1,014 research outputs found
Dirac gap-induced graphene quantum dot in an electrostatic potential
A spatially modulated Dirac gap in a graphene sheet leads to charge
confinement, thus enabling a graphene quantum dot to be formed without the
application of external electric and magnetic fields [Appl. Phys. Lett.
\textbf{97}, 243106 (2010)]. This can be achieved provided the Dirac gap has a
local minimum in which the states become localised. In this work, the physics
of such a gap-induced dot is investigated in the continuum limit by solving the
Dirac equation. It is shown that gap-induced confined states couple to the
states introduced by an electrostatic quantum well potential. Hence the region
in which the resulting hybridized states are localised can be tuned with the
potential strength, an effect which involves Klein tunneling. The proposed
quantum dot may be used to probe quasi-relativistic effects in graphene, while
the induced confined states may be useful for graphene-based nanostructures.Comment: 12 pages, 7 figure
Certainty in Heisenberg's uncertainty principle: Revisiting definitions for estimation errors and disturbance
We revisit the definitions of error and disturbance recently used in
error-disturbance inequalities derived by Ozawa and others by expressing them
in the reduced system space. The interpretation of the definitions as
mean-squared deviations relies on an implicit assumption that is generally
incompatible with the Bell-Kochen-Specker-Spekkens contextuality theorems, and
which results in averaging the deviations over a non-positive-semidefinite
joint quasiprobability distribution. For unbiased measurements, the error
admits a concrete interpretation as the dispersion in the estimation of the
mean induced by the measurement ambiguity. We demonstrate how to directly
measure not only this dispersion but also every observable moment with the same
experimental data, and thus demonstrate that perfect distributional estimations
can have nonzero error according to this measure. We conclude that the
inequalities using these definitions do not capture the spirit of Heisenberg's
eponymous inequality, but do indicate a qualitatively different relationship
between dispersion and disturbance that is appropriate for ensembles being
probed by all outcomes of an apparatus. To reconnect with the discussion of
Heisenberg, we suggest alternative definitions of error and disturbance that
are intrinsic to a single apparatus outcome. These definitions naturally
involve the retrodictive and interdictive states for that outcome, and produce
complementarity and error-disturbance inequalities that have the same form as
the traditional Heisenberg relation.Comment: 15 pages, 8 figures, published versio
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