10,663 research outputs found
Heating and thermal squeezing in parametrically-driven oscillators with added noise
In this paper we report a theoretical model based on Green functions, Floquet
theory and averaging techniques up to second order that describes the dynamics
of parametrically-driven oscillators with added thermal noise. Quantitative
estimates for heating and quadrature thermal noise squeezing near and below the
transition line of the first parametric instability zone of the oscillator are
given. Furthermore, we give an intuitive explanation as to why heating and
thermal squeezing occur. For small amplitudes of the parametric pump the
Floquet multipliers are complex conjugate of each other with a constant
magnitude. As the pump amplitude is increased past a threshold value in the
stable zone near the first parametric instability, the two Floquet multipliers
become real and have different magnitudes. This creates two different effective
dissipation rates (one smaller and the other larger than the real dissipation
rate) along the stable manifolds of the first-return Poincare map. We also show
that the statistical average of the input power due to thermal noise is
constant and independent of the pump amplitude and frequency. The combination
of these effects cause most of heating and thermal squeezing. Very good
agreement between analytical and numerical estimates of the thermal
fluctuations is achieved.Comment: Submitted to Phys. Rev. E, 29 pages, 12 figures. arXiv admin note:
substantial text overlap with arXiv:1108.484
Parallel structurally-symmetric sparse matrix-vector products on multi-core processors
We consider the problem of developing an efficient multi-threaded
implementation of the matrix-vector multiplication algorithm for sparse
matrices with structural symmetry. Matrices are stored using the compressed
sparse row-column format (CSRC), designed for profiting from the symmetric
non-zero pattern observed in global finite element matrices. Unlike classical
compressed storage formats, performing the sparse matrix-vector product using
the CSRC requires thread-safe access to the destination vector. To avoid race
conditions, we have implemented two partitioning strategies. In the first one,
each thread allocates an array for storing its contributions, which are later
combined in an accumulation step. We analyze how to perform this accumulation
in four different ways. The second strategy employs a coloring algorithm for
grouping rows that can be concurrently processed by threads. Our results
indicate that, although incurring an increase in the working set size, the
former approach leads to the best performance improvements for most matrices.Comment: 17 pages, 17 figures, reviewed related work section, fixed typo
Spectral function and quasiparticle weight in the generalized t-J model
We extend to the spectral function an approach which allowed us to calculate
the quasiparticle weight for destruction of a real electron Z_c sigma (k) (in
contrast to that of creation of a spinless holon Z_h(k) in a generalized
model, using the self-consistent Born approximation (SCBA). We compare our
results with those obtained using the alternative approach of Sushkov et al.,
which also uses the SCBA. The results for Z_c sigma (k) are also compared with
results obtained using the string picture and with exact diagonalizations of a
32-site square cluster. While on a qualitative level, all results look similar,
our SCBA approach seems to compare better with the ED one. The effect of
hopping beyond nearest neighbors, and that of the three-site term are
discussed.Comment: 7 pages, 6 figure
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