3,733 research outputs found
Density wave and supersolid phases of correlated bosons in an optical lattice
Motivated by the recent experiment on the Bose-Einstein condensation of
Cr atoms with long-range dipolar interactions (Werner J. et al., Phys.
Rev. Lett., 94 (2005) 183201), we consider a system of bosons with repulsive
nearest and next-nearest neighbor interactions in an optical lattice. The
ground state phase diagram, calculated using the Gutzwiller ansatz, shows,
apart from the superfluid (SF) and the Mott insulator (MI), two modulated
phases, \textit{i.e.}, the charge density wave (CDW) and the supersolid (SS).
Excitation spectra are also calculated which show a gap in the insulators,
gapless, phonon mode in the superfluid and the supersolid, and a mode softening
of superfluid excitations in the vicinity of the modulated phases. We discuss
the possibility of observing these phases in cold dipolar atoms and propose
experiments to detect them
Algorithmic Verification of Asynchronous Programs
Asynchronous programming is a ubiquitous systems programming idiom to manage
concurrent interactions with the environment. In this style, instead of waiting
for time-consuming operations to complete, the programmer makes a non-blocking
call to the operation and posts a callback task to a task buffer that is
executed later when the time-consuming operation completes. A co-operative
scheduler mediates the interaction by picking and executing callback tasks from
the task buffer to completion (and these callbacks can post further callbacks
to be executed later). Writing correct asynchronous programs is hard because
the use of callbacks, while efficient, obscures program control flow.
We provide a formal model underlying asynchronous programs and study
verification problems for this model. We show that the safety verification
problem for finite-data asynchronous programs is expspace-complete. We show
that liveness verification for finite-data asynchronous programs is decidable
and polynomial-time equivalent to Petri Net reachability. Decidability is not
obvious, since even if the data is finite-state, asynchronous programs
constitute infinite-state transition systems: both the program stack and the
task buffer of pending asynchronous calls can be potentially unbounded.
Our main technical construction is a polynomial-time semantics-preserving
reduction from asynchronous programs to Petri Nets and conversely. The
reduction allows the use of algorithmic techniques on Petri Nets to the
verification of asynchronous programs.
We also study several extensions to the basic models of asynchronous programs
that are inspired by additional capabilities provided by implementations of
asynchronous libraries, and classify the decidability and undecidability of
verification questions on these extensions.Comment: 46 pages, 9 figure
Improving the Sensitivity of LISA
It has been shown in the past, that the six Doppler data streams obtained
LISA configuration can be combined by appropriately delaying the data streams
for cancelling the laser frequency noise. Raw laser noise is several orders of
magnitude above the other noises and thus it is essential to bring it down to
the level of shot, acceleration noises. A rigorous and systematic formalism
using the techniques of computational commutative algebra was developed which
generates all the data combinations cancelling the laser frequency noise. The
relevant data combinations form a first module of syzygies. In this paper we
use this formalism for optimisation of the LISA sensitivity by analysing the
noise and signal covariance matrices. The signal covariance matrix, averaged
over polarisations and directions, is calculated for binaries whose frequency
changes at most adiabatically. We then present the extremal SNR curves for all
the data combinations in the module. They correspond to the eigenvectors of the
noise and signal covariance matrices. We construct LISA `network' SNR by
combining the outputs of the eigenvectors which improves the LISA sensitivity
substantially. The maximum SNR curve can yield an improvement upto 70 % over
the Michelson, mainly at high frequencies, while the improvement using the
network SNR ranges from 40 % to over 100 %. Finally, we describe a simple toy
model, in which LISA rotates in a plane. In this analysis, we estimate the
improvement in the LISA sensitivity, if one switches from one data combination
to another as it rotates. Here the improvement in sensitivity, if one switches
optimally over three cyclic data combinations of the eigenvector is about 55 %
on an average over the LISA band-width. The corresponding SNR improvement is 60
%, if one maximises over the module.Comment: 16 pages, 10 figures, Submitted to Class. Quant. Gravit
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