115 research outputs found
An ansatz for the nonlinear Demkov-Kunike problem for cold molecule formation
We study nonlinear mean-field dynamics of ultracold molecule formation in the
case when the external field configuration is defined by the level-crossing
Demkov-Kunike model, characterized by a bell-shaped coupling and finite
variation of the detuning. Analyzing the fast sweep rate regime of the strong
interaction limit, which models a situation when the peak value of the coupling
is large enough and the resonance crossing is sufficiently fast, we construct a
highly accurate ansatz to describe the temporal dynamics of the molecule
formation in the mentioned interaction regime. The absolute error of the
constructed approximation is less than 3*10^-6 for the final transition
probability while at certain time points it might increase up to 10^-3.
Examining the role of the different terms in the constructed approximation, we
prove that in the fast sweep rate regime of the strong interaction limit the
temporal dynamics of the atom-molecule conversion effectively consists of the
process of resonance crossing, which is governed by a nonlinear equation,
followed by atom-molecular coherent oscillations which are basically described
by a solution of the linear problem, associated with the considered nonlinear
one.Comment: Accepted for publication in J. Contemp. Phys. (Armenian National
Academy of Sciences) 8 pages, 4 figure
Gaussian quantum operator representation for bosons
We introduce a Gaussian quantum operator representation, using the most general possible multimode Gaussian operator basis. The representation unifies and substantially extends existing phase-space representations of density matrices for Bose systems and also includes generalized squeezed-state and thermal bases. It enables first-principles dynamical or equilibrium calculations in quantum many-body systems, with quantum uncertainties appearing as dynamical objects. Any quadratic Liouville equation for the density operator results in a purely deterministic time evolution. Any cubic or quartic master equation can be treated using stochastic methods
Dynamics of evaporative cooling in magnetically trapped atomic hydrogen
We study the evaporative cooling of magnetically trapped atomic hydrogen on
the basis of the kinetic theory of a Bose gas. The dynamics of trapped atoms is
described by the coupled differential equations, considering both the
evaporation and dipolar spin relaxation processes. The numerical time-evolution
calculations quantitatively agree with the recent experiment of Bose-Einstein
condensation with atomic hydrogen. It is demonstrated that the balance between
evaporative cooling and heating due to dipolar relaxation limits the number of
condensates to 9x10^8 and the corresponding condensate fraction to a small
value of 4% as observed experimentally.Comment: 5 pages, REVTeX, 3 eps figures, Phys. Rev. A in pres
Spectral method for the time-dependent Gross-Pitaevskii equation with a harmonic trap
We study the numerical resolution of the time-dependent Gross-Pitaevskii
equation, a non-linear Schroedinger equation used to simulate the dynamics of
Bose-Einstein condensates. Considering condensates trapped in harmonic
potentials, we present an efficient algorithm by making use of a spectral
Galerkin method, using a basis set of harmonic oscillator functions, and the
Gauss-Hermite quadrature. We apply this algorithm to the simulation of
condensate breathing and scissors modes.Comment: 23 pages, 5 figure
Asymptotic solutions to the Gross-Pitaevskii gain equation: Growth of a Bose-Einstein condensate
We give an asymptotic analytic solution for the generic atom-laser system with gain in a D-dimensional trap, and show that this has a non-Thomas-Fermi behavior. The effect is due to Bose-enhanced condensate growth, which creates a local-density maximum and a corresponding outward momentum component. In addition, the solution predicts amplified center-of-mass oscillations, leading to enhanced center-of-mass temperature
Quantum Corrections to Dilute Bose Liquids
It was recently shown (A. Bulgac. Phys. Rev. Lett. {\bf 89}, 050402 (2002))
that an entirely new class of quantum liquids with widely tunable properties
could be manufactured from bosons (boselets), fermions (fermilets) and their
mixtures (ferbolets) by controlling their interaction properties by the means
of a Feshbach resonance. We extend the previous mean--field analysis of these
quantum liquids by computing the lowest order quantum corrections to the ground
state energy and the depletion of the Bose--Einstein condensate and by
estimating higher order corrections as well. We show that the quantum
corrections are relatively small and controlled by the diluteness parameter
, even though strictly speaking in this case there is no
low density expansion.Comment: final published version, typos corrected, updated references and
added one referenc
Modulation control and spectral shaping of optical fiber supercontinuum generation in the picosecond regime
Numerical simulations are used to study how fiber supercontinuum generation
seeded by picosecond pulses can be actively controlled through the use of input
pulse modulation. By carrying out multiple simulations in the presence of
noise, we show how tailored supercontinuum Spectra with increased bandwidth and
improved stability can be generated using an input envelope modulation of
appropriate frequency and depth. The results are discussed in terms of the
non-linear propagation dynamics and pump depletion.Comment: Aspects of this work were presented in Paper ThJ2 at OECC/ACOFT 2008,
Sydney Australia 7-10 July (2008). Journal paper submitted for publication 30
July 200
Quadratic-nonlinear Landau-Zener transition for association of an atomic Bose-Einstein condensate with inter-particle elastic interactions included
We study the strong coupling limit of a quadratic-nonlinear Landau-Zener
problem for coherent photo- and magneto-association of cold atoms taking into
account the atom-atom, atom-molecule, and molecule-molecule elastic scattering.
Using an exact third-order nonlinear differential equation for the molecular
state probability, we develop a variational approach which enables us to
construct a highly accurate and simple analytic approximation describing the
time dynamics of the coupled atom-molecule system. We show that the
approximation describing time evolution of the molecular state probability can
be written as a sum of two distinct terms; the first one, being a solution to a
limit first-order nonlinear equation, effectively describes the process of the
molecule formation while the second one, being a scaled solution to the linear
Landau-Zener problem (but now with negative effective Landau-Zener parameter as
long as the strong coupling regime is considered), corresponds to the remaining
oscillations which come up when the process of molecule formation is over.Comment: 19 pages, 7 figures, accepted for publication in Eur. Phys. J.
Multidimensional quantum solitons with nondegenerate parametric interactions: Photonic and Bose-Einstein condensate environments
We consider the quantum theory of three fields interacting via parametric and repulsive quartic couplings. This can be applied to treat photonic chi((2)) and chi((3)) interactions, and interactions in atomic Bose-Einstein condensates or quantum Fermi gases, describing coherent molecule formation together with a-wave scattering. The simplest two-particle quantum solitons or bound-state solutions of the idealized Hamiltonian, without a momentum cutoff, are obtained exactly. They have a pointlike structure in two and three dimensions-even though the corresponding classical theory is nonsingular. We show that the solutions can be regularized with a momentum cutoff. The parametric quantum solitons have much more realistic length scales and binding energies than chi((3)) quantum solitons, and the resulting effects could potentially be experimentally tested in highly nonlinear optical parametric media or interacting matter-wave systems. N-particle quantum solitons and the ground state energy are analyzed using a variational approach. Applications to atomic/molecular Bose-Einstein condensates (BEC's) are given, where we predict the possibility of forming coupled BEC solitons in three space dimensions, and analyze superchemistry dynamics
An Integrated TCGA Pan-Cancer Clinical Data Resource to Drive High-Quality Survival Outcome Analytics
For a decade, The Cancer Genome Atlas (TCGA) program collected clinicopathologic annotation data along with multi-platform molecular profiles of more than 11,000 human tumors across 33 different cancer types. TCGA clinical data contain key features representing the democratized nature of the data collection process. To ensure proper use of this large clinical dataset associated with genomic features, we developed a standardized dataset named the TCGA Pan-Cancer Clinical Data Resource (TCGA-CDR), which includes four major clinical outcome endpoints. In addition to detailing major challenges and statistical limitations encountered during the effort of integrating the acquired clinical data, we present a summary that includes endpoint usage recommendations for each cancer type. These TCGA-CDR findings appear to be consistent with cancer genomics studies independent of the TCGA effort and provide opportunities for investigating cancer biology using clinical correlates at an unprecedented scale. Analysis of clinicopathologic annotations for over 11,000 cancer patients in the TCGA program leads to the generation of TCGA Clinical Data Resource, which provides recommendations of clinical outcome endpoint usage for 33 cancer types
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