Quantized Excitation Spectrum of the Classical Harmonic Oscillator in Zero-Point Radiation

We report that upon excitation by a single pulse, the classical harmonic oscillator immersed in classical electromagnetic zero-point radiation, as described by random electrodynamics, exhibits a quantized excitation spectrum in agreement to that of the quantum harmonic oscillator. This numerical result is interesting in view of the generally accepted idea that classical theories do not support quantized energy spectra.Comment: 5 pages, 3 figure

Dualism between Optical and Difference Parametric Amplification

Breaking the symmetry in a coupled wave system can result in unusual amplification behavior. In the case of difference parametric amplification the resonant pump frequency is equal to the difference, instead of the sum, frequency of the normal modes. We show that sign reversal in the symmetry relation of parametric coupling give rise to difference parametric amplification as a dual of optical parametric amplification. For optical systems, our result can potentially be used for efficient XUV amplification

Tensor products of Drinfeld modules and convolutions of Goss LL-series

Following the same framework of the special value results of convolutions of Goss and Pellarin $L$-series attached to Drinfeld modules that take values in Tate algebras by Papanikolas and the author, we establish special value results of convolutions of two Goss $L$-series attached to Drinfeld modules that take values in ${\mathbb{F}_q}(\!(\frac{1}{\theta})\!).$ Applying the class module formula of Fang to tensor products of two Drinfeld modules, we provide special value formulas for their $L$-functions. By way of the theory of Schur polynomials these identities take the form of specializations of convolutions of Rankin-Selberg type. Finally, we show an explicit computation of the regulators appearing in Fang's class module formula for tensor products as well as symmetric and alternating squares of Drinfeld modules.Comment: arXiv admin note: substantial text overlap with arXiv:2206.1493

Bis(4′-chloro-2,2′:6′,2′′-terpyridine-κ3 N,N′,N′′)iron(II) dinitrate dihydrate

The title complex, [Fe(C15H10ClN3)2](NO3)2·2H2O, has a six-coordinate iron(II) center balanced by two nitrate anions. The Fe atom lies on a twofold rotation axis. The complex exhibits an octa­hedral coordination configuration, where the dihedral angle between the two planar tridentate ligands is 92.4 (1)°. The crystal structure involves O—H⋯O hydrogen bonds