76,917 research outputs found
Chen ranks and resonance
The Chen groups of a group are the lower central series quotients of the
maximal metabelian quotient of . Under certain conditions, we relate the
ranks of the Chen groups to the first resonance variety of , a jump locus
for the cohomology of . In the case where is the fundamental group of
the complement of a complex hyperplane arrangement, our results positively
resolve Suciu's Chen ranks conjecture. We obtain explicit formulas for the Chen
ranks of a number of groups of broad interest, including pure Artin groups
associated to Coxeter groups, and the group of basis-conjugating automorphisms
of a finitely generated free group.Comment: final version, to appear in Advances in Mathematic
Civic Engagement and Service Learning Partnerships
Service learning is designed to promote volunteerism and civic awareness. Community engagement in higher education specifically involves university members partnering with local community organizations to address a need. Students engage with community partners through service learning and other activities (Moore & Mendez, 2014). Service learning is a practice that connects new knowledge and social responsibility through active learning (Benson & Younkin, 1996).https://digitalscholarship.unlv.edu/btp_expo/1083/thumbnail.jp
Formal proof of the AVM-1 microprocessor using the concept of generic interpreters
A microprocessor designated AVM-1 was designed to demonstrate the use of generic interpreters in verifying hierarchically decomposed microprocessor specifications. This report is intended to document the high-order language (HOL) code verifying AVM-1. The organization of the proof is discussed and some technical details concerning the execution of the proof scripts in HOL are presented. The proof scripts used to verify AVM-1 are also presented
The formal verification of generic interpreters
The task assignment 3 of the design and validation of digital flight control systems suitable for fly-by-wire applications is studied. Task 3 is associated with formal verification of embedded systems. In particular, results are presented that provide a methodological approach to microprocessor verification. A hierarchical decomposition strategy for specifying microprocessors is also presented. A theory of generic interpreters is presented that can be used to model microprocessor behavior. The generic interpreter theory abstracts away the details of instruction functionality, leaving a general model of what an interpreter does
Measurement of the ac Stark shift with a guided matter-wave interferometer
We demonstrate the effectiveness of a guided-wave Bose-Einstein condensate
interferometer for practical measurements. Taking advantage of the large arm
separations obtainable in our interferometer, the energy levels of the 87Rb
atoms in one arm of the interferometer are shifted by a calibrated laser beam.
The resulting phase shifts are used to determine the ac polarizability at a
range of frequencies near and at the atomic resonance. The measured values are
in good agreement with theoretical expectations. However, we observe a
broadening of the transition near the resonance, an indication of collective
light scattering effects. This nonlinearity may prove useful for the production
and control of squeezed quantum states.Comment: 5 pages, three figure
Towards composition of verified hardware devices
Computers are being used where no affordable level of testing is adequate. Safety and life critical systems must find a replacement for exhaustive testing to guarantee their correctness. Through a mathematical proof, hardware verification research has focused on device verification and has largely ignored system composition verification. To address these deficiencies, we examine how the current hardware verification methodology can be extended to verify complete systems
Quantum Zeno Effect Explains Magnetic-Sensitive Radical-Ion-Pair Reactions
Chemical reactions involving radical-ion pairs are ubiquitous in biology,
since not only are they at the basis of the photosynthetic reaction chain, but
are also assumed to underlie the biochemical magnetic compass used by avian
species for navigation. Recent experiments with magnetic-sensitive radical-ion
pair reactions provided strong evidence for the radical-ion-pair
magnetoreception mechanism, verifying the expected magnetic sensitivities and
chemical product yield changes. It is here shown that the theoretical
description of radical-ion-pair reactions used since the 70's cannot explain
the observed data, because it is based on phenomenological equations masking
quantum coherence effects. The fundamental density matrix equation derived here
from basic quantum measurement theory considerations naturally incorporates the
quantum Zeno effect and readily explains recent experimental observations on
low- and high-magnetic-field radical-ion-pair reactions.Comment: 10 pages, 5 figure
Cooling a micro-mechanical resonator by quantum back-action from a noisy qubit
We study the role of qubit dephasing in cooling a mechanical resonator by
quantum back-action. With a superconducting flux qubit as a specific example,
we show that ground-state cooling of a mechanical resonator can only be
realized if the qubit dephasing rate is sufficiently low.Comment: 5 pages, 3 figure
Cooperative effects in Josephson junctions in a cavity in the strong coupling regime
We analyze the behavior of systems of two and three qubits made by Josephson
junctions, treated in the two level approximation, driven by a radiation mode
in a cavity. The regime we consider is a strong coupling one recently
experimentally reached for a single junction. Rabi oscillations are obtained
with the frequency proportional to integer order Bessel functions in the limit
of a large photon number, similarly to the case of the single qubit. A
selection rule is derived for the appearance of Rabi oscillations. A quantum
amplifier built with a large number of Josephson junctions in a cavity in the
strong coupling regime is also described.Comment: 9 pages, no figures. Version accepted for publication in Physical
Review
Effect of random interactions in spin baths on decoherence
We study the decoherence of a central spin 1/2 induced by a spin bath with
intrabath interactions. Since we are interested in the cumulative effect of
interaction and disorder, we study baths comprising Ising spins with random
ferro- and antiferromagnetic interactions between the spins. Using the
resolvent operator method which goes beyond the standard Born-Markov master
equation approach, we show that, in the weak coupling regime, the decoherence
of the central spin at all times is entirely determined by the local-field
distribution or equivalently, the dynamical structure factor of the Ising bath.
We present analytic results for the Ising spin chain bath at arbitrary
temperature for different distributions of the intrabath interaction strengths.
We find clear evidence of non-Markovian behavior in the low temperature regime.
We also consider baths described by Ising models on higher-dimensional
lattices. We find that interactions lead to a significant reduction of the
decoherence. An important feature of interacting spinbaths is the saturation of
the asymptotic Markovian decay rate at high temperatures, as opposed to the
conventional Ohmic boson bath.Comment: 13 page
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