16,814 research outputs found
The Lefschetz-Lunts formula for deformation quantization modules
We adapt to the case of deformation quantization modules a formula of V.
Lunts who calculates the trace of a kernel acting on Hochschild homology.Comment: 19 pages; Mathematische Zeitschrift 201
Bayesian least squares deconvolution
Aims. To develop a fully Bayesian least squares deconvolution (LSD) that can
be applied to the reliable detection of magnetic signals in noise-limited
stellar spectropolarimetric observations using multiline techniques. Methods.
We consider LSD under the Bayesian framework and we introduce a flexible
Gaussian Process (GP) prior for the LSD profile. This prior allows the result
to automatically adapt to the presence of signal. We exploit several linear
algebra identities to accelerate the calculations. The final algorithm can deal
with thousands of spectral lines in a few seconds. Results. We demonstrate the
reliability of the method with synthetic experiments and we apply it to real
spectropolarimetric observations of magnetic stars. We are able to recover the
magnetic signals using a small number of spectral lines, together with the
uncertainty at each velocity bin. This allows the user to consider if the
detected signal is reliable. The code to compute the Bayesian LSD profile is
freely available.Comment: 8 pages, accepted for publication in A&
Chiral bound states in the continuum
We present a distinct mechanism for the formation of bound states in the
continuum (BICs). In chiral quantum systems there appear zero-energy states in
which the wave function has finite amplitude only in one of the subsystems
defined by the chiral symmetry. When the system is coupled to leads with a
continuum energy band, part of these states remain bound. We derive some
algebraic rules for the number of these states depending on the dimensionality
and rank of the total Hamiltonian. We examine the transport properties of such
systems including the appearance of Fano resonances in some limiting cases.
Finally, we discuss experimental setups based on microwave dielectric
resonators and atoms in optical lattices where these predictions can be tested.Comment: 9 pages, 8 figures. v2: includes results specific to honeycomb
lattice; matches published versio
Spectral statistics of molecular resonances in erbium isotopes: How chaotic are they?
We perform a comprehensive analysis of the spectral statistics of the
molecular resonances in Er and Er observed in recent ultracold
collision experiments [Frisch et al., Nature {\bf 507}, 475 (2014)] with the
aim of determining the chaoticity of this system. We calculate different
independent statistical properties to check their degree of agreement with
random matrix theory (RMT), and analyze if they are consistent with the
possibility of having missing resonances. The analysis of the short-range
fluctuations as a function of the magnetic field points to a steady increase of
chaoticity until G. The repulsion parameter decreases for higher
magnetic fields, an effect that can be interpreted as due to missing
resonances. The analysis of long-range fluctuations allows us to be more
quantitative and estimate a fraction of missing levels. Finally, a
study of the distribution of resonance widths provides additional evidence
supporting missing resonances of small width compared with the experimental
magnetic field resolution. We conclude that further measurements with increased
resolution will be necessary to give a final answer to the problem of missing
resonances and the agreement with RMT.Comment: 9 pages, 6 figure
Ordering in Heisenberg Spin Glasses
For five different Heisenberg spin glass systems, torque experiments were
performed in applied magnetic fields up to . The Dzyaloshinski-Moriya
random anisotropy strengths, the in-field torque onset temperatures, and the
torque relaxation were measured. Critical exponents were estimated
independently using a standard protocol. The data are strong evidence for a
true spin glass ordered state which survives under high applied magnetic
fields; they can be interpreted consistently in terms of a chiral ordering
model with replica symmetry breaking as proposed by Kawamura and coworkers.Comment: 4 pages 4 figures. Revised version accepted by PR
Fast and Compact Distributed Verification and Self-Stabilization of a DFS Tree
We present algorithms for distributed verification and silent-stabilization
of a DFS(Depth First Search) spanning tree of a connected network. Computing
and maintaining such a DFS tree is an important task, e.g., for constructing
efficient routing schemes. Our algorithm improves upon previous work in various
ways. Comparable previous work has space and time complexities of bits per node and respectively, where is the highest
degree of a node, is the number of nodes and is the diameter of the
network. In contrast, our algorithm has a space complexity of bits
per node, which is optimal for silent-stabilizing spanning trees and runs in
time. In addition, our solution is modular since it utilizes the
distributed verification algorithm as an independent subtask of the overall
solution. It is possible to use the verification algorithm as a stand alone
task or as a subtask in another algorithm. To demonstrate the simplicity of
constructing efficient DFS algorithms using the modular approach, We also
present a (non-sielnt) self-stabilizing DFS token circulation algorithm for
general networks based on our silent-stabilizing DFS tree. The complexities of
this token circulation algorithm are comparable to the known ones
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