14 research outputs found
The Moment Problem for Continuous Positive Semidefinite Linear functionals
Let be a locally convex topology on the countable dimensional
polynomial -algebra \rx:=\reals[X_1,...,X_n]. Let be a closed
subset of , and let be a finitely generated
quadratic module in \rx. We investigate the following question: When is the
cone \Pos(K) (of polynomials nonnegative on ) included in the closure of
? We give an interpretation of this inclusion with respect to representing
continuous linear functionals by measures. We discuss several examples; we
compute the closure of M=\sos with respect to weighted norm- topologies.
We show that this closure coincides with the cone \Pos(K) where is a
certain convex compact polyhedron.Comment: 14 page
Single-electron transistors in electromagnetic environments
The current-voltage (I-V) characteristics of single-electron transistors
(SETs) have been measured in various electromagnetic environments. Some SETs
were biased with one-dimensional arrays of dc superconducting quantum
interference devices (SQUIDs). The purpose was to provide the SETs with a
magnetic-field-tunable environment in the superconducting state, and a
high-impedance environment in the normal state. The comparison of SETs with
SQUID arrays and those without arrays in the normal state confirmed that the
effective charging energy of SETs in the normal state becomes larger in the
high-impedance environment, as expected theoretically. In SETs with SQUID
arrays in the superconducting state, as the zero-bias resistance of the SQUID
arrays was increased to be much larger than the quantum resistance R_K = h/e^2
= 26 kohm, a sharp Coulomb blockade was induced, and the current modulation by
the gate-induced charge was changed from e periodic to 2e periodic at a bias
point 0<|V|<2D_0/e, where D_0 is the superconducting energy gap. The author
discusses the Coulomb blockade and its dependence on the gate-induced charge in
terms of the single Josephson junction with gate-tunable junction capacitance.Comment: 8 pages with 10 embedded figures, RevTeX4, published versio