Trim-to-Coherence Fourier Transform

We introduce a discrete Fourier transform technique which extracts more spectral information from a given time series data set than conventional discrete Fourier transform (DFT). Valid information is obtained between the spectral bins of conventional DFT, scalloping error is greatly reduced, and amplitude and phase of Fourier components are more true to the process under study as with conventional DFT. We call the general idea Trim-to-Coherence Fourier Transform, and its particular embodiment ‘Phase-Rotation Fourier Transform’. Treatment of the raw data is minimally invasive; e.g. there is no zero padding.     

λ-definierbare Funktionen auf Peanoalgebren

Ohne Zusammenfassung     

Experimental investigation of Risken–Nummedal–Graham–Haken laser instability in fiber ring lasers

It has been suggested (by Pessina et al. in 1997) that the observed spontaneous mode beating of erbium-doped-fiber ring lasers can be explained as the multimode instability described in 1968 by Risken and Nummedal and by Graham and Haken (the RNGH instability), which is based on Rabi-splitting-induced gain. If true, this would constitute the first ever example of this instability in an actual experiment. We test the hypothesis through a quantitative experimental investigation. We demonstrate that there is indeed a clear, marked onset of the instability, a fact that went unnoticed in all previous experiments because it is very close to the lasing threshold. We intentionally raise cavity loss to better separate onset of lasing and of instability. We obtain quantitative information on the instability onset. An interpretation as the predicted second threshold is reasonable provided inhomogeneous gain line broadening is taken into account. We also observe that instability above its onset exists only intermittently; this may hint at a subcritical bifurcation and noise-driven transitions. In any event, the RNGH mechanism is present, if not in a pure form. PACS 42.65.Sf; 42.60.Mi; 42.55.Wd     

On a theorem of Tate

We study applications of divisibility properties of recurrence sequences to Tate’s theory of abelian varieties over finite fields.      

Pyrazolyc 3-hydroxychromones: Regulation of ESIPT reaction by the “flavonol-like” intramolecular hydrogen bonding to carbonyl group oxygen,which dominates over the “alternative” H-bond to heterocyclic nitrogen

Two isomeric pyrazole derivatives of 3-hydroxychromone (3HC) with and without the possibility of the multiple intramolecular hydrogen bonds formation were compared theoretically and experimentally with the aim to find out whether the excited state intramolecular proton transfer (ESIPT) reaction follows the traditional to the most of 3HCs “flavonol-like” direction towards the CO group oxygen or an “alternative” direction towards the heterocyclic nitrogen atom.Quantum-chemical modeling and comparative study of the experimental spectral parameters of the title compounds indicated the preferential realization of “flavonol-like” ESIPT to oxygen channel.The 3HC systems with the “alternative” intramolecular hydrogen bond to nitrogen were characterized as low fluorescent and practically unable to ESIPT with participation of the nitrogen containing heterocyclic unit.     

A new form of symplectically invariant multimode uncertainty relations

We derive symplectically invariant uncertainty relations for a set of canonically conjugated variables. The uncertainty relations obtained are multimode analogs of the Robertson–Schrödinger inequalities. Our uncertainty relations are equivalent to the necessary and sufficient conditions for a matrix to be a correlation matrix of some quantum state, obtained by R. Simon and coauthors. The advantage of our inequalities, compared to that suggested by Simon, consists in its simplicity and more obvious symplectic invariance. We derive our inequalities for the case of a two-mode system in explicit form. Particular cases of small and large degrees of correlation between the first and second modes are analyzed in detail.