20,756 research outputs found
Anharmonicity Induced Resonances for Ultracold Atoms and their Detection
When two atoms interact in the presence of an anharmonic potential, such as
an optical lattice, the center of mass motion cannot be separated from the
relative motion. In addition to generating a confinement-induced resonance (or
shifting the position of an existing Feshbach resonance), the external
potential changes the resonance picture qualitatively by introducing new
resonances where molecular excited center of mass states cross the scattering
threshold. We demonstrate the existence of these resonances, give their
quantitative characterization in an optical superlattice, and propose an
experimental scheme to detect them through controlled sweeping of the magnetic
field.Comment: 6 pages, 5 figures; expanded presentatio
Disclination in Lorentz Space-Time
The disclination in Lorentz space-time is studied in detail by means of
topological properties of -mapping. It is found the space-time
disclination can be described in term of a Dirac spinor. The size of the
disclination, which is proved to be the difference of two sets of su(2)% -like
monopoles expressed by two mixed spinors, is quantized topologically in terms
of topological invariantswinding number. The projection of space-time
disclination density along an antisymmetric tensor field is characterized by
Brouwer degree and Hopf index.Comment: Revtex, 7 page
Comment on "Quantum Phase Slips and Transport in Ultrathin Superconducting Wires"
In a recent Letter (Phys. Rev. Lett.78, 1552 (1997) ), Zaikin, Golubev, van
Otterlo, and Zimanyi criticized the phenomenological time-dependent
Ginzburg-Laudau model which I used to study the quantum phase-slippage rate for
superconducting wires. They claimed that they developed a "microscopic" model,
made qualitative improvement on my overestimate of the tunnelling barrier due
to electromagnetic field. In this comment, I want to point out that, i), ZGVZ's
result on EM barrier is expected in my paper; ii), their work is also
phenomenological; iii), their renormalization scheme is fundamentally flawed;
iv), they underestimated the barrier for ultrathin wires; v), their comparison
with experiments is incorrect.Comment: Substantial changes made. Zaikin et al's main result was expected
from my work. They underestimated tunneling barrier for ultrathin wires by
one order of magnitude in the exponen
The Topological Structure of the Space-Time Disclination
The space-time disclination is studied by making use of the decomposition
theory of gauge potential in terms of antisymmetric tensor field and
-mapping method. It is shown that the self-dual and anti-self-dual parts
of the curvature compose the space-time disclinations which are classified in
terms of topological invariants--winding number. The projection of space-time
disclination density along an antisymmetric tensor field is quantized
topologically and characterized by Brouwer degree and Hopf index.Comment: 18 pages, Revte
Effective Hamiltonian for fermions in an optical lattice across Feshbach resonance
We derive the Hamiltonian for cold fermionic atoms in an optical lattice
across a broad Feshbach resonance, taking into account of both multiband
occupations and neighboring-site collisions. Under typical configurations, the
resulting Hamiltonian can be dramatically simplified to an effective
single-band model, which describes a new type of resonance between the local
dressed molecules and the valence bond states of fermionic atoms at neighboring
sites. On different sides of such a resonance, the effective Hamiltonian is
reduced to either a t-J model for the fermionic atoms or an XXZ model for the
dressed molecules. The parameters in these models are experimentally tunable in
the full range, which allows for observation of various phase transitions.Comment: 5 pages, 2 figure
Effective low-dimensional Hamiltonian for strongly interacting atoms in a transverse trap
We derive an effective low-dimensional Hamiltonian for strongly interacting
ultracold atoms in a transverse trapping potential near a wide Feshbach
resonance. The Hamiltonian includes crucial information about transverse
excitations in an effective model with renormalized interaction between atoms
and composite dressed molecules. We fix all the parameters in the Hamiltonian
for both one- and two-dimensional cases.Comment: v2: 5 pages, 1 figure; expanded presentation of the formalis
Fokker-Planck equations for nonlinear dynamical systems driven by non-Gaussian Levy processes
The Fokker-Planck equations describe time evolution of probability densities
of stochastic dynamical systems and are thus widely used to quantify random
phenomena such as uncertainty propagation. For dynamical systems driven by
non-Gaussian L\'evy processes, however, it is difficult to obtain explicit
forms of Fokker-Planck equations because the adjoint operators of the
associated infinitesimal generators usually do not have exact formulation. In
the present paper, Fokker- Planck equations are derived in terms of infinite
series for nonlinear stochastic differential equations with non-Gaussian L\'evy
processes. A few examples are presented to illustrate the method.Comment: 14 page
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