1,400 research outputs found
Ehrenfest breakdown of the mean-field dynamics of Bose gases
The mean-field dynamics of a Bose gas is shown to break down at time where is the Lyapunov exponent of the mean-field
theory, is the number of bosons, and is a system-dependent constant.
The breakdown time is essentially the Ehrenfest time that
characterizes the breakdown of the correspondence between classical and quantum
dynamics. This breakdown can be well described by the quantum fidelity defined
for reduced density matrices. Our results are obtained with the formalism in
particle-number phase space and are illustrated with a triple-well model. The
logarithmic quantum-classical correspondence time may be verified
experimentally with Bose-Einstein condensates.Comment: 6 pages, 4 figure
Covariance matrix estimation for stationary time series
We obtain a sharp convergence rate for banded covariance matrix estimates of
stationary processes. A precise order of magnitude is derived for spectral
radius of sample covariance matrices. We also consider a thresholded covariance
matrix estimator that can better characterize sparsity if the true covariance
matrix is sparse. As our main tool, we implement Toeplitz [Math. Ann. 70 (1911)
351-376] idea and relate eigenvalues of covariance matrices to the spectral
densities or Fourier transforms of the covariances. We develop a large
deviation result for quadratic forms of stationary processes using m-dependence
approximation, under the framework of causal representation and physical
dependence measures.Comment: Published in at http://dx.doi.org/10.1214/11-AOS967 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Exotic orbits due to spin-spin coupling around Kerr black holes
We report exotic orbital phenomena of spinning test particles orbiting around
a Kerr black hole, i.e., some orbits of spinning particles are asymmetrical
about the equatorial plane. When a nonspinning test particle orbits around a
Kerr black hole in a strong field region, due to relativistic orbital
precessions, the pattern of trajectories is symmetrical about the equatorial
plane of the Kerr black hole. However, the patterns of the spinning particles'
orbit are no longer symmetrical about the equatorial plane for some orbital
configurations and large spins. We argue that these asymmetrical patterns come
from the spin-spin interactions between spinning particles and Kerr black
holes, because the directions of spin-spin forces can be arbitrary, and
distribute asymmetrically about the equatorial plane.Comment: 15 pages, 20 figure
Determining the nature of white dwarfs from low-frequency gravitational waves
An extreme-mass-ratio system composed of a white dwarf (WD) and a massive
black hole can be observed by the low-frequency gravitational wave detectors,
such as the Laser Interferometer Space Antenna (LISA). When the mass of the
black hole is around , the WD will be disrupted by the
tidal interaction at the final inspiraling stage. The event position and time
of the tidal disruption of the WD can be accurately determined by the
gravitational wave signals. Such position and time depend upon the mass of the
black hole and especially on the density of the WD. We present the theory by
using LISA-like gravitational wave detectors, the mass-radius relation and then
the equations of state of WDs could be strictly constrained (accuracy up to
). We also point out that LISA can accurately predict the disruption
time of a WD, and forecast the electromagnetic follow-up of this tidal
disruption event.Comment: 7 pages, 2 figure
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