19,089 research outputs found
Adiabatic Elimination in a Lambda System
This paper deals with different ways to extract the effective two-dimensional
lower level dynamics of a lambda system excited by off-resonant laser beams. We
present a commonly used procedure for elimination of the upper level, and we
show that it may lead to ambiguous results. To overcome this problem and better
understand the applicability conditions of this scheme, we review two rigorous
methods which allow us both to derive an unambiguous effective two-level
Hamiltonian of the system and to quantify the accuracy of the approximation
achieved: the first one relies on the exact solution of the Schrodinger
equation, while the second one resorts to the Green's function formalism and
the Feshbach projection operator technique.Comment: 14 pages, 3 figure
Tur\'an Graphs, Stability Number, and Fibonacci Index
The Fibonacci index of a graph is the number of its stable sets. This
parameter is widely studied and has applications in chemical graph theory. In
this paper, we establish tight upper bounds for the Fibonacci index in terms of
the stability number and the order of general graphs and connected graphs.
Tur\'an graphs frequently appear in extremal graph theory. We show that Tur\'an
graphs and a connected variant of them are also extremal for these particular
problems.Comment: 11 pages, 3 figure
Cryptographic Randomized Response Techniques
We develop cryptographically secure techniques to guarantee unconditional
privacy for respondents to polls. Our constructions are efficient and
practical, and are shown not to allow cheating respondents to affect the
``tally'' by more than their own vote -- which will be given the exact same
weight as that of other respondents. We demonstrate solutions to this problem
based on both traditional cryptographic techniques and quantum cryptography.Comment: 21 page
Frequency response in surface-potential driven electro-hydrodynamics
Using a Fourier approach we offer a general solution to calculations of slip
velocity within the circuit description of the electro-hydrodynamics in a
binary electrolyte confined by a plane surface with a modulated surface
potential. We consider the case with a spatially constant intrinsic surface
capacitance where the net flow rate is in general zero while harmonic rolls as
well as time-averaged vortex-like components may exist depending on the spatial
symmetry and extension of the surface potential. In general the system displays
a resonance behavior at a frequency corresponding to the inverse RC time of the
system. Different surface potentials share the common feature that the
resonance frequency is inversely proportional to the characteristic length
scale of the surface potential. For the asymptotic frequency dependence above
resonance we find a 1/omega^2 power law for surface potentials with either an
even or an odd symmetry. Below resonance we also find a power law omega^alpha
with alpha being positive and dependent of the properties of the surface
potential. Comparing a tanh potential and a sech potential we qualitatively
find the same slip velocity, but for the below-resonance frequency response the
two potentials display different power law asymptotics with alpha=1 and
alpha~2, respectively.Comment: 4 pages including 1 figure. Accepted for PR
Trees with Given Stability Number and Minimum Number of Stable Sets
We study the structure of trees minimizing their number of stable sets for
given order and stability number . Our main result is that the
edges of a non-trivial extremal tree can be partitioned into stars,
each of size or , so that every vertex is included in at most two
distinct stars, and the centers of these stars form a stable set of the tree.Comment: v2: Referees' comments incorporate
Deformation of LeBrun's ALE metrics with negative mass
In this article we investigate deformations of a scalar-flat K\"ahler metric
on the total space of complex line bundles over CP^1 constructed by C. LeBrun.
In particular, we find that the metric is included in a one-dimensional family
of such metrics on the four-manifold, where the complex structure in the
deformation is not the standard one.Comment: 20 pages, no figure. V2: added two references, filled a gap in the
proof of Theorem 1.2. V3: corrected a wrong statement about Kuranishi family
of a Hirzebruch surface stated in the last paragraph in the proof of Theorem
1.2, and fixed a relevant error in the proof. Also added a reference [24]
about Kuranishi family of Hirzebruch surface
Increased anxiety and depression in Danish cardiac patients with a type D personality:Cross-validation of the type D scale (DS14)
- …