34,159 research outputs found
Wave packet transmission of Bloch electron manipulated by magnetic field
We study the phenomenon of wave packet revivals of Bloch electrons and
explore how to control them by a magnetic field for quantum information
transfer. It is showed that the single electron system can be modulated into a
linear dispersion regime by the "quantized" flux and then an electronic wave
packet with the components localized in this regime can be transferred without
spreading. This feature can be utilized to perform the high-fidelity transfer
of quantum information encoded in the polarization of the spin. Beyond the
linear approximation, the re-localization and self-interference occur as the
novel phenomena of quantum coherence.Comment: 6 pages, 5 figures, new content adde
Of McKay Correspondence, Non-linear Sigma-model and Conformal Field Theory
The ubiquitous ADE classification has induced many proposals of often
mysterious correspondences both in mathematics and physics. The mathematics
side includes quiver theory and the McKay Correspondence which relates finite
group representation theory to Lie algebras as well as crepant resolutions of
Gorenstein singularities. On the physics side, we have the graph-theoretic
classification of the modular invariants of WZW models, as well as the relation
between the string theory nonlinear -models and Landau-Ginzburg
orbifolds. We here propose a unification scheme which naturally incorporates
all these correspondences of the ADE type in two complex dimensions. An
intricate web of inter-relations is constructed, providing a possible guideline
to establish new directions of research or alternate pathways to the standing
problems in higher dimensions.Comment: 35 pages, 4 figures; minor corrections, comments on toric geometry
and references adde
Quantum state swapping via qubit network with Hubbard interaction
We study the quantum state transfer (QST) in a class of qubit network with
on-site interaction, which is described by the generalized Hubbard model with
engineered couplings. It is proved that the system of two electrons with
opposite spins in this quantum network of sites can be rigorously reduced
into one dimensional engineered single Bloch electron models with central
potential barrier. With this observation we find that such system can perform a
perfect QST, the quantum swapping between two distant electrons with opposite
spins. Numerical results show such QST and the resonant-tunnelling for the
optimal on-site interaction strengths.Comment: 4 pages, 3 figure
Bounded Gaps Between Products of Distinct Primes
Let be an integer. We adapt the Maynard-Tao sieve to produce the
asymptotically best-known bounded gaps between products of distinct primes.
Our result applies to positive-density subsets of the primes that satisfy
certain equidistribution conditions. This improves on the work of Thorne and
Sono
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