562 research outputs found
Projective dynamics and first integrals
We present the theory of tensors with Young tableau symmetry as an efficient
computational tool in dealing with the polynomial first integrals of a natural
system in classical mechanics. We relate a special kind of such first
integrals, already studied by Lundmark, to Beltrami's theorem about
projectively flat Riemannian manifolds. We set the ground for a new and simple
theory of the integrable systems having only quadratic first integrals. This
theory begins with two centered quadrics related by central projection, each
quadric being a model of a space of constant curvature. Finally, we present an
extension of these models to the case of degenerate quadratic forms.Comment: 39 pages, 2 figure
Bases for qudits from a nonstandard approach to SU(2)
Bases of finite-dimensional Hilbert spaces (in dimension d) of relevance for
quantum information and quantum computation are constructed from angular
momentum theory and su(2) Lie algebraic methods. We report on a formula for
deriving in one step the (1+p)p qupits (i.e., qudits with d = p a prime
integer) of a complete set of 1+p mutually unbiased bases in C^p. Repeated
application of the formula can be used for generating mutually unbiased bases
in C^d with d = p^e (e > or = 2) a power of a prime integer. A connection
between mutually unbiased bases and the unitary group SU(d) is briefly
discussed in the case d = p^e.Comment: From a talk presented at the 13th International Conference on
Symmetry Methods in Physics (Dubna, Russia, 6-9 July 2009) organized in
memory of Prof. Yurii Fedorovich Smirnov by the Bogoliubov Laboratory of
Theoretical Physics of the JINR and the ICAS at Yerevan State University
Weak mutually unbiased bases
Quantum systems with variables in are considered. The
properties of lines in the phase space of
these systems, are studied. Weak mutually unbiased bases in these systems are
defined as bases for which the overlap of any two vectors in two different
bases, is equal to or alternatively to one of the
(where is a divisor of apart from ). They are designed for the
geometry of the phase space, in the sense
that there is a duality between the weak mutually unbiased bases and the
maximal lines through the origin. In the special case of prime , there are
no divisors of apart from and the weak mutually unbiased bases are
mutually unbiased bases
Statistical Mechanics of Vacancy and Interstitial Strings in Hexagonal Columnar Crystals
Columnar crystals contain defects in the form of vacancy/interstitial loops
or strings of vacancies and interstitials bounded by column ``heads'' and
``tails''. These defect strings are oriented by the columnar lattice and can
change size and shape by movement of the ends and forming kinks along the
length. Hence an analysis in terms of directed living polymers is appropriate
to study their size and shape distribution, volume fraction, etc. If the
entropy of transverse fluctuations overcomes the string line tension in the
crystalline phase, a string proliferation transition occurs, leading to a
supersolid phase. We estimate the wandering entropy and examine the behaviour
in the transition regime. We also calculate numerically the line tension of
various species of vacancies and interstitials in a triangular lattice for
power-law potentials as well as for a modified Bessel function interaction
between columns as occurs in the case of flux lines in type-II superconductors
or long polyelectrolytes in an ionic solution. We find that the centered
interstitial is the lowest energy defect for a very wide range of interactions;
the symmetric vacancy is preferred only for extremely short interaction ranges.Comment: 22 pages (revtex), 15 figures (encapsulated postscript
On the convex central configurations of the symmetric (ℓ + 2)-body problem
For the 4-body problem there is the following conjecture: Given arbitrary positive masses, the planar 4-body problem has a unique convex central configuration for each ordering of the masses on its convex hull. Until now this conjecture has remained open. Our aim is to prove that this conjecture cannot be extended to the (ℓ + 2)-body problem with ℓ ⩾ 3. In particular, we prove that the symmetric (2n + 1)-body problem with masses m1 = … = m2n−1 = 1 and m2n = m2n+1 = m sufficiently small has at least two classes of convex central configuration when n = 2, five when n = 3, and four when n = 4. We conjecture that the (2n + 1)-body problem has at least n classes of convex central configurations for n > 4 and we give some numerical evidence that the conjecture can be true. We also prove that the symmetric (2n + 2)-body problem with masses m1 = … = m2n = 1 and m2n+1 = m2n+2 = m sufficiently small has at least three classes of convex central configuration when n = 3, two when n = 4, and three when n = 5. We also conjecture that the (2n + 2)-body problem has at least [(n +1)/2] classes of convex central configurations for n > 5 and we give some numerical evidences that the conjecture can be true
Symmetric informationally complete positive operator valued measure and probability representation of quantum mechanics
Symmetric informationally complete positive operator valued measures
(SIC-POVMs) are studied within the framework of the probability representation
of quantum mechanics. A SIC-POVM is shown to be a special case of the
probability representation. The problem of SIC-POVM existence is formulated in
terms of symbols of operators associated with a star-product quantization
scheme. We show that SIC-POVMs (if they do exist) must obey general rules of
the star product, and, starting from this fact, we derive new relations on
SIC-projectors. The case of qubits is considered in detail, in particular, the
relation between the SIC probability representation and other probability
representations is established, the connection with mutually unbiased bases is
discussed, and comments to the Lie algebraic structure of SIC-POVMs are
presented.Comment: 22 pages, 1 figure, LaTeX, partially presented at the Workshop
"Nonlinearity and Coherence in Classical and Quantum Systems" held at the
University "Federico II" in Naples, Italy on December 4, 2009 in honor of
Prof. Margarita A. Man'ko in connection with her 70th birthday, minor
misprints are corrected in the second versio
Predicting the Impact of Climate Change on Threatened Species in UK Waters
Global climate change is affecting the distribution of marine species and is thought to represent a threat to biodiversity. Previous studies project expansion of species range for some species and local extinction elsewhere under climate change. Such range shifts raise concern for species whose long-term persistence is already threatened by other human disturbances such as fishing. However, few studies have attempted to assess the effects of future climate change on threatened vertebrate marine species using a multi-model approach. There has also been a recent surge of interest in climate change impacts on protected areas. This study applies three species distribution models and two sets of climate model projections to explore the potential impacts of climate change on marine species by 2050. A set of species in the North Sea, including seven threatened and ten major commercial species were used as a case study. Changes in habitat suitability in selected candidate protected areas around the UK under future climatic scenarios were assessed for these species. Moreover, change in the degree of overlap between commercial and threatened species ranges was calculated as a proxy of the potential threat posed by overfishing through bycatch. The ensemble projections suggest northward shifts in species at an average rate of 27 km per decade, resulting in small average changes in range overlap between threatened and commercially exploited species. Furthermore, the adverse consequences of climate change on the habitat suitability of protected areas were projected to be small. Although the models show large variation in the predicted consequences of climate change, the multi-model approach helps identify the potential risk of increased exposure to human stressors of critically endangered species such as common skate (Dipturus batis) and angelshark (Squatina squatina)
Four-body co-circular central configurations
We classify the set of central configurations lying on a common circle in the Newtonian
four-body problem. Using mutual distances as coordinates, we show that the set of four-body
co-circular central configurations with positive masses is a two-dimensional surface, a graph
over two of the exterior side-lengths. Two symmetric families, the kite and isosceles trapezoid,
are investigated extensively. We also prove that a co-circular central configuration requires a
specific ordering of the masses and find explicit bounds on the mutual distances. In contrast to
the general four-body case, we show that if any two masses of a four-body co-circular central
configuration are equal, then the configuration has a line of symmetry.Peer ReviewedPostprint (author’s final draft
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Education and health knowledge: Evidence from UK compulsory schooling reform
We investigate if there is a causal link between education and health knowledge using data from the 1984/85 and 1991/92 waves of the UK Health and Lifestyle Survey (HALS). Uniquely, the survey asks respondents what they think are the main causes of ten common health conditions, and we compare these answers to those given by medical professionals to form an index of health knowledge. For causal identification we use increases in the UK minimum school leaving age in 1947 (from 14 to 15) and 1972 (from 15 to 16) to provide exogenous variation in education. These reforms predominantly induced adolescents who would have left school to stay for one additionally mandated year. OLS estimates suggest that education significantly increases health knowledge, with a one-year increase in schooling increasing the health knowledge index by 15% of a standard deviation. In contrast, estimates from instrumental-variable models show that increased schooling due to the education reforms did not significantly affect health knowledge. This main result is robust to numerous specification tests and alternative formulations of the health knowledge index. Further research is required to determine whether there is also no causal link between higher levels of education – such as post-school qualifications – and health knowledge
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