interpretation of SQL's in the context
of continuous quantum measurement.Comment: Replaced version: changed title, fixed algebra error at the very end,
conclusions modified accordingly. Four pages, one eps figur
Cluster counting: The Hoshen-Kopelman algorithm vs. spanning tree approaches
Two basic approaches to the cluster counting task in the percolation and
related models are discussed. The Hoshen-Kopelman multiple labeling technique
for cluster statistics is redescribed. Modifications for random and aperiodic
lattices are sketched as well as some parallelised versions of the algorithm
are mentioned. The graph-theoretical basis for the spanning tree approaches is
given by describing the "breadth-first search" and "depth-first search"
procedures. Examples are given for extracting the elastic and geometric
"backbone" of a percolation cluster. An implementation of the "pebble game"
algorithm using a depth-first search method is also described.Comment: LaTeX, uses ijmpc1.sty(included), 18 pages, 3 figures, submitted to
Intern. J. of Modern Physics
Optimal Unravellings for Feedback Control in Linear Quantum Systems
For quantum systems with linear dynamics in phase space much of classical
feedback control theory applies. However, there are some questions that are
sensible only for the quantum case, such as: given a fixed interaction between
the system and the environment what is the optimal measurement on the
environment for a particular control problem? We show that for a broad class of
optimal (state-based) control problems (the stationary
Linear-Quadratic-Gaussian class), this question is a semi-definite program.
Moreover, the answer also applies to Markovian (current-based) feedback.Comment: 5 pages. Version published by Phys. Rev. Let
Holocene Environmental Change in the Frobisher Bay Area, Baffin Island, N.W.T.: Deglaciation, Emergence, and the Sequence of Vegetation and Climate
The late-glacial and Holocene paleoenvironmental sequence for the Frobisher Bay area is outlined using glacial, sea level, and palynological evidence. A rapid retreat of ice from the late Foxe glacial maximum in the lower part of the bay after 11,000 BP was followed by a series of stillstands or minor readvances between ca. 8500 and 7000 BP and possibly later, before the final disappearance of the inland ice centred near Amadjuak Lake. Lithostratigraphy of three buried organic sections which together represent deposition occurring over the period from 5500 to 400 BP indicates a change from a relatively warm, moist environment before 5500 BP to neoglacial conditions, with the coldest phases centred around 5000, 2700, 1200 BP and probably sometime after 400 radiocarbon years BP. As evidenced by peat growth and pollen data, milder, wetter conditions prevailed from 4500 to 3000 BP and again from ca. 2600 to 1800 BP. Peat growth and soil organic fractions point to lesser mild intervals ca. 900 BP and 400 BP, but these are not apparent in the pollen assemblage. The pollen record does not extend to the last four centuries; however, lichenometric studies of neoglacial moraines by DOWDESWELL (1984) show that the maximum late Holocene advance of glaciers in the area occurred within the last century. Modern pollen samples indicate that the present vegetation of the inner Frobisher Bay area is comparable to that of the milder intervals of the late Holocene.La présente étude porte sur l'évolution paléoenvironnementale fini-glaciaire et holocène de la région de la baie de Frobisher et se fonde sur les niveaux marins ainsi que sur des témoins polliniques et glaciaires. Le retrait rapide des glaciers dans la partie intérieure de la baie depuis 11 000 BP a été suivi d'épisodes de stabilité et de récurrences mineures entre 8500 et 7000 ans BP. et peut-être plus tard, avant la disparition définitive des glaces continentales dont le centre se trouvait près du lac Amadjuak. L'analyse a porté sur trois sections de sol enfoui qui représentent les dépôts accumulés entre 5500 et 400 ans BP. La lithostratigraphie révèle le passage d'un climat relativement humide et chaud, il y a plus de 5500 ans, à un climat néoglaciaire dont les périodes les plus froides se situent vers 5000, 2700 et 1200 ans BP et probablement après 400 ans BP. La tourbe et les données polliniques témoignent de conditions climatiques plus douces et plus humides pour les périodes allant de 4500 à 3000 ans BP et d'environ 2600 à 1800 ans BP. Mais, contrairement aux associations polliniques, la tourbe et certaines portions organiques de sol font penser qu'ont existé des intervalles plus frais environ de 900 à 400 ans BP. Les données pollinique ne donnent aucun renseignement sur les quatre derniers siècles. Cependant, les études Ii-chénométriques que DOWDESWELL (1984) a faites sur les moraines néoglaciaires révèlent que, dans la région pendant l'Holocène supérieur, l'avancée maximale des glaces s'est produite au siècle dernier. Des échantillons polliniques récents démontrent que la végétation actuelle de l'intérieur de la baie de Frobisher ressemble à celle qu'on trouvait pendant les intervalles tempérés de l'Holocène supérieur.Die spàtglaziale und holozàne Abfolge des Palâomilieus im Gebiete der Frobisher Bucht wird durch glaziale, Meeresspiegel- und palynologische Beweise umrissen. Ein rasches Zurùckweichen des Eises aus dem niederen Teil der Bucht hat sich nach 11 000 BP ereignet. gefolgt von mehreren Stillstânden oder kleinerem Wiedervorrùcken zwischen etwa 8500 und 7000 BP oder evtl. spater, bevor das Inlandeis schliesslich verschwunden ist. Drei verdeckte Bodenprofile sind analysiert worden, die zu-sammen die Ablagerung der Zeit von 5500 bis 400 BP darstellen. Die Lithostratigraphie hat eine relativ warme, feuchte Umgebung vor 5500 BP ergeben, die sich alsdann zu neoglazialen Zustânden geàndert hat, mit dem Mittel der kâltesten Phasen um etwa 5000, 2700, und wahrscheinlich auch irgandwann nach 400 Radiokohlenstoffjahren BP. Torfwuchs sowie auch palynologische Daten zeigen, dass milde, feuchte Zustânde von 4500 bis 3000 BP und dann nochmals von etwa 2600 bis 1800 BP vorgeherrscht haben. Der Torfwuchs und der organische Anteil des Bodens deuten auch auf kleinere milde Zeitspannen um etwa 900 und 400 BP, aber dièse sind nicht aus der Pollenvergesellschaftung ersichtlich. Fur die jùngsten vier Jahrhunderte fehlen Pollenunterlagen; aber durch Untersuchung der Flechten auf neoglazialen Morânen hat DOWDESWELL (1984) fur dieses Gebiet ein spatholozànes Gletschervorrùcken wahrend des letzten Jahrhunderts belegen konnen. Pollenmuster beweisen. dass sich im Gebiet der inneren Frobisher Bucht die heutige Pflanzendecke gut mit der Vegetation mlldererer Spâtholozànintervalle vergleichen làsst
De Finetti's construction as a categorical limit
This paper reformulates a classical result in probability theory from the
1930s in modern categorical terms: de Finetti's representation theorem is
redescribed as limit statement for a chain of finite spaces in the Kleisli
category of the Giry monad. This new limit is used to identify among
exchangeable coalgebras the final one.Comment: In proceedings of CMCS 202
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