19,236 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
The semileptonic decays of the B_c meson
We study the semileptonic transitions B_c to \eta_c, J/\psi, D, D^*, B, B^*,
B_s, B_s^* in the framework of a relativistic constituent quark model. We use
experimental data on leptonic J/\psi decay, lattice and QCD sum rule results on
leptonic B_c decay, and on radiative \eta_c transitions to adjust the quark
model parameters. We compute all form factors of the above semileptonic
B_c-transitions and give predictions for various semileptonic B_c decay modes
including their \tau-modes when they are kinematically accessible. The
implications of heavy quark symmetry for the semileptonic decays are discussed
and are shown to be manifest in our explicit relativistic quark model
calculation. A comparison of our results with the results of other calculations
is performed.Comment: 31 pages Latex (uses epsf, revtex). Section II expanded, typos
corrected. This version will appear in Phys. Rev.
Simulation of Jahn-Teller-Dicke Magnetic Structural Phase Transition with Trapped Ions
We study theoretically the collective Ee Jahn-Teller-Dicke
distortion in a system of trapped ions. We focus in the limit of infinite range
interactions in which an ensemble of effective spins interacts with two
collective vibrational modes with U(1) symmetric couplings. Our model is
exactly solvable in the thermodynamical limit and it is amenable to be solved
by exact numerical diagonalization for a moderate number of ions. We show that
trapped ions are ideally suited to study the emergence of spontaneous symmetry
breaking of a continuous symmetry and magnetic structural phase transition in a
mesoscopic system.Comment: 19 pages, 7 figure
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