5,846 research outputs found
Non-Poissonian level spacing statistics of classically integrable quantum systems based on the Berry-Robnik approach
Along the line of thoughts of Berry and Robnik\cite{[1]}, we investigated the
gap distribution function of systems with infinitely many independent
components, and discussed the level-spacing distribution of classically
integrable quantum systems. The level spacing distribution is classified into
three cases: Case 1: Poissonian if , Case 2: Poissonian
for large , but possibly not for small if , and
Case 3: sub-Poissonian if . Thus, even when the energy
levels of individual components are statistically independent, non-Poisson
level spacing distributions are possible.Comment: 5 pages, 0 figur
Long-Range Spectral Statistics of Classically Integrable Systems --Investigation along the Line of the Berry-Robnik Approach--
Extending the argument of Ref.\citen{[4]} to the long-range spectral
statistics of classically integrable quantum systems, we examine the level
number variance, spectral rigidity and two-level cluster function. These
observables are obtained by applying the approach of Berry and Robnik\cite{[0]}
and the mathematical framework of Pandey \cite{[2]} to systems with infinitely
many components, and they are parameterized by a single function ,
where corresponds to Poisson statistics, and
indicates deviations from Poisson statistics. This implies that even when the
spectral components are statistically independent, non-Poissonian spectral
statistics are possible.Comment: 13 pages, 4 figure
Hole Transport in p-Type ZnO
A two-band model involving the A- and B-valence bands was adopted to analyze
the temperature dependent Hall effect measured on N-doped \textit{p}-type ZnO.
The hole transport characteristics (mobilities, and effective Hall factor) are
calculated using the ``relaxation time approximation'' as a function of
temperature. It is shown that the lattice scattering by the acoustic
deformation potential is dominant. In the calculation of the scattering rate
for ionized impurity mechanism, the activation energy of 100 or 170 meV is used
at different compensation ratios between donor and acceptor concentrations. The
theoretical Hall mobility at acceptor concentration of
cm is about 70 cmVs with the activation energy of 100 meV
and the compensation ratio of 0.8 at 300 K. We also found that the compensation
ratios conspicuously affected the Hall mobilities.Comment: 5page, 5 figures, accepted for publication in Jpn. J. Appl. Phy
Long-Term Evolution of Massive Black Hole Binaries. II. Binary Evolution in Low-Density Galaxies
We use direct-summation N-body integrations to follow the evolution of binary
black holes at the centers of galaxy models with large, constant-density cores.
Particle numbers as large as 400K are considered. The results are compared with
the predictions of loss-cone theory, under the assumption that the supply of
stars to the binary is limited by the rate at which they can be scattered into
the binary's influence sphere by gravitational encounters. The agreement
between theory and simulation is quite good; in particular, we are able to
quantitatively explain the observed dependence of binary hardening rate on N.
We do not verify the recent claim of Chatterjee, Hernquist & Loeb (2003) that
the hardening rate of the binary stabilizes when N exceeds a particular value,
or that Brownian wandering of the binary has a significant effect on its
evolution. When scaled to real galaxies, our results suggest that massive black
hole binaries in gas-poor nuclei would be unlikely to reach gravitational-wave
coalescence in a Hubble time.Comment: 13 pages, 8 figure
Evolution of Massive Blackhole Triples I -- Equal-mass binary-single systems
We present the result of -body simulations of dynamical evolution of
triple massive blackhole (BH) systems in galactic nuclei. We found that in most
cases two of the three BHs merge through gravitational wave (GW) radiation in
the timescale much shorter than the Hubble time, before ejecting one BH through
a slingshot. In order for a binary BH to merge before ejecting out the third
one, it has to become highly eccentric since the gravitational wave timescale
would be much longer than the Hubble time unless the eccentricity is very high.
We found that two mechanisms drive the increase of the eccentricity of the
binary. One is the strong binary-single BH interaction resulting in the
thermalization of the eccentricity. The second is the Kozai mechanism which
drives the cyclic change of the inclination and eccentricity of the inner
binary of a stable hierarchical triple system. Our result implies that many of
supermassive blackholes are binaries.Comment: 20 pages, 12 figure
Instability of the Gravitational N-Body Problem in the Large-N Limit
We use a systolic N-body algorithm to evaluate the linear stability of the
gravitational N-body problem for N up to 1.3 x 10^5, two orders of magnitude
greater than in previous experiments. For the first time, a clear ~ln
N-dependence of the perturbation growth rate is seen. The e-folding time for N
= 10^5 is roughly 1/20 of a crossing time.Comment: Accepted for publication in The Astrophysical Journa
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