24,642 research outputs found
Global dispersive solutions for the Gross-Pitaevskii equation in two and three dimensions
We study asymptotic behaviour at time infinity of solutions close to the
non-zero constant equilibrium for the Gross-Pitaevskii equation in two and
three spatial dimensions. We construct a class of global solutions with
prescribed dispersive asymptotic behavior, which is given in terms of the
linearized evolution
Dynamical Properties of a Growing Surface on a Random Substrate
The dynamics of the discrete Gaussian model for the surface of a crystal
deposited on a disordered substrate is investigated by Monte Carlo simulations.
The mobility of the growing surface was studied as a function of a small
driving force and temperature . A continuous transition is found from
high-temperature phase characterized by linear response to a low-temperature
phase with nonlinear, temperature dependent response. In the simulated regime
of driving force the numerical results are in general agreement with recent
dynamic renormalization group predictions.Comment: 10 pages, latex, 3 figures, to appear in Phys. Rev. E (RC
Stable directions for small nonlinear Dirac standing waves
We prove that for a Dirac operator with no resonance at thresholds nor
eigenvalue at thresholds the propagator satisfies propagation and dispersive
estimates. When this linear operator has only two simple eigenvalues close
enough, we study an associated class of nonlinear Dirac equations which have
stationary solutions. As an application of our decay estimates, we show that
these solutions have stable directions which are tangent to the subspaces
associated with the continuous spectrum of the Dirac operator. This result is
the analogue, in the Dirac case, of a theorem by Tsai and Yau about the
Schr\"{o}dinger equation. To our knowledge, the present work is the first
mathematical study of the stability problem for a nonlinear Dirac equation.Comment: 62 page
Spin Relaxation Times of Single-Wall Carbon Nanotubes
We have measured temperature ()- and power-dependent electron spin
resonance in bulk single-wall carbon nanotubes to determine both the
spin-lattice and spin-spin relaxation times, and . We observe that
increases linearly with from 4 to 100 K, whereas {\em
decreases} by over a factor of two when is increased from 3 to 300 K. We
interpret the trend as spin-lattice relaxation via
interaction with conduction electrons (Korringa law) and the decreasing
dependence of as motional narrowing. By analyzing the latter, we
find the spin hopping frequency to be 285 GHz. Last, we show that the Dysonian
lineshape asymmetry follows a three-dimensional variable-range hopping behavior
from 3 to 20 K; from this scaling relation, we extract a localization length of
the hopping spins to be 100 nm.Comment: 6 pages, 3 figure
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