13,015 research outputs found
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic
in Lorentzian conformal geometry which parallels the theory of Willmore
surfaces in , are studied in this paper. We define two kinds of transforms
for such a surface, which produce the so-called left/right polar surfaces and
the adjoint surfaces. These new surfaces are again conformal Willmore surfaces.
For them holds interesting duality theorem. As an application spacelike
Willmore 2-spheres are classified. Finally we construct a family of homogeneous
spacelike Willmore tori.Comment: 19 page
Complete stationary surfaces in with total curvature
Applying the general theory about complete spacelike stationary (i.e. zero
mean curvature) surfaces in 4-dimensional Lorentz space , we
classify those regular algebraic ones with total Gaussian curvature . Such surfaces must be oriented and be congruent to either
the generalized catenoids or the generalized enneper surfaces. For
non-orientable stationary surfaces, we consider the Weierstrass representation
on the oriented double covering (of genus ) and generalize
Meeks and Oliveira's M\"obius bands. The total Gaussian curvature are shown to
be at least when is
algebraic-type. We conjecture that there do not exist non-algebraic examples
with .Comment: 22 page
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms
Spacelike Willmore surfaces in 4-dimensional Lorentzian space forms, a topic
in Lorentzian conformal geometry which parallels the theory of Willmore
surfaces in , are studied in this paper. We define two kinds of transforms
for such a surface, which produce the so-called left/right polar surfaces and
the adjoint surfaces. These new surfaces are again conformal Willmore surfaces.
For them holds interesting duality theorem. As an application spacelike
Willmore 2-spheres are classified. Finally we construct a family of homogeneous
spacelike Willmore tori.Comment: 19 page
Passive scheme with a photon-number-resolving detector for monitoring the untrusted source in a plug-and-play quantum-key-distribution system
A passive scheme with a beam splitter and a photon-number-resolving (PNR)
detector is proposed to verify the photon statistics of an untrusted source in
a plug-and-play quantum-key-distribution system by applying a three-intensity
decoy-state protocol. The practical issues due to statistical fluctuation and
detection noise are analyzed. The simulation results show that the scheme can
work efficiently when the total number of optical pulses sent from Alice to Bob
is above 10^8, and the dark count rate of the PNR detector is below 0.5
counts/pulse, which is realizable with current techniques. Furthermore, we
propose a practical realization of the PNR detector with a variable optical
attenuator combined with a threshold detector.Comment: 8 pages, 6 figure
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