6,502 research outputs found
An Equivalent Hermitian Hamiltonian for the non-Hermitian -x^4 Potential
The potential -x^4, which is unbounded below on the real line, can give rise
to a well-posed bound state problem when x is taken on a contour in the
lower-half complex plane. It is then PT-symmetric rather than Hermitian.
Nonetheless it has been shown numerically to have a real spectrum, and a proof
of reality, involving the correspondence between ordinary differential
equations and integral systems, was subsequently constructed for the general
class of potentials -(ix)^N. For PT-symmetric but non-Hermitian Hamiltonians
the natural PT metric is not positive definite, but a dynamically-defined
positive-definite metric can be defined, depending on an operator Q. Further,
with the help of this operator an equivalent Hermitian Hamiltonian h can be
constructed. This programme has been carried out exactly for a few soluble
models, and the first few terms of a perturbative expansion have been found for
the potential m^2x^2+igx^3. However, until now, the -x^4 potential has proved
intractable. In the present paper we give explicit, closed-form expressions for
Q and h, which are made possible by a particular parametrization of the contour
in the complex plane on which the problem is defined. This constitutes an
explicit proof of the reality of the spectrum. The resulting equivalent
Hamiltonian has a potential with a positive quartic term together with a linear
term.Comment: New reference [10] added and discussed. Minor typographical
correction
Dynamical evolution of a doubly-quantized vortex imprinted in a Bose-Einstein Condensate
The recent experiment by Y. Shin \emph{et al.} [Phys. Rev. Lett. \textbf{93},
160406 (2004)] on the decay of a doubly quantized vortex imprinted in Na condensates is analyzed by numerically solving the Gross-Pitaevskii
equation. Our results, which are in very good quantitative agreement with the
experiment, demonstrate that the vortex decay is mainly a consequence of
dynamical instability. Despite apparent contradictions, the local density
approach is consistent with the experimental results. The monotonic increase
observed in the vortex lifetimes is a consequence of the fact that, for large
condensates, the measured lifetimes incorporate the time it takes for the
initial perturbation to reach the central slice. When considered locally, the
splitting occurs approximately at the same time in every condensate, regardless
of its size.Comment: 5 pages, 4 figure
An Extinction Map and Color Magnitude Diagram for the Globular Cluster NGC 3201
Differential variations of up to mag on a scale of
arcminutes across NGC 3201 are presented in the form of an extinction map. This
map, created by calculating average values for stars in small
subregions of the field with respect to a fiducial region, greatly improves the
appearance of the CMD of the cluster. We describe how we implemented this
technique in detail with our data for NGC 3201. A comparison between our map
and that of the same region extracted from the COBE/DIRBE reddening maps
published by Schlegel, Finkbeiner, & Davis (1998) (SFD) displays larger-scale
similarities between the two maps as well as smaller-scale features which show
up in our map but not in the SFD map. Several methods of determining an
zeropoint to add to our differential extinction map are presented.
Isochrone fitting proved to be the most successful one, but it produces an
average for the cluster which is smaller than previously published
values by . Finally, our results seem to support the statement
by Arce & Goodman (1999) that the SFD maps overestimate the reddening in
regions of high extinction.Comment: 19 pages, 12 figures, 1 table, accepted for publication in AJ (March
2001). Full resolution version may be obtained at
http://www.astro.lsa.umich.edu/users/kaspar/html/ngc3201.pdf (PDF) and at
http://www.astro.lsa.umich.edu/users/kaspar/html/ngc3201.ps.gz (PS
Enlarging instruction streams
The stream fetch engine is a high-performance fetch architecture based on the concept of an instruction stream. We call a sequence of instructions from the target of a taken branch to the next taken branch, potentially containing multiple basic blocks, a stream. The long length of instruction streams makes it possible for the stream fetch engine to provide a high fetch bandwidth and to hide the branch predictor access latency, leading to performance results close to a trace cache at a lower implementation cost and complexity. Therefore, enlarging instruction streams is an excellent way to improve the stream fetch engine. In this paper, we present several hardware and software mechanisms focused on enlarging those streams that finalize at particular branch types. However, our results point out that focusing on particular branch types is not a good strategy due to Amdahl's law. Consequently, we propose the multiple-stream predictor, a novel mechanism that deals with all branch types by combining single streams into long virtual streams. This proposal tolerates the prediction table access latency without requiring the complexity caused by additional hardware mechanisms like prediction overriding. Moreover, it provides high-performance results which are comparable to state-of-the-art fetch architectures but with a simpler design that consumes less energy.Peer ReviewedPostprint (published version
On the Path-Integral Derivation of the Anomaly for the Hermitian Equivalent of the Complex -Symmetric Quartic Hamiltonian
It can be shown using operator techniques that the non-Hermitian
-symmetric quantum mechanical Hamiltonian with a "wrong-sign" quartic
potential is equivalent to a Hermitian Hamiltonian with a positive
quartic potential together with a linear term. A naive derivation of the same
result in the path-integral approach misses this linear term. In a recent paper
by Bender et al. it was pointed out that this term was in the nature of a
parity anomaly and a more careful, discretized treatment of the path integral
appeared to reproduce it successfully. However, on re-examination of this
derivation we find that a yet more careful treatment is necessary, keeping
terms that were ignored in that paper. An alternative, much simpler derivation
is given using the additional potential that has been shown to appear whenever
a change of variables to curvilinear coordinates is made in a functional
integral.Comment: LaTeX, 12 pages, no figure
Static locality analysis for cache management
Most memory references in numerical codes correspond to array references whose indices are affine functions of surrounding loop indices. These array references follow a regular predictable memory pattern that can be analysed at compile time. This analysis can provide valuable information like the locality exhibited by the program, which can be used to implement more intelligent caching strategy. In this paper we propose a static locality analysis oriented to the management of data caches. We show that previous proposals on locality analysis are not appropriate when the proposals have a high conflict miss ratio. This paper examines those proposals by introducing a compile-time interference analysis that significantly improve the performance of them. We first show how this analysis can be used to characterize the dynamic locality properties of numerical codes. This evaluation show for instance that a large percentage of references exhibit any type of locality. This motivates the use of a dual data cache, which has a module specialized to exploit temporal locality, and a selective cache respectively. Then, the performance provided by these two cache organizations is evaluated. In both organizations, the static locality analysis is responsible for tagging each memory instruction accordingly to the particular type(s) of locality that it exhibits.Peer ReviewedPostprint (published version
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