2,701 research outputs found
Kochen-Specker theorem for a single qubit using positive operator-valued measures
A proof of the Kochen-Specker theorem for a single two-level system is
presented. It employs five eight-element positive operator-valued measures and
a simple algebraic reasoning based on the geometry of the dodecahedron.Comment: REVTeX4, 4 pages, 2 figure
Non-Contextual Hidden Variables and Physical Measurements
For a hidden variable theory to be indistinguishable from quantum theory for
finite precision measurements, it is enough that its predictions agree for some
measurement within the range of precision. Meyer has recently pointed out that
the Kochen-Specker theorem, which demonstrates the impossibility of a
deterministic hidden variable description of ideal spin measurements on a spin
1 particle, can thus be effectively nullified if only finite precision
measurements are considered. We generalise this result: it is possible to
ascribe consistent outcomes to a dense subset of the set of projection valued
measurements, or to a dense subset of the set of positive operator valued
measurements, on any finite dimensional system. Hence no Kochen-Specker like
contradiction can rule out hidden variable theories indistinguishable from
quantum theory by finite precision measurements in either class.Comment: Typo corrected. Final version: to appear in Phys. Rev. Let
Maximally Causal Quantum Mechanics
We present a new causal quantum mechanics in one and two dimensions developed
recently at TIFR by this author and V. Singh. In this theory both position and
momentum for a system point have Hamiltonian evolution in such a way that the
ensemble of system points leads to position and momentum probability densities
agreeing exactly with ordinary quantum mechanics.Comment: 7 pages,latex,no figures,to appear in Praman
Classical Lie algebras and Drinfeld doubles
The Drinfeld double structure underlying the Cartan series An, Bn, Cn, Dn of
simple Lie algebras is discussed.
This structure is determined by two disjoint solvable subalgebras matched by
a pairing. For the two nilpotent positive and negative root subalgebras the
pairing is natural and in the Cartan subalgebra is defined with the help of a
central extension of the algebra.
A new completely determined basis is found from the compatibility conditions
in the double and a different perspective for quantization is presented. Other
related Drinfeld doubles on C are also considered.Comment: 11 pages. submitted for publication to J. Physics
Shoot growth of woody trees and shrubs is predicted by maximum plant height and associated traits
1. The rate of elongation and thickening of individual branches (shoots) varies across plant species. This variation is important for the outcome of competition and other plant-plant interactions. Here we compared rates of shoot growth across 44 species from tropical, warm temperate, and cool temperate forests of eastern Australia.2. Shoot growth rate was found to correlate with a suite of traits including the potential height of the species, xylem-specific conductivity, leaf size, leaf area per xylem cross-section, twig diameter (at 40 cm length), wood density and modulus of elasticity.3. Within this suite of traits, maximum plant height was the clearest correlate of growth rates, explaining 50 to 67% of the variation in growth overall (p p 4. Growth rates were not strongly correlated with leaf nitrogen or leaf mass per unit leaf area.5. Correlations between growth and maximum height arose both across latitude (47%, p p p p < 0.0001), reflecting intrinsic differences across species and sites
On Zurek's derivation of the Born rule
Recently, W. H. Zurek presented a novel derivation of the Born rule based on
a mechanism termed environment-assisted invariance, or "envariance" [W. H.
Zurek, Phys. Rev. Lett. 90(2), 120404 (2003)]. We review this approach and
identify fundamental assumptions that have implicitly entered into it,
emphasizing issues that any such derivation is likely to face.Comment: 8 pages; v2: minor clarifications added; v3: reference to Zurek's
quant-ph/0405161 added. To appear in Foundations of Physics (Cushing Volume
On the nature of continuous physical quantities in classical and quantum mechanics
Within the traditional Hilbert space formalism of quantum mechanics, it is
not possible to describe a particle as possessing, simultaneously, a sharp
position value and a sharp momentum value. Is it possible, though, to describe
a particle as possessing just a sharp position value (or just a sharp momentum
value)? Some, such as Teller (Journal of Philosophy, 1979), have thought that
the answer to this question is No -- that the status of individual continuous
quantities is very different in quantum mechanics than in classical mechanics.
On the contrary, I shall show that the same subtle issues arise with respect to
continuous quantities in classical and quantum mechanics; and that it is, after
all, possible to describe a particle as possessing a sharp position value
without altering the standard formalism of quantum mechanics.Comment: 26 pages, LaTe
Integrable potentials on spaces with curvature from quantum groups
A family of classical integrable systems defined on a deformation of the
two-dimensional sphere, hyperbolic and (anti-)de Sitter spaces is constructed
through Hamiltonians defined on the non-standard quantum deformation of a sl(2)
Poisson coalgebra. All these spaces have a non-constant curvature that depends
on the deformation parameter z. As particular cases, the analogues of the
harmonic oscillator and Kepler--Coulomb potentials on such spaces are proposed.
Another deformed Hamiltonian is also shown to provide superintegrable systems
on the usual sphere, hyperbolic and (anti-)de Sitter spaces with a constant
curvature that exactly coincides with z. According to each specific space, the
resulting potential is interpreted as the superposition of a central harmonic
oscillator with either two more oscillators or centrifugal barriers. The
non-deformed limit z=0 of all these Hamiltonians can then be regarded as the
zero-curvature limit (contraction) which leads to the corresponding
(super)integrable systems on the flat Euclidean and Minkowskian spaces.Comment: 19 pages, 1 figure. Two references adde
Harvest Demographics of Temperate-breeding Canada Geese in South Dakota, 1967–1995
In South Dakota, breeding giant Canada geese (Branta canadensis maxima) have increased substantially, and harvest management strategies have been implemented to maximize hunting opportunity (e.g., special early-September seasons) on local, as well as molt-migrant giant Canada geese (B. c. interior) while still protecting lesser abundant Arcticbreeding Canada geese and cackling geese (e.g., B. hutchinsii, B. minima). Information on important parameters, such as survival and recovery rates, are generally lacking for giant Canada geese in the northern Great Plains. Patterns in Canada goose band recoveries can provide insight into the distribution, chronology, and harvest pressures to which a given goose population segment is exposed. We studied spatial and temporal recovery patterns of molting Canada geese during annual banding efforts in South Dakota between 1967 and 1995. Recovery rates (% ± SE) for Canada geese increased over time in both western South Dakota (0.034 ± 0.005 [1967 to 1976], 0.056 ± 0.009 [1977 to 1986]) and eastern (0.026 ± 0.002 [1967 to 1978], 0.058 ± 0.003 [1987 to 1995]) South Dakota. Although recovery rates for Canada geese west of the Missouri River (WR) and east of the Missouri River (ER) were relatively similar, recovery distribution and harvest chronology indicate spatial and temporal differences for geese banded in these 2 geographic regions. Overall, Canada geese banded in South Dakota were recovered in 23 states and 5 Canadian provinces, and recovery distribution varied relative to banding region. Distribution of recoveries suggests a south-southwesterly movement for WR-banded geese compared to a south-southeasterly movement for ERbanded geese. For WR-banded geese, 40 to 52% and 30 to 34% of direct and indirect recoveries, respectively, occurred in December. In contrast, for ER-banded geese, 19 to 38% and 15 to 19% of direct and indirect recoveries, respectively, occurred in December. Waterfowl managers need to consider that recovery rates and harvest chronology of banded giant Canada geese may vary geographically within a state or province. Refinement of harvest management strategies at multiple spatial scales may be required
Quantum discord and noncontextual hidden variables models
It is shown that theoretically viable noncontextual hidden variables models
in lead to conflicting dispersion free expressions in the analysis of the
conditional measurement of two non-orthogonal projectors.
No satisfactory criterion of the quantum discord, which relies on the
analysis of conditional measurement, is formulated in the hidden
variables space due to a lack of uniqueness of the dispersion free
representation.
We also make a speculative comment on a "many-worlds interpretation" of
hidden variables models to account for the conditional measurement.Comment: 5 pages (to appear in PRA
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