208 research outputs found
Symplectic structures associated to Lie-Poisson groups
The Lie-Poisson analogues of the cotangent bundle and coadjoint orbits of a
Lie group are considered. For the natural Poisson brackets the symplectic
leaves in these manifolds are classified and the corresponding symplectic forms
are described. Thus the construction of the Kirillov symplectic form is
generalized for Lie-Poisson groups.Comment: 30 page
The quantum dilogarithm and representations quantum cluster varieties
We construct, using the quantum dilogarithm, a series of *-representations of
quantized cluster varieties. This includes a construction of infinite
dimensional unitary projective representations of their discrete symmetry
groups - the cluster modular groups. The examples of the latter include the
classical mapping class groups of punctured surfaces.
One of applications is quantization of higher Teichmuller spaces.
The constructed unitary representations can be viewed as analogs of the Weil
representation. In both cases representations are given by integral operators.
Their kernels in our case are the quantum dilogarithms.
We introduce the symplectic/quantum double of cluster varieties and related
them to the representations.Comment: Dedicated to David Kazhdan for his 60th birthday. The final version.
To appear in Inventiones Math. The last Section of the previous versions was
removed, and will become a separate pape
Stability of Repulsive Bose-Einstein Condensates in a Periodic Potential
The cubic nonlinear Schr\"odinger equation with repulsive nonlinearity and an
elliptic function potential models a quasi-one-dimensional repulsive dilute gas
Bose-Einstein condensate trapped in a standing light wave. New families of
stationary solutions are presented. Some of these solutions have neither an
analog in the linear Schr\"odinger equation nor in the integrable nonlinear
Schr\"odinger equation. Their stability is examined using analytic and
numerical methods. All trivial-phase stable solutions are deformations of the
ground state of the linear Schr\"odinger equation. Our results show that a
large number of condensed atoms is sufficient to form a stable, periodic
condensate. Physically, this implies stability of states near the Thomas-Fermi
limit.Comment: 12 pages, 17 figure
Glueball spectrum based on a rigorous three-dimensional relativistic equation for two-gluon bound states I: Derivation of the relativistic equation
A rigorous three-dimensional relativistic equation satisfied by two-gluon
bound states is derived from the QCD with massive gluons. With the gluon fields
and the quark fields being expanded in terms of the gluon multipole fields and
the spherical Dirac spinors respectively, the equation is well established in
the angular momentum representation and hence is much convenient for solving
the problem of two-gluon glueball spectra. In particular, the interaction
kernel in the equation is exactly derived and given a closed expression which
includes all the interactions taking place in the two-gluon glueballs. The
kernel contains only a few types of Green's functions and commutators.
Therefore, it is not only easily calculated by the perturbation method, but
also provides a suitable basis for nonperturbative investigations
Reduction and Realization in Toda and Volterra
We construct a new symplectic, bi-hamiltonian realization of the KM-system by
reducing the corresponding one for the Toda lattice. The bi-hamiltonian pair is
constructed using a reduction theorem of Fernandes and Vanhaecke. In this paper
we also review the important work of Moser on the Toda and KM-systems.Comment: 17 page
Stability of trapped Bose-Einstein condensates
In three-dimensional trapped Bose-Einstein condensate (BEC), described by the
time-dependent Gross-Pitaevskii-Ginzburg equation, we study the effect of
initial conditions on stability using a Gaussian variational approach and exact
numerical simulations. We also discuss the validity of the criterion for
stability suggested by Vakhitov and Kolokolov. The maximum initial chirp
(initial focusing defocusing of cloud) that can lead a stable condensate to
collapse even before the number of atoms reaches its critical limit is obtained
for several specific cases. When we consider two- and three-body nonlinear
terms, with negative cubic and positive quintic terms, we have the conditions
for the existence of two phases in the condensate. In this case, the magnitude
of the oscillations between the two phases are studied considering sufficient
large initial chirps. The occurrence of collapse in a BEC with repulsive
two-body interaction is also shown to be possible.Comment: 15 pages, 11 figure
Atom capture by nanotube and scaling anomaly
The existence of bound state of the polarizable neutral atom in the inverse
square potential created by the electric field of single walled charged carbon
nanotube (SWNT) is shown to be theoretically possible. The consideration of
inequivalent boundary conditions due to self-adjoint extensions lead to this
nontrivial bound state solution. It is also shown that the scaling anomaly is
responsible for the existence of bound state. Binding of the polarizable atoms
in the coupling constant interval \eta^2\in[0,1) may be responsible for the
smearing of the edge of steps in quantized conductance, which has not been
considered so far in literature.Comment: Accepted in Int.J.Theor.Phy
On non-local variational problems with lack of compactness related to non-linear optics
We give a simple proof of existence of solutions of the dispersion manage-
ment and diffraction management equations for zero average dispersion,
respectively diffraction. These solutions are found as maximizers of non-linear
and non-local vari- ational problems which are invariant under a large
non-compact group. Our proof of existence of maximizer is rather direct and
avoids the use of Lions' concentration compactness argument or Ekeland's
variational principle.Comment: 30 page
Comparison of different stomatal conductance algorithms for ozone flux modelling
A multiplicative and a semi-mechanistic, BWB-type [Ball, J.T., Woodrow, I.E., Berry, J.A., 1987. A model predicting stomatalconductance and its contribution to the control of photosynthesis under different environmental conditions. In: Biggens, J. (Ed.), Progress in Photosynthesis Research, vol. IV. Martinus Nijhoff, Dordrecht, pp. 221–224.] algorithm for calculating stomatalconductance (gs) at the leaf level have been parameterised for two crop and two tree species to test their use in regional scale ozone deposition modelling. The algorithms were tested against measured, site-specific data for durum wheat, grapevine, beech and birch of different European provenances. A direct comparison of both algorithms showed a similar performance in predicting hourly means and daily time-courses of gs, whereas the multiplicative algorithm outperformed the BWB-type algorithm in modelling seasonal time-courses due to the inclusion of a phenology function. The re-parameterisation of the algorithms for local conditions in order to validate ozone deposition modelling on a European scale reveals the higher input requirements of the BWB-type algorithm as compared to the multiplicative algorithm because of the need of the former to model net photosynthesis (An
Measuring Cigarette Smoking Risk Perceptions
Risk perception is an important construct in many health behavior theories. Smoking risk perceptions are thoughts and feelings about the harms associated with cigarette smoking. Wide variation in the terminology, definition, and assessment of this construct makes it difficult to draw conclusions about the associations of risk perceptions with smoking behaviors. To understand optimal methods of assessing adults' cigarette smoking risk perceptions (among both smokers and nonsmokers), we reviewed best practices from the tobacco control literature, and where gaps were identified, we looked more broadly to the research on risk perceptions in other health domains. Based on this review, we suggest assessments of risk perceptions (1) about multiple smoking-related health harms, (2) about harms over a specific timeframe, and (3) for the person affected by the harm. For the measurement of perceived likelihood in particular (ie, the perceived chance of harm from smoking based largely on deliberative thought), we suggest including (4) unconditional and conditional items (stipulating smoking behavior) and (5) absolute and comparative items and including (6) comparisons to specific populations through (7) direct and indirect assessments. We also suggest including (8) experiential (ostensibly automatic, somatic perceptions of vulnerability to a harm) and affective (emotional reactions to a potential harm) risk perception items. We also offer suggestions for (9) response options and (10) the assessment of risk perception at multiple time points. Researchers can use this resource to inform the selection, use, and future development of smoking risk perception measures. Implications: Incorporating the measurement suggestions for cigarette smoking risk perceptions that are presented will help researchers select items most appropriate for their research questions and will contribute to greater consistency in the assessment of smoking risk perceptions among adults
- …