2,502 research outputs found
Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach
We discuss interacting and non-interacting one dimensional atomic systems
trapped in an optical lattice plus a parabolic potential. We show that, in the
tight-binding approximation, the non-interacting problem is exactly solvable in
terms of Mathieu functions. We use the analytic solutions to study the
collective oscillations of ideal bosonic and fermionic ensembles induced by
small displacements of the parabolic potential. We treat the interacting boson
problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From
analysis of the dependence upon lattice depth of the low-energy excitation
spectrum of the interacting system, we consider the problems of
"fermionization" of a Bose gas, and the superfluid-Mott insulator transition.
The spectrum of the noninteracting system turns out to provide a useful guide
to understanding the collective oscillations of the interacting system,
throughout a large and experimentally relevant parameter regime.Comment: 19 pages, 15 figures Minor modification were done and new references
were adde
A note on the moduli-induced gravitino problem
The cosmological moduli problem has been recently reconsidered. Papers [1,2]
show that even heavy moduli (m_\phi > 10^5 GeV) can be a problem for cosmology
if a branching ratio of the modulus into gravitini is large. In this paper, we
discuss the tachyonic decay of moduli into the Standard Model's degrees of
freedom, e.g. Higgs particles, as a resolution to the moduli-induced gravitino
problem. Rough estimates on model dependent parameters set a lower bound on the
allowed moduli at around 10^8 ~ 10^9 GeV.Comment: 6 pages, references added, identical to the published versio
Hooke's law correlation in two-electron systems
We study the properties of the Hooke's law correlation energy (\Ec),
defined as the correlation energy when two electrons interact {\em via} a
harmonic potential in a -dimensional space. More precisely, we investigate
the ground state properties of two model systems: the Moshinsky atom (in
which the electrons move in a quadratic potential) and the spherium model (in
which they move on the surface of a sphere). A comparison with their Coulombic
counterparts is made, which highlights the main differences of the \Ec in
both the weakly and strongly correlated limits. Moreover, we show that the
Schr\"odinger equation of the spherium model is exactly solvable for two values
of the dimension (), and that the exact wave function is
based on Mathieu functions.Comment: 7 pages, 5 figure
Quantum corrections from a path integral over reparametrizations
We study the path integral over reparametrizations that has been proposed as
an ansatz for the Wilson loops in the large- QCD and reproduces the area law
in the classical limit of large loops. We show that a semiclassical expansion
for a rectangular loop captures the L\"uscher term associated with
dimensions and propose a modification of the ansatz which reproduces the
L\"uscher term in other dimensions, which is observed in lattice QCD. We repeat
the calculation for an outstretched ellipse advocating the emergence of an
analog of the L\"uscher term and verify this result by a direct computation of
the determinant of the Laplace operator and the conformal anomaly
Preheating after N-flation
We study preheating in N-flation, assuming the Mar\v{c}enko-Pastur mass
distribution, equal energy initial conditions at the beginning of inflation and
equal axion-matter couplings, where matter is taken to be a single, massless
bosonic field. By numerical analysis we find that preheating via parametric
resonance is suppressed, indicating that the old theory of perturbative
preheating is applicable. While the tensor-to-scalar ratio, the non-Gaussianity
parameters and the scalar spectral index computed for N-flation are similar to
those in single field inflation (at least within an observationally viable
parameter region), our results suggest that the physics of preheating can
differ significantly from the single field case.Comment: 14 pages, 14 figures, references added, fixed typo
Faraday waves in binary non-miscible Bose-Einstein condensates
We show by extensive numerical simulations and analytical variational
calculations that elongated binary non-miscible Bose-Einstein condensates
subject to periodic modulations of the radial confinement exhibit a Faraday
instability similar to that seen in one-component condensates. Considering the
hyperfine states of Rb condensates, we show that there are two
experimentally relevant stationary state configurations: the one in which the
components form a dark-bright symbiotic pair (the ground state of the system),
and the one in which the components are segregated (first excited state). For
each of these two configurations, we show numerically that far from resonances
the Faraday waves excited in the two components are of similar periods, emerge
simultaneously, and do not impact the dynamics of the bulk of the condensate.
We derive analytically the period of the Faraday waves using a variational
treatment of the coupled Gross-Pitaevskii equations combined with a
Mathieu-type analysis for the selection mechanism of the excited waves.
Finally, we show that for a modulation frequency close to twice that of the
radial trapping, the emergent surface waves fade out in favor of a forceful
collective mode that turns the two condensate components miscible.Comment: 13 pages, 10 figure
Excitation of a Kaluza-Klein mode by parametric resonance
In this paper we investigate a parametric resonance phenomenon of a
Kaluza-Klein mode in a -dimensional generalized Kaluza-Klein theory. As the
origin of the parametric resonance we consider a small oscillation of a scale
of the compactification around a today's value of it. To make our arguments
definite and for simplicity we consider two classes of models of the
compactification: those by () and those by (, ). For these models we show that
parametric resonance can occur for the Kaluza-Klein mode. After that, we give
formulas of a creation rate and a number of created quanta of the Kaluza-Klein
mode due to the parametric resonance, taking into account the first and the
second resonance band. By using the formulas we calculate those quantities for
each model of the compactification. Finally we give conditions for the
parametric resonance to be efficient and discuss cosmological implications.Comment: 36 pages, Latex file, Accepted for publication in Physical Review
Fractional-Period Excitations in Continuum Periodic Systems
We investigate the generation of fractional-period states in continuum
periodic systems. As an example, we consider a Bose-Einstein condensate
confined in an optical-lattice potential. We show that when the potential is
turned on non-adiabatically, the system explores a number of transient states
whose periodicity is a fraction of that of the lattice. We illustrate the
origin of fractional-period states analytically by treating them as resonant
states of a parametrically forced Duffing oscillator and discuss their
transient nature and potential observability.Comment: 10 pages, 6 figures (some with multiple parts); revised version:
minor clarifications of a couple points, to appear in Physical Review
Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements
The behavior of orbits in charged-particle beam transport systems, including
both linear and circular accelerators as well as final focus sections and
spectrometers, can depend sensitively on nonlinear fringe-field and
high-order-multipole effects in the various beam-line elements. The inclusion
of these effects requires a detailed and realistic model of the interior and
fringe fields, including their high spatial derivatives. A collection of
surface fitting methods has been developed for extracting this information
accurately from 3-dimensional field data on a grid, as provided by various
3-dimensional finite-element field codes. Based on these realistic field
models, Lie or other methods may be used to compute accurate design orbits and
accurate transfer maps about these orbits. Part I of this work presents a
treatment of straight-axis magnetic elements, while Part II will treat bending
dipoles with large sagitta. An exactly-soluble but numerically challenging
model field is used to provide a rigorous collection of performance benchmarks.Comment: Accepted to PRST-AB. Changes: minor figure modifications, reference
added, typos corrected
- …