40,915 research outputs found
A generalization of the q-Saalschutz sum and the Burge transform
A generalization of the q-(Pfaff)-Saalschutz summation formula is proved.
This implies a generalization of the Burge transform, resulting in an
additional dimension of the ``Burge tree''. Limiting cases of our summation
formula imply the (higher-level) Bailey lemma, provide a new decomposition of
the q-multinomial coefficients, and can be used to prove the Lepowsky and Primc
formula for the A_1^{(1)} string functions.Comment: 18 pages, AMSLaTe
Robust Online Monitoring of Signal Temporal Logic
Signal Temporal Logic (STL) is a formalism used to rigorously specify
requirements of cyberphysical systems (CPS), i.e., systems mixing digital or
discrete components in interaction with a continuous environment or analog com-
ponents. STL is naturally equipped with a quantitative semantics which can be
used for various purposes: from assessing the robustness of a specification to
guiding searches over the input and parameter space with the goal of falsifying
the given property over system behaviors. Algorithms have been proposed and
implemented for offline computation of such quantitative semantics, but only
few methods exist for an online setting, where one would want to monitor the
satisfaction of a formula during simulation. In this paper, we formalize a
semantics for robust online monitoring of partial traces, i.e., traces for
which there might not be enough data to decide the Boolean satisfaction (and to
compute its quantitative counterpart). We propose an efficient algorithm to
compute it and demonstrate its usage on two large scale real-world case studies
coming from the automotive domain and from CPS education in a Massively Open
Online Course (MOOC) setting. We show that savings in computationally expensive
simulations far outweigh any overheads incurred by an online approach
Theory of the spatial structure of non-linear lasing modes
A self-consistent integral equation is formulated and solved iteratively
which determines the steady-state lasing modes of open multi-mode lasers. These
modes are naturally decomposed in terms of frequency dependent biorthogonal
modes of a linear wave equation and not in terms of resonances of the cold
cavity. A one-dimensional cavity laser is analyzed and the lasing mode is found
to have non-trivial spatial structure even in the single-mode limit. In the
multi-mode regime spatial hole-burning and mode competition is treated exactly.
The formalism generalizes to complex, chaotic and random laser media.Comment: 4 pages, 3 figure
Pump-induced Exceptional Points in Lasers
We demonstrate that the above-threshold behavior of a laser can be strongly
affected by exceptional points which are induced by pumping the laser
nonuniformly. At these singularities, the eigenstates of the non-Hermitian
operator which describes the lasing modes coalesce. In their vicinity, the
laser may turn off even when the overall pump power deposited in the system is
increased. Such signatures of a pump- induced exceptional point can be
experimentally probed with coupled ridge or microdisk lasers.Comment: 4.5 pages, 4 figures, final version including additional FDTD dat
Correlated Quantum Memory: Manipulating Atomic Entanglement via Electromagnetically Induced Transparency
We propose a feasible scheme of quantum state storage and manipulation via
electromagnetically induced transparency (EIT) in flexibly
multi-ensembles of three-level atoms. For different atomic array
configurations, one can properly steer the signal and the control lights to
generate different forms of atomic entanglement within the framework of linear
optics. These results shed new light on designing the versatile quantum memory
devices by using, e.g., an atomic grid.Comment: 5 pages, 1 figur
Coalescence and Anti-Coalescence Interference of Two-Photon Wavepacket in a Beam Splitter
We study a general theory on the interference of two-photon wavepacket in a
beam splitter (BS). We find that the perfect coalescence interference requires
a symmetric spectrum of two-photon wavepacket which can be entangled or
un-entangled. Furthermore, we introduce a two-photon wavepacket with
anti-symmetric spectrum, which is related with photon entanglement and shows a
perfect anti-coalescence effect. The theory present uniform and complete
explanation to two-photon interference.Comment: 5 pages, 2 figure
Interaction-induced mode switching in steady-state microlasers
We demonstrate that due to strong modal interactions through cross-gain
saturation, the onset of a new lasing mode can switch off an existing mode via
a negative power slope. In this process of interaction-induced mode switching
(IMS) the two involved modes maintain their identities, i.e. they do not change
their spatial field patterns or lasing frequencies. For a fixed pump profile, a
simple analytic criterion for the occurrence of IMS is given in terms of their
self- and cross-interaction coefficients and non-interacting thresholds, which
is verified for the example of a two-dimensional microdisk laser. When the
spatial pump profile is varied as the pump power is increased, IMS can be
induced even when it would not occur with a fixed pump profile, as we show for
two coupled laser cavities. Our findings apply to steady-state lasing and are
hence different from dynamical mode switching or hopping. IMS may have
potential applications in robust and flexible all-optical switching.Comment: 14 pages, 5 figure
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