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Concept# Lambda

Summary

Lambda ('l{md@; uppercase Λ, lowercase λ; λάμ(β)δα, lám(b)da) is the eleventh letter of the Greek alphabet, representing the voiced alveolar lateral approximant l. In the system of Greek numerals, lambda has a value of 30. Lambda is derived from the Phoenician Lamed . Lambda gave rise to the Latin L and the Cyrillic El (Л). The ancient grammarians and dramatists give evidence to the pronunciation as laːbdaː (λάβδα) in Classical Greek times. In Modern Greek, the name of the letter, Λάμδα, is pronounced ˈlam.ða.
In early Greek alphabets, the shape and orientation of lambda varied. Most variants consisted of two straight strokes, one longer than the other, connected at their ends. The angle might be in the upper-left, lower-left ("Western" alphabets) or top ("Eastern" alphabets). Other variants had a vertical line with a horizontal or sloped stroke running to the right. With the general adoption of the Ionic alphabet, Greek settled on an angle at the top; the Romans put the angle at the

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An optically-active multi-layer dielectric structure comprises an optically active zone between two mirrors forming a Fabry-Perot microcavity. The optically active zone comprises an optically active material of wavelength lambda centred in a layer of high refractory index medium of optical thickness less than lambda/2 surrounded by two layers of low refractory index medium each of optical thickness less than &lambda/4,the combined optical thickness of said three layers making up the optically active zone being less than or equal to 3lambda/4. This structure behaves like a lambda/2 high index cavity except that there is a maximum of the optical field in the centre of the cavity instead of the usual node. This phase-shifted structure is useful for planar light emitting devices, vertical cavity lasers, and photo-detectors.

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We report a systematic study of the magnetoelectric (ME) voltage coefficient as a complex quantity in the particulate composite of ferroelectric solid solution 0.94Pb(Fe1/2N1/2)O-3-0.06PbTiO(3)(PFN-PT) with CoFe2O4(CFO) and NiFe2O4 (NFO) ferrites. The results show that the real part of the ME voltage coefficient (alpha') is highly influenced by the magnetostrictive phase through lambda(H). NFO produces larger alpha' at a lower magnetic field, which originates from the softer magnetic properties. In addition, alpha' was found to be positive for NFO composite, while CFO composite shows a negative ME voltage coefficient at high magnetic fields. We argue that the field dependence of alpha' can be interpreted using the dynamic piezomagnetic coefficient, q(ac) = partial derivative lambda(ac)/partial derivative H. The imaginary part of the ME voltage coefficient (alpha '') was also determined for all composites. Both the alpha' and alpha '' show a peak at the same magnetic field, which is attributed to the maximum dynamic piezomagnetism when the magnetic domains are collectively rotated by the dc bias magnetic field. Our results show that the ME voltage coefficient in the composites of PFN-PT/(Co,Ni)Fe2O4 is highly influenced by the content, magnetic softness and field dependence behaviour of magnetostriction of the piezomagnetic phase.

2019We study fixed points with N scalar fields in 4 - epsilon dimensions to leading order in epsilon using a bottom-up approach. We do so by analyzing O(N) invariants of the quartic coupling lambda(ijkl) that describes such CFTs. In particular, we show that lambda(iijj) and lambda ijkl2 are restricted to a specific domain, refining a result by Rychkov and Stergiou. We also study averages of one-loop anomalous dimensions of composite operators without gradients. In many cases, we are able to show that the O(N) fixed point maximizes such averages. In the final part of this work, we generalize our results to theories with N complex scalars and to bosonic QED. In particular we show that to leading order in epsilon, there are no bosonic QED fixed points with N < 183 flavors.