17,026 research outputs found
Generating ring currents, solitons, and svortices by stirring a Bose-Einstein condensate in a toroidal trap
We propose a simple stirring experiment to generate quantized ring currents
and solitary excitations in Bose-Einstein condensates in a toroidal trap
geometry. Simulations of the 3D Gross-Pitaevskii equation show that pure ring
current states can be generated efficiently by adiabatic manipulation of the
condensate, which can be realized on experimental time scales. This is
illustrated by simulated generation of a ring current with winding number two.
While solitons can be generated in quasi-1D tori, we show the even more robust
generation of hybrid, solitonic vortices (svortices) in a regime of wider
confinement. Svortices are vortices confined to essentially one-dimensional
dynamics, which obey a similar phase-offset--velocity relationship as solitons.
Marking the transition between solitons and vortices, svortices are a distinct
class of symmetry-breaking stationary and uniformly rotating excited solutions
of the 2D and 3D Gross-Pitaevskii equation in a toroidal trapping potential.
Svortices should be observable in dilute-gas experiments.Comment: 8 pages, 4 figures; accepted for publication in J. Phys. B (Letters
Option pricing in affine generalized Merton models
In this article we consider affine generalizations of the Merton jump
diffusion model [Merton, J. Fin. Econ., 1976] and the respective pricing of
European options. On the one hand, the Brownian motion part in the Merton model
may be generalized to a log-Heston model, and on the other hand, the jump part
may be generalized to an affine process with possibly state dependent jumps.
While the characteristic function of the log-Heston component is known in
closed form, the characteristic function of the second component may be unknown
explicitly. For the latter component we propose an approximation procedure
based on the method introduced in [Belomestny et al., J. Func. Anal., 2009]. We
conclude with some numerical examples
Shear induced breaking of large internal solitary waves
The stability properties of 24 experimentally generated internal solitary waves (ISWs) of extremely large amplitude, all with minimum Richardson number less than 1/4, are investigated. The study is supplemented by fully nonlinear calculations in a three-layer fluid. The waves move along a linearly stratified pycnocline (depth h2) sandwiched between a thin upper layer (depth h1) and a deep lower layer (depth h3), both homogeneous. In particular, the wave-induced velocity profile through the pycnocline is measured by particle image velocimetry (PIV) and obtained in computation. Breaking ISWs were found to have amplitudes (a1) in the range a1>2.24 āh1h2(1+h2/h1), while stable waves were on or below this limit. Breaking ISWs were investigated for 0.27 0.86 and stable waves for Lx/Ī» < 0.86. The results show a sort of threshold-like behaviour in terms of Lx/Ī». The results demonstrate that the breaking threshold of Lx/Ī» = 0.86 was sharper than one based on a minimum Richardson number and reveal that the Richardson number was found to become almost antisymmetric across relatively thick pycnoclines, with the minimum occurring towards the top part of the pycnoclinePostprintPeer reviewe
Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion
On a multi-assets Black-Scholes economy, we introduce a class of barrier
options. In this model we apply a generalized reflection principle in a context
of the finite reflection group acting on a Euclidean space to give a valuation
formula and the semi-static hedge.Comment: Asia-Pacific Financial Markets, online firs
Localized Asymmetric Atomic Matter Waves in Two-Component Bose-Einstein Condensates Coupled with Two Photon Microwave Field
We investigate localized atomic matter waves in two-component Bose-Einstein
condensates coupled by the two photon microwave field. Interestingly, the
oscillations of localized atomic matter waves will gradually decay and finally
become non-oscillating behavior even if existing coupling field. In particular,
atom numbers occupied in two different hyperfine spin states will appear
asymmetric occupations after some time evolution.Comment: 4 pages, 4 figure
Tunable tunneling: An application of stationary states of Bose-Einstein condensates in traps of finite depth
The fundamental question of how Bose-Einstein condensates tunnel into a
barrier is addressed. The cubic nonlinear Schrodinger equation with a finite
square well potential, which models a Bose-Einstein condensate in a
quasi-one-dimensional trap of finite depth, is solved for the complete set of
localized and partially localized stationary states, which the former evolve
into when the nonlinearity is increased. An immediate application of these
different solution types is tunable tunneling. Magnetically tunable Feshbach
resonances can change the scattering length of certain Bose-condensed atoms,
such as Rb, by several orders of magnitude, including the sign, and
thereby also change the mean field nonlinearity term of the equation and the
tunneling of the wavefunction. We find both linear-type localized solutions and
uniquely nonlinear partially localized solutions where the tails of the
wavefunction become nonzero at infinity when the nonlinearity increases. The
tunneling of the wavefunction into the non-classical regime and thus its
localization therefore becomes an external experimentally controllable
parameter.Comment: 11 pages, 5 figure
Bose-Einstein condensates in standing waves: The cubic nonlinear Schroedinger equation with a periodic potential
We present a new family of stationary solutions to the cubic nonlinear
Schroedinger equation with a Jacobian elliptic function potential. In the limit
of a sinusoidal potential our solutions model a dilute gas Bose-Einstein
condensate trapped in a standing light wave. Provided the ratio of the height
of the variations of the condensate to its DC offset is small enough, both
trivial phase and nontrivial phase solutions are shown to be stable. Numerical
simulations suggest such stationary states are experimentally observable.Comment: 4 pages, 4 figure
Spontaneous soliton formation and modulational instability in Bose-Einstein condensates
The dynamics of an elongated attractive Bose-Einstein condensate in an
axisymmetric harmonic trap is studied. It is shown that density fringes caused
by self-interference of the condensate order parameter seed modulational
instability. The latter has novel features in contradistinction to the usual
homogeneous case known from nonlinear fiber optics. Several open questions in
the interpretation of the recent creation of the first matter-wave bright
soliton train [Strecker {\it et al.} Nature {\bf 417} 150 (2002)] are
addressed. It is shown that primary transverse collapse, followed by secondary
collapse induced by soliton--soliton interactions, produce bursts of hot atoms
at different time scales.Comment: 4 pages, 3 figures. Phys. Rev. Lett. in pres
- ā¦