613 research outputs found
On the rational subset problem for groups
We use language theory to study the rational subset problem for groups and
monoids. We show that the decidability of this problem is preserved under graph
of groups constructions with finite edge groups. In particular, it passes
through free products amalgamated over finite subgroups and HNN extensions with
finite associated subgroups. We provide a simple proof of a result of
Grunschlag showing that the decidability of this problem is a virtual property.
We prove further that the problem is decidable for a direct product of a group
G with a monoid M if and only if membership is uniformly decidable for
G-automata subsets of M. It follows that a direct product of a free group with
any abelian group or commutative monoid has decidable rational subset
membership.Comment: 19 page
Quantum theory for electron spin decoherence induced by nuclear spin dynamics in semiconductor quantum computer architectures: Spectral diffusion of localized electron spins in the nuclear solid-state environment
We consider the decoherence of a single localized electron spin due to its
coupling to the lattice nuclear spin bath in a semiconductor quantum computer
architecture. In the presence of an external magnetic field and at low
temperatures, the dominant decoherence mechanism is the spectral diffusion of
the electron spin resonance frequency due to the temporally fluctuating random
magnetic field associated with the dipolar interaction induced flip-flops of
nuclear spin pairs. The electron spin dephasing due to this random magnetic
field depends intricately on the quantum dynamics of the nuclear spin bath,
making the coupled decoherence problem difficult to solve. We provide a
formally exact solution of this non-Markovian quantum decoherence problem which
numerically calculates accurate spin decoherence at short times, which is of
particular relevance in solid-state spin quantum computer architectures. A
quantum cluster expansion method is developed, motivated, and tested for the
problem of localized electron spin decoherence due to dipolar fluctuations of
lattice nuclear spins. The method is presented with enough generality for
possible application to other types of spin decoherence problems. We present
numerical results which are in quantitative agreement with electron spin echo
measurements in phosphorus doped silicon. We also present spin echo decay
results for quantum dots in GaAs which differ qualitatively from that of the
phosphorus doped silicon system. Our theoretical results provide the ultimate
limit on the spin coherence (at least, as characterized by Hahn spin echo
measurements) of localized electrons in semiconductors in the low temperature
and the moderate to high magnetic field regime of interest in scalable
semiconductor quantum computer architectures.Comment: 23 pages, 15 figure
Wavefunction considerations for the central spin decoherence problem in a nuclear spin bath
Decoherence of a localized electron spin in a solid state material (the
``central spin'' problem) at low temperature is believed to be dominated by
interactions with nuclear spins in the lattice. This decoherence is partially
suppressed through the application of a large magnetic field that splits the
energy levels of the electron spin and prevents depolarization. However,
dephasing decoherence resulting from a dynamical nuclear spin bath cannot be
removed in this way. Fluctuations of the nuclear field lead to uncertainty of
the electron's precessional frequency in a process known as spectral diffusion.
This article considers the effect of the electron's wavefunction shape upon
spectral diffusion and provides wavefunction dependent decoherence time
formulas for free induction decay as well as spin echoes and concatenated
dynamical decoupling schemes for enhancing coherence. We also discuss dephasing
of a qubit encoded in singlet-triplet states of a double quantum dot. A central
theoretical result of this work is the development of a continuum approximation
for the spectral diffusion problem which we have applied to GaAs and InAs
materials specifically
Interactions between vaccinia virus and sensitized macrophages in vitro
The action of peritoneal exudate cells (PEC) from normal and vaccinia virus infected mice on infectious vaccinia virus particles was investigatedin vitro. PEC from immune mice showed a significantly higher infectivity titre reduction (virus clearance, VC) than normal cells. This effect could be clearly attributed to the macrophage. Vaccinia virus multiplied in PEC from normal animals while there was no virus propagation in cells from immunized mice. The release of adsorbed or engulfed virus was reduced significantly in PEC from immunized animals. Anti-vaccinia-antibodies seem to activate normal macrophages to increased virus clearance. This stimulating effect was demonstrable only in the IgG fraction of the antiserum.
The activity of macrophages from mice injected three times over a period of 14 days with vaccinia virus could be entirely blocked with anti-mouse-IgG, while PEC from mice injected one time six days previously were not inhibited
Theory of the ground state spin of the NV- center in diamond: I. Fine structure, hyperfine structure, and interactions with electric, magnetic and strain fields
The ground state spin of the negatively charged nitrogen-vacancy center in
diamond has been the platform for the recent rapid expansion of new frontiers
in quantum metrology and solid state quantum information processing. In ambient
conditions, the spin has been demonstrated to be a high precision magnetic and
electric field sensor as well as a solid state qubit capable of coupling with
nearby nuclear and electronic spins. However, in spite of its many outstanding
demonstrations, the theory of the spin has not yet been fully developed and
there does not currently exist thorough explanations for many of its
properties, such as the anisotropy of the electron g-factor and the existence
of Stark effects and strain splittings. In this work, the theory of the ground
state spin is fully developed for the first time using the molecular orbital
theory of the center in order to provide detailed explanations for the spin's
fine and hyperfine structures and its interactions with electric, magnetic and
strain fields.Comment: 12 pages, 3 figures, 3 table
Decay of Rabi oscillations induced by magnetic dipole interactions in diluted paramagnetic solids
Decay of Rabi oscillations of equivalent spins diluted in diamagnetic solid
matrix and coupled by magnetic dipole interactions is studied. It is shown that
these interactions result in random shifts of spin transient nutation
frequencies and thus lead to the decay of the transient signal. Averaging over
random spatial distribution of spins within the solid and over their spectral
positions within magnetic resonance line, we obtain analytical expressions for
the decay of Rabi oscillations. The rate of the decay in the case when the
half-width of magnetic resonance line exceeds Rabi frequency is found to depend
on the intensity of resonant microwave field and on the spin concentration. The
results are compared with the literature data for E1' centers in glassy silica
and [AlO4] centers in quartz.Comment: 14 pages, 3 figure
Electron spin as a spectrometer of nuclear spin noise and other fluctuations
This chapter describes the relationship between low frequency noise and
coherence decay of localized spins in semiconductors. Section 2 establishes a
direct relationship between an arbitrary noise spectral function and spin
coherence as measured by a number of pulse spin resonance sequences. Section 3
describes the electron-nuclear spin Hamiltonian, including isotropic and
anisotropic hyperfine interactions, inter-nuclear dipolar interactions, and the
effective Hamiltonian for nuclear-nuclear coupling mediated by the electron
spin hyperfine interaction. Section 4 describes a microscopic calculation of
the nuclear spin noise spectrum arising due to nuclear spin dipolar flip-flops
with quasiparticle broadening included. Section 5 compares our explicit
numerical results to electron spin echo decay experiments for phosphorus doped
silicon in natural and nuclear spin enriched samples.Comment: Book chapter in "Electron spin resonance and related phenomena in low
dimensional structures", edited by Marco Fanciulli. To be published by
Springer-Verlag in the TAP series. 35 pages, 9 figure
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