25,323 research outputs found
Hamiltonian approach to slip-stacking dynamics
Hamiltonian dynamics has been applied to study the slip-stacking dynamics.
The canonical-perturbation method is employed to obtain the second-harmonic
correction term in the slip-stacking Hamiltonian. The Hamiltonian approach
provides a clear optimal method for choosing the slip-stacking parameter and
improving stacking efficiency. The dynamics are applied specifically to the
Fermilab Booster-Recycler complex. The dynamics can also be applied to other
accelerator complexes.Comment: 10 p
Geometric Numerical Integration Applied to The Elastic Pendulum at Higher Order Resonance
In this paper we study the performance of a symplectic numerical integrator
based on the splitting method. This method is applied to a subtle problem i.e.
higher order resonance of the elastic pendulum. In order to numerically study
the phase space of the elastic pendulum at higher order resonance, a numerical
integrator which preserves qualitative features after long integration times is
needed. We show by means of an example that our symplectic method offers a
relatively cheap and accurate numerical integrator.Comment: 15 pages, 6 figure
Lattice Induced Resonances in One Dimensional Bosonic Systems
We study the resonant effects produced when a Feshbach dimer crosses a
scattering continuum band of atoms in an optical lattice. We numerically obtain
the exact spectrum of two particles in a one-dimensional lattice and develop an
effective atom-dimer Hamiltonian that accurately captures resonant effects. The
lattice-induced resonances lead to the formation of bound states simultaneously
above and below the scattering continuum and significantly modify the curvature
of the dimer dispersion relation. The nature of the atom-dimer coupling depends
strongly on the parity of the dimer state leading to a novel coupling in the
case of negative parity dimers. From the exact solutions we extract the dimer
Wannier function from which we quantitatively determine the effective
Hamiltonian parameters for a many-body description.Comment: 4 pages, 3 figures, published versio
Response of Bose gases in time-dependent optical superlattices
The dynamic response of ultracold Bose gases in one-dimensional optical
lattices and superlattices is investigated based on exact numerical time
evolutions in the framework of the Bose-Hubbard model. The system is excited by
a temporal amplitude modulation of the lattice potential, as it was done in
recent experiments. For regular lattice potentials, the dynamic signatures of
the superfluid to Mott-insulator transition are studied and the position and
the fine-structure of the resonances is explained by a linear response
analysis. Using direct simulations and the perturbative analysis it is shown
that in the presence of a two-colour superlattice the excitation spectrum
changes significantly when going from the homogeneous Mott-insulator the quasi
Bose-glass phase. A characteristic and experimentally accessible signature for
the quasi Bose-glass is the appearance of low-lying resonances and a
suppression of the dominant resonance of the Mott-insulator phase.Comment: 20 pages, 9 figures; added references and corrected typo
Excitation of interfacial waves via near---resonant surface---interfacial wave interactions
We consider interactions between surface and interfacial waves in the two
layer system. Our approach is based on the Hamiltonian structure of the
equations of motion, and includes the general procedure for diagonalization of
the quadratic part of the Hamiltonian. Such diagonalization allows us to derive
the interaction crossection between surface and interfacial waves and to derive
the coupled kinetic equations describing spectral energy transfers in this
system. Our kinetic equation allows resonant and near resonant interactions. We
find that the energy transfers are dominated by the class III resonances of
\cite{Alam}. We apply our formalism to calculate the rate of growth for
interfacial waves for different values of the wind velocity. Using our kinetic
equation, we also consider the energy transfer from the wind generated surface
waves to interfacial waves for the case when the spectrum of the surface waves
is given by the JONSWAP spectrum and interfacial waves are initially absent. We
find that such energy transfer can occur along a timescale of hours; there is a
range of wind speeds for the most effective energy transfer at approximately
the wind speed corresponding to white capping of the sea. Furthermore,
interfacial waves oblique to the direction of the wind are also generated
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