9,119 research outputs found
Floer theory for negative line bundles via Gromov-Witten invariants
Let M be the total space of a negative line bundle over a closed symplectic
manifold. We prove that the quotient of quantum cohomology by the kernel of a
power of quantum cup product by the first Chern class of the line bundle is
isomorphic to symplectic cohomology. We also prove this for negative vector
bundles and the top Chern class. We explicitly calculate the symplectic and
quantum cohomologies of O(-n) over P^m. For n=1, M is the blow-up of C^{m+1} at
the origin and symplectic cohomology has rank m. The symplectic cohomology
vanishes if and only if the first Chern class of the line bundle is nilpotent
in quantum cohomology. We prove a Kodaira vanishing theorem and a Serre
vanishing theorem for symplectic cohomology. In general, we construct a
representation of \pi_1(Ham(X,\omega)) on the symplectic cohomology of
symplectic manifolds X conical at infinity.Comment: 53 pages; version 3: improved discussion of maximum principle for
negative vector bundles. The final version is published in Advances in
Mathematic
Regional landform thresholds
Remote sensing technology allows us to recognize manifestations of regional thresholds, especially in the spatial characteristics of process agents. For example, a change in river channel pattern over a short distance reflects a threshold alteration in the physical controls of discharge and/or sediment. It is, therefore, a valuable indication of conditions as they exist. However, we probably will have difficulty determining whether the systemic parameters are now close to threshold conditions at which a different change will occur. This, of course, is a temporal and magnitude problem which is difficult to solve from the spatial characteristics
Vector constants of motion for time-dependent Kepler and isotropic harmonic oscillator potentials
A method of obtaining vector constants of motion for time-independent as well
as time-dependent central fields is discussed. Some well-established results
are rederived in this alternative way and new ones obtained.Comment: 18 pages, no figures, regular Latex article forma
The use of entropy for analysis and control of cognitive models
Measures of entropy are useful for explaining the behaviour of cognitive models. We demonstrate that entropy can not only help to analyse the performance of the model, but it can be used to control model pararmeters and improve the match between the model and data. We present a cognitive model that uses local computations of entropy to moderate its own behaviour and matches the data fairly well
Conservation Laws and the Multiplicity Evolution of Spectra at the Relativistic Heavy Ion Collider
Transverse momentum distributions in ultra-relativistic heavy ion collisions
carry considerable information about the dynamics of the hot system produced.
Direct comparison with the same spectra from collisions has proven
invaluable to identify novel features associated with the larger system, in
particular, the "jet quenching" at high momentum and apparently much stronger
collective flow dominating the spectral shape at low momentum. We point out
possible hazards of ignoring conservation laws in the comparison of high- and
low-multiplicity final states. We argue that the effects of energy and momentum
conservation actually dominate many of the observed systematics, and that
collisions may be much more similar to heavy ion collisions than generally
thought.Comment: 15 pages, 14 figures, submitted to PRC; Figures 2,4,5,6,12 updated,
Tables 1 and 3 added, typo in Tab.V fixed, appendix B partially rephrased,
minor typo in Eq.B1 fixed, minor wording; references adde
Deformations of symplectic cohomology and exact Lagrangians in ALE spaces
We prove that the only exact Lagrangian submanifolds in an ALE space are
spheres. ALE spaces are the simply connected hyperkahler manifolds which at
infinity look like C^2/G for any finite subgroup G of SL(2,C). They can be
realized as the plumbing of copies of the cotangent bundle of a 2-sphere
according to ADE Dynkin diagrams. The proof relies on symplectic cohomology.Comment: 35 pages, 3 figures, minor changes and corrected typo
Quantum Channels and Representation Theory
In the study of d-dimensional quantum channels , an assumption
which is not very restrictive, and which has a natural physical interpretation,
is that the corresponding Kraus operators form a representation of a Lie
algebra. Physically, this is a symmetry algebra for the interaction
Hamiltonian. This paper begins a systematic study of channels defined by
representations; the famous Werner-Holevo channel is one element of this
infinite class. We show that the channel derived from the defining
representation of SU(n) is a depolarizing channel for all , but for most
other representations this is not the case. Since the Bloch sphere is not
appropriate here, we develop technology which is a generalization of Bloch's
technique. Our method works by representing the density matrix as a polynomial
in symmetrized products of Lie algebra generators, with coefficients that are
symmetric tensors. Using these tensor methods we prove eleven theorems, derive
many explicit formulas and show other interesting properties of quantum
channels in various dimensions, with various Lie symmetry algebras. We also
derive numerical estimates on the size of a generalized ``Bloch sphere'' for
certain channels. There remain many open questions which are indicated at
various points through the paper.Comment: 28 pages, 1 figur
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