2,864 research outputs found
Rosepack Document 1: Guidelines for Writing Semi-portable Fortran
Transferring Fortran subroutines from one manufacturer's machine to another or from one operating system to another puts certain constrains on the construction of the Fortran statements that are used in the subroutines. The reliable performance of this mathematical software should be unaffected by the host environment in which the software is used or by the compiler from which the code is generated. In short, the algorithm is to he independent of the computing environment in which it is run. The subroutines of ROSEPACK (Robust Statistics Estimation Package) are Fortran IV source code designed to be semi-portable where semi-portable is defined to mean transportable with minimum change.*
Synthetic dimensions in ultracold molecules: quantum strings and membranes
Synthetic dimensions alter one of the most fundamental properties in nature,
the dimension of space. They allow, for example, a real three-dimensional
system to act as effectively four-dimensional. Driven by such possibilities,
synthetic dimensions have been engineered in ongoing experiments with ultracold
matter. We show that rotational states of ultracold molecules can be used as
synthetic dimensions extending to many - potentially hundreds of - synthetic
lattice sites. Microwaves coupling rotational states drive fully controllable
synthetic inter-site tunnelings, enabling, for example, topological band
structures. Interactions leads to even richer behavior: when molecules are
frozen in a real space lattice with uniform synthetic tunnelings, dipole
interactions cause the molecules to aggregate to a narrow strip in the
synthetic direction beyond a critical interaction strength, resulting in a
quantum string or a membrane, with an emergent condensate that lives on this
string or membrane. All these phases can be detected using measurements of
rotational state populations.Comment: 5-page article + 4 figures + references; 7 pages + 4 figures in
Supplemen
Induced Subgraphs of Johnson Graphs
The Johnson graph J(n,N) is defined as the graph whose vertices are the
n-subsets of the set {1,2,...,N}, where two vertices are adjacent if they share
exactly n - 1 elements. Unlike Johnson graphs, induced subgraphs of Johnson
graphs (JIS for short) do not seem to have been studied before. We give some
necessary conditions and some sufficient conditions for a graph to be JIS,
including: in a JIS graph, any two maximal cliques share at most two vertices;
all trees, cycles, and complete graphs are JIS; disjoint unions and Cartesian
products of JIS graphs are JIS; every JIS graph of order n is an induced
subgraph of J(m,2n) for some m <= n. This last result gives an algorithm for
deciding if a graph is JIS. We also show that all JIS graphs are edge move
distance graphs, but not vice versa.Comment: 12 pages, 4 figure
Accessing Rydberg-dressed interactions using many-body Ramsey dynamics
We demonstrate that Ramsey spectroscopy can be used to observe
Rydberg-dressed interactions. In contrast to many prior proposals, our scheme
operates comfortably within experimentally measured lifetimes, and accesses a
regime where quantum superpositions are crucial. The key idea is to build a
spin-1/2 from one level that is Rydberg-dressed and another that is not. These
levels may be hyperfine or long-lived electronic states. An Ising spin model
governs the Ramsey dynamics, for which we derive an exact solution. Due to the
structure of Rydberg interactions, the dynamics differs significantly from that
in other spin systems. As one example, spin echo can increase the rate at which
coherence decays. The results also apply to bare (undressed) Rydberg states as
a special case, for which we quantitatively reproduce recent ultrafast
experiments without fitting
The Singular Value Analysis in Matrix Computation
This paper discusses the robustness and the computational stability of the singular value decomposition algorithm used at the NBER Computer Research Center. The effect of perturbations on input data is explored. Suggestions are made for using the algorithm to get information about the rank of a real square or rectangular matrix. The algorithm can also be used to compute the best approximate solution of linear system of equations in the least squares sense, to solve linear systems of equations with equality constraints, and to determine dependencies or near dependencies among the rows or columns of a matrix. A copy of the subroutine that is used and some examples on which it has been tested are included in the appendixes.
A Model for Scattering with Proliferating Resonances: Many Coupled Square Wells
We present a multichannel model for elastic interactions, comprised of an
arbitrary number of coupled finite square-well potentials, and derive
semi-analytic solutions for its scattering behavior. Despite the model's
simplicity, it is flexible enough to include many coupled short-ranged
resonances in the vicinity of the collision threshold, as is necessary to
describe ongoing experiments in ultracold molecules and lanthanide atoms. We
also introduce a simple, but physically realistic, statistical ensemble for
parameters in this model. We compute the resulting probability distributions of
nearest-neighbor resonance spacings and analyze them by fitting to the Brody
distribution. We quantify the ability of alternative distribution functions,
for resonance spacing and resonance number variance, to describe the crossover
regime. The analysis demonstrates that the multichannel square-well model with
the chosen ensemble of parameters naturally captures the crossover from
integrable to chaotic scattering as a function of closed channel coupling
strength.Comment: 11 pages, 8 figure
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