24,039 research outputs found
Nuclear Spins as Quantum Memory in Semiconductor Nanostructures
We theoretically consider solid state nuclear spins in a semiconductor
nanostructure environment as long-lived, high-fidelity quantum memory. In
particular, we calculate, in the limit of a strong applied magnetic field, the
fidelity versus time of P donor nuclear spins in random bath environments of Si
and GaAs, and the lifetime of excited intrinsic spins in polarized Si and GaAs
environments. In the former situation, the nuclear spin dephases due to
spectral diffusion induced by the dipolar interaction among nuclei in the bath.
We calculate the decay of nuclear spin quantum memory in the context of Hahn
and Carr-Purcell-Meiboom-Gill (CPMG) refocused spin echoes using a formally
exact cluster expansion technique which has previously been successful in
dealing with electron spin dephasing in a solid state nuclear spin bath. With
decoherence dominated by transverse dephasing (T2), we find it feasible to
maintain high fidelity (losses of less than 10^{-6}) quantum memory on nuclear
spins for times of the order of 100 microseconds (GaAs:P) and 1 to 2
milliseconds (natural Si:P) using CPMG pulse sequences of just a few (~2-4)
applied pulses. We also consider the complementary situation of a central
flipped intrinsic nuclear spin in a bath of completely polarized nuclear spins
where decoherence is caused by the direct flip-flop of the central spin with
spins in the bath. Exact numerical calculations that include a sufficiently
large neighborhood of surrounding nuclei show lifetimes on the order of 1-5 ms
for both GaAs and natural Si. Our calculated nuclear spin coherence times may
have significance for solid state quantum computer architectures using
localized electron spins in semiconductors where nuclear spins have been
proposed for quantum memory storage
On the coarsest topology preserving continuity
We study a topology on a space of functions, called sticking topology, with
the property to be the weakest among the topologies preserving continuity. In
suitable frameworks, this topology preserves borelianity, local integrability,
right continuity and other properties. It is coarser than the locally uniform
convergence and it allows the presence of gliding humps as we show on examples.
We prove relative compactness criteria for this topology and we consider some
extensions.Comment: 14
Generalization of Clausius-Mossotti approximation in application to short-time transport properties of suspensions
In 1983 Felderhof, Ford and Cohen gave microscopic explanation of the famous
Clausius-Mossotti formula for the dielectric constant of nonpolar dielectric.
They based their considerations on the cluster expansion of the dielectric
constant, which relates this macroscopic property with the microscopic
characteristics of the system. In this article, we analyze the cluster
expansion of Felderhof, Ford and Cohen by performing its resummation
(renormalization). Our analysis leads to the ring expansion for the macroscopic
characteristic of the system, which is an expression alternative to the cluster
expansion. Using similarity of structures of the cluster expansion and the ring
expansion, we generalize (renormalize) the Clausius-Mossotti approximation. We
apply our renormalized Clausius-Mossotti approximation to the case of the
short-time transport properties of suspensions, calculating the effective
viscosity and the hydrodynamic function with the translational self-diffusion
and the collective diffusion coefficient. We perform calculations for
monodisperse hard-sphere suspensions in equilibrium with volume fraction up to
45%. To assess the renormalized Clausius-Mossotti approximation, it is compared
with numerical simulations and the Beenakker-Mazur method. The results of our
renormalized Clausius-Mossotti approximation lead to comparable or much less
error (with respect to the numerical simulations), than the Beenakker-Mazur
method for the volume fractions below (apart from a small
range of wave vectors in hydrodynamic function). For volume fractions above
, the Beenakker-Mazur method gives in most cases lower
error, than the renormalized Clausius-Mossotti approximation
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