19,390 research outputs found
Boussinesq-type equations from nonlinear realizations of
We construct new coset realizations of infinite-dimensional linear
symmetry associated with Zamolodchikov's algebra which are
different from the previously explored Toda realization of
. We deduce the Boussinesq and modified Boussinesq equations as
constraints on the geometry of the corresponding coset manifolds.The main
characteristic features of these realizations are:i. Among the coset parameters
there are the space and time coordinates and which enter the Boussinesq
equations, all other coset parameters are regarded as fields depending on these
coordinates;ii. The spin 2 and 3 currents of and two spin 1 Kac-
Moody currents as well as two spin 0 fields related to the currents via
Miura maps, come out as the only essential parameters-fields of these cosets.
The remaining coset fields are covariantly expressed through them;iii.The Miura
maps get a new geometric interpretation as covariant constraints
which relate the above fields while passing from one coset manifold to another;
iv. The Boussinesq equation and two kinds of the modified Boussinesq equations
appear geometrically as the dynamical constraints accomplishing
covariant reductions of original coset manifolds to their two-dimensional
geodesic submanifolds;v. The zero-curvature representations for these equations
arise automatically as a consequence of the covariant reduction. The approach
proposed could provide a universal geometric description of the relationship
between -type algebras and integrable hierarchies.Comment: 23 pages, LaTe
N=2 Super - Algebra and N=2 Super Boussinesq Equations
We study classical super- algebra and its interplay with
supersymmetric extensions of the Boussinesq equation in the framework of the
nonlinear realization method and the inverse Higgs - covariant reduction
approach. These techniques have been previously applied by us in the bosonic
case to give a new geometric interpretation of the Boussinesq hierarchy.
Here we deduce the most general super Boussinesq equation and two kinds
of the modified super Boussinesq equations, as well as the super Miura
maps relating these systems to each other, by applying the covariant reduction
to certain coset manifolds of linear super- symmetry
associated with super-. We discuss the integrability properties of
the equations obtained and their correspondence with the formulation based on
the notion of the second hamiltonian structure.Comment: LaTeX, 30
Scalable quantum search using trapped ions
We propose a scalable implementation of Grover's quantum search algorithm in
a trapped-ion quantum information processor. The system is initialized in an
entangled Dicke state by using simple adiabatic techniques. The
inversion-about-average and the oracle operators take the form of single
off-resonant laser pulses, addressing, respectively, all and half of the ions
in the trap. This is made possible by utilizing the physical symmetrie of the
trapped-ion linear crystal. The physical realization of the algorithm
represents a dramatic simplification: each logical iteration (oracle and
inversion about average) requires only two physical interaction steps, in
contrast to the large number of concatenated gates required by previous
approaches. This does not only facilitate the implementation, but also
increases the overall fidelity of the algorithm.Comment: 6 pages, 2 figure
Two-photon double ionization of helium in the region of photon energies 42-50 eV
We report the total integrated cross-section (TICS) of two-photon double
ionization of helium in the photon energy range from 42 to 50 eV. Our
computational procedure relies on a numerical solution of the time-dependent
Schr\"odinger equation on a square-integrable basis and subsequent projection
of this solution on a set of final states describing two electrons in
continuum. Close to the threshold, we reproduce results previously known from
the literature. The region 47-50 eV seems to have been previously unexplored.
Our results suggest that TICS, as a function of the photon energy, grows
monotonously in the region 42-50 eV. We also present fully resolved triple
differential cross sections for selected photon energies.Comment: 12 pages, 3 figure
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