355,194 research outputs found
A Combinatorial Formula for Certain Elements of Upper Cluster Algebras
We develop an elementary formula for certain non-trivial elements of upper
cluster algebras. These elements have positive coefficients. We show that when
the cluster algebra is acyclic these elements form a basis. Using this formula,
we show that each non-acyclic skew-symmetric cluster algebra of rank 3 is
properly contained in its upper cluster algebra
Adiabatic Mach-Zehnder interferometry on a quantized Bose-Josephson junction
We propose a scheme to achieve Mach-Zehnder interferometry using a quantized Bose-Josephson
junction with a negative charging energy. The quantum adiabatic evolution through a dynamical
bifurcation is used to accomplish the beam splitting and recombination. The negative charging energy
ensures the existence of a path-entangled state which enhances the phase measurement precision to the
Heisenberg limit. A feasible detection procedure is also presented. The scheme should be realizable with
current technology
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