1,034 research outputs found
Interface Problems for Dispersive equations
The interface problem for the linear Schr\"odinger equation in
one-dimensional piecewise homogeneous domains is examined by providing an
explicit solution in each domain. The location of the interfaces is known and
the continuity of the wave function and a jump in their derivative at the
interface are the only conditions imposed. The problem of two semi-infinite
domains and that of two finite-sized domains are examined in detail. The
problem and the method considered here extend that of an earlier paper by
Deconinck, Pelloni and Sheils (2014). The dispersive nature of the problem
presents additional difficulties that are addressed here.Comment: 18 pages, 6 figures. arXiv admin note: text overlap with
arXiv:1402.3007, Studies in Applied Mathematics 201
Instabilities of one-dimensional stationary solutions of the cubic nonlinear Schrodinger equation
The two-dimensional cubic nonlinear Schrodinger equation admits a large
family of one-dimensional bounded traveling-wave solutions. All such solutions
may be written in terms of an amplitude and a phase. Solutions with piecewise
constant phase have been well studied previously. Some of these solutions were
found to be stable with respect to one-dimensional perturbations. No such
solutions are stable with respect to two-dimensional perturbations. Here we
consider stability of the larger class of solutions whose phase is dependent on
the spatial dimension of the one-dimensional wave form. We study the spectral
stability of such nontrivial-phase solutions numerically, using Hill's method.
We present evidence which suggests that all such nontrivial-phase solutions are
unstable with respect to both one- and two-dimensional perturbations.
Instability occurs in all cases: for both the elliptic and hyperbolic nonlinear
Schrodinger equations, and in the focusing and defocusing case.Comment: Submitted: 13 pages, 3 figure
Linearly Coupled Bose-Einstein Condensates: From Rabi Oscillations and Quasi-Periodic Solutions to Oscillating Domain Walls and Spiral Waves
In this paper, an exact unitary transformation is examined that allows for
the construction of solutions of coupled nonlinear Schr{\"o}dinger equations
with additional linear field coupling, from solutions of the problem where this
linear coupling is absent. The most general case where the transformation is
applicable is identified. We then focus on the most important special case,
namely the well-known Manakov system, which is known to be relevant for
applications in Bose-Einstein condensates consisting of different hyperfine
states of Rb. In essence, the transformation constitutes a distributed,
nonlinear as well as multi-component generalization of the Rabi oscillations
between two-level atomic systems. It is used here to derive a host of periodic
and quasi-periodic solutions including temporally oscillating domain walls and
spiral waves.Comment: 6 pages, 4 figures, Phys. Rev. A (in press
Qubit State Discrimination
We show how one can solve the problem of discriminating between qubit states.
We use the quantum state discrimination duality theorem and the Bloch sphere
representation of qubits which allows for an easy geometric and analytical
representation of the optimal guessing strategies.Comment: 6 pages, 4 figures. v2 has small corrections and changes in
reference
Pole dynamics for the Flierl-Petviashvili equation and zonal flow
We use a systematic method which allows us to identify a class of exact
solutions of the Flierl-Petvishvili equation. The solutions are periodic and
have one dimensional geometry. We examine the physical properties and find that
these structures can have a significant effect on the zonal flow generation.Comment: Latex 40 pages, seven figures eps included. Effect of variation of
g_3 is studied. New references adde
On the numerical evaluation of algebro-geometric solutions to integrable equations
Physically meaningful periodic solutions to certain integrable partial
differential equations are given in terms of multi-dimensional theta functions
associated to real Riemann surfaces. Typical analytical problems in the
numerical evaluation of these solutions are studied. In the case of
hyperelliptic surfaces efficient algorithms exist even for almost degenerate
surfaces. This allows the numerical study of solitonic limits. For general real
Riemann surfaces, the choice of a homology basis adapted to the
anti-holomorphic involution is important for a convenient formulation of the
solutions and smoothness conditions. Since existing algorithms for algebraic
curves produce a homology basis not related to automorphisms of the curve, we
study symplectic transformations to an adapted basis and give explicit formulae
for M-curves. As examples we discuss solutions of the Davey-Stewartson and the
multi-component nonlinear Schr\"odinger equations.Comment: 29 pages, 20 figure
Measurement of the Neutron Radius of Pb-208 through Parity Violation in Electron Scattering
We report the first measurement of the parity-violating asymmetry A(PV) in the elastic scattering of polarized electrons from Pb-208. APV is sensitive to the radius of the neutron distribution (R-n). The result A(PV) = 0.656 +/- 0.060(stat) +/- 0.014(syst) ppm corresponds to a difference between the radii of the neutron and proton distributions R-n - R-p = 0.33(-0.18)(+0.16) fm and provides the first electroweak observation of the neutron skin which is expected in a heavy, neutron-rich nucleus
Vortices in Bose-Einstein Condensates: Some Recent Developments
In this brief review we summarize a number of recent developments in the
study of vortices in Bose-Einstein condensates, a topic of considerable
theoretical and experimental interest in the past few years. We examine the
generation of vortices by means of phase imprinting, as well as via dynamical
instabilities. Their stability is subsequently examined in the presence of
purely magnetic trapping, and in the combined presence of magnetic and optical
trapping. We then study pairs of vortices and their interactions, illustrating
a reduced description in terms of ordinary differential equations for the
vortex centers. In the realm of two vortices we also consider the existence of
stable dipole clusters for two-component condensates. Last but not least, we
discuss mesoscopic patterns formed by vortices, the so-called vortex lattices
and analyze some of their intriguing dynamical features. A number of
interesting future directions are highlighted.Comment: 24 pages, 8 figs, ws-mplb.cls, to appear in Modern Physics Letters B
(2005
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