603 research outputs found
Resonance solutions of the nonlinear Schr\"odinger equation in an open double-well potential
The resonance states and the decay dynamics of the nonlinear Schr\"odinger
(or Gross-Pitaevskii) equation are studied for a simple, however flexible model
system, the double delta-shell potential. This model allows analytical
solutions and provides insight into the influence of the nonlinearity on the
decay dynamics. The bifurcation scenario of the resonance states is discussed,
as well as their dynamical stability properties. A discrete approximation using
a biorthogonal basis is suggested which allows an accurate description even for
only two basis states in terms of a nonlinear, nonhermitian matrix problem.Comment: 21 pages, 14 figure
Bloch oscillations of Bose-Einstein condensates: Quantum counterpart of dynamical instability
We study the Bloch dynamics of a quasi one-dimensional Bose-Einstein
condensate of cold atoms in a tilted optical lattice modeled by a Hamiltonian
of Bose-Hubbard type: The corresponding mean-field system described by a
discrete nonlinear Schr\"odinger equation can show a dynamical (or modulation)
instability due to chaotic dynamics and equipartition over the quasimomentum
modes. It is shown, that these phenomena are related to a depletion of the
Floquet-Bogoliubov states and a decoherence of the condensate in the
many-particle description. Three different types of dynamics are distinguished:
(i) decaying oscillations in the region of dynamical instability, and (ii)
persisting Bloch oscillations or (iii) periodic decay and revivals in the
region of stability.Comment: 12 pages, 14 figure
Bose-Einstein condensates on tilted lattices: coherent, chaotic and subdiffusive dynamics
The dynamics of a (quasi)one-dimensional interacting atomic Bose-Einstein
condensate in a tilted optical lattice is studied in a discrete mean-field
approximation, i.e., in terms of the discrete nonlinear Schr\"odinger equation.
If the static field is varied the system shows a plethora of dynamical
phenomena. In the strong field limit we demonstrate the existence of (almost)
non-spreading states which remain localized on the lattice region populated
initially and show coherent Bloch oscillations with fractional revivals in the
momentum space (so called quantum carpets). With decreasing field, the dynamics
becomes irregular, however, still confined in configuration space. For even
weaker fields we find sub-diffusive dynamics with a wave-packet width spreading
as .Comment: 4 pages, 5 figure
Quantum mechanics on a circle: Husimi phase space distributions and semiclassical coherent state propagators
We discuss some basic tools for an analysis of one-dimensionalquantum systems
defined on a cyclic coordinate space. The basic features of the generalized
coherent states, the complexifier coherent states are reviewed. These states
are then used to define the corresponding (quasi)densities in phase space. The
properties of these generalized Husimi distributions are discussed, in
particular their zeros.Furthermore, the use of the complexifier coherent states
for a semiclassical analysis is demonstrated by deriving a semiclassical
coherent state propagator in phase space.Comment: 29 page
Chaotic Evolution in Quantum Mechanics
A quantum system is described, whose wave function has a complexity which
increases exponentially with time. Namely, for any fixed orthonormal basis, the
number of components required for an accurate representation of the wave
function increases exponentially.Comment: 8 pages (LaTeX 16 kB, followed by PostScript 2 kB for figure
Instabilities, nonhermiticity and exceptional points in the cranking model
A cranking harmonic oscillator model, widely used for the physics of fast
rotating nuclei and Bose-Einstein condensates, is re-investigated in the
context of PT-symmetry. The instability points of the model are identified as
exceptional points. It is argued that - even though the Hamiltonian appears
hermitian at first glance - it actually is not hermitian within the region of
instability.Comment: 4 pages, 1 figur
Evolution of Liouville density of a chaotic system
An area-preserving map of the unit sphere, consisting of alternating twists
and turns, is mostly chaotic. A Liouville density on that sphere is specified
by means of its expansion into spherical harmonics. That expansion initially
necessitates only a finite number of basis functions. As the dynamical mapping
proceeds, it is found that the number of non-negligible coefficients increases
exponentially with the number of steps. This is to be contrasted with the
behavior of a Schr\"odinger wave function which requires, for the analogous
quantum system, a basis of fixed size.Comment: LaTeX 4 pages (27 kB) followed by four short PostScript files (2 kB +
2 kB + 1 kB + 4 kB
Signature of Chaotic Diffusion in Band Spectra
We investigate the two-point correlations in the band spectra of spatially
periodic systems that exhibit chaotic diffusion in the classical limit. By
including level pairs pertaining to non-identical quasimomenta, we define form
factors with the winding number as a spatial argument. For times smaller than
the Heisenberg time, they are related to the full space-time dependence of the
classical diffusion propagator. They approach constant asymptotes via a regime,
reflecting quantal ballistic motion, where they decay by a factor proportional
to the number of unit cells. We derive a universal scaling function for the
long-time behaviour. Our results are substantiated by a numerical study of the
kicked rotor on a torus and a quasi-one-dimensional billiard chain.Comment: 8 pages, REVTeX, 5 figures (eps
The Strange Quark Contribution to the Proton's Magnetic Moment
We report a new determination of the strange quark contribution to the
proton's magnetic form factor at a four-momentum transfer Q2 = 0.1 (GeV/c)^2
from parity-violating e-p elastic scattering. The result uses a revised
analysis of data from the SAMPLE experiment which was carried out at the
MIT-Bates Laboratory. The data are combined with a calculation of the proton's
axial form factor GAe to determine the strange form factor GMs(Q2=0.1)=0.37 +-
0.20 +- 0.26 +- 0.07. The extrapolation of GMs to its Q2=0 limit and comparison
with calculations is also discussed.Comment: 6 pages, 1 figure, submitted to Phys. Lett.
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