22,624 research outputs found
Conditions for entanglement transformation between a class of multipartite pure states with generalized Schmidt decompositions
In this note we generalize Nielsen's marjoization criterion for the
convertibility of bipartite pure states [Phys. Rev. Lett \textbf{83},
436(1999)] to a special class of multipartite pure states which have
generalized Schmidt decompositions.Comment: 3 pages (Revetex 4), no figures. A brief note on entanglement
transformation. Comments are welcom
Optimal time decay of the non cut-off Boltzmann equation in the whole space
In this paper we study the large-time behavior of perturbative classical
solutions to the hard and soft potential Boltzmann equation without the angular
cut-off assumption in the whole space \threed_x with \DgE. We use the
existence theory of global in time nearby Maxwellian solutions from
\cite{gsNonCutA,gsNonCut0}. It has been a longstanding open problem to
determine the large time decay rates for the soft potential Boltzmann equation
in the whole space, with or without the angular cut-off assumption
\cite{MR677262,MR2847536}. For perturbative initial data, we prove that
solutions converge to the global Maxwellian with the optimal large-time decay
rate of O(t^{-\frac{\Ndim}{2}+\frac{\Ndim}{2r}}) in the
L^2_\vel(L^r_x)-norm for any .Comment: 31 pages, final version to appear in KR
Nonlocal Dynamics of Passive Tracer Dispersion with Random Stopping
We investigate the nonlocal behavior of passive tracer dispersion with random
stopping at various sites in fluids. This kind of dispersion processes is
modeled by an integral partial differential equation, i.e., an
advection-diffusion equation with a memory term. We have shown the exponential
decay of the passive tracer concentration, under suitable conditions for the
velocity field and the probability distribution of random stopping time.Comment: 7 page
Dissipative Quasigeostrophic Dynamics under Random Forcing
The quasigeostrophic model is a simplified geophysical fluid model at
asymptotically high rotation rate or at small Rossby number. We consider the
quasigeostrophic equation with dissipation under random forcing in bounded
domains. We show that global unique solutions exist for appropriate initial
data. Unlike the deterministic quasigeostrophic equation whose well-posedness
is well-known, there seems no rigorous result on global existence and
uniqueness of the randomly forced quasigeostrophic equation. Our work provides
such a rigorous result on global existence and uniqueness, under very mild
conditions.Comment: LaTeX, 15 page
Topological Properties of Spatial Coherence Function
Topology of the spatial coherence function is considered in details. The
phase singularity (coherence vortices) structures of coherence function are
classified by Hopf index and Brouwer degree in topology. The coherence flux
quantization and the linking of the closed coherence vortices are also studied
from the topological properties of the spatial coherence function.Comment: 9 page
Approximation of Random Slow Manifolds and Settling of Inertial Particles under Uncertainty
A method is provided for approximating random slow manifolds of a class of
slow-fast stochastic dynamical systems. Thus approximate, low dimensional,
reduced slow systems are obtained analytically in the case of sufficiently
large time scale separation. To illustrate this dimension reduction procedure,
the impact of random environmental fluctuations on the settling motion of
inertial particles in a cellular flow field is examined. It is found that noise
delays settling for some particles but enhances settling for others. A
deterministic stable manifold is an agent to facilitate this phenomenon.
Overall, noise appears to delay the settling in an averaged sense.Comment: 27 pages, 9 figure
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