Spectrum of a family of operators

Having as start point the classic definitions of resolvent set and spectrum of a linear bounded operator on a Banach space, we introduce the resolvent set and spectrum of a family of linear bounded operators on a Banach space. In addition, we present some results which adapt to asymptotic case the classic results.Comment: 23 page

Growth and economic crises in Turkey: leaving behind a turbulent past?

Turkey's performance in the current crisis shows that it has managed to weather the global stormy conditions relatively well and avoid collapsing into a full-fledged currency and financial crisis. On the face of it, one could conclude economic reforms introduced since 2001 have paid off and today's performance marks a clean break with the past. But there are also indications that the Turkish economy still retains some of its old vulnerabilities. By determining how resilient Turkey's economy has become to domestic and international economic volatility, one can better assess the sustainability of the accelerated economic convergence process on which Turkey embarked after the 2001 crisis.Economic crisis, external vulnerabilities, growth, economic convergence, fiscal consolidation, structural reforms, enlargement, boom-bust growth pattern, Macovei

Quantum dynamics of a two-level emitter with modulated transition frequency

The resonant quantum dynamics of an excited two-level emitter is investigated via classical modulation of its transition frequency while simultaneously the radiator interacts with a broadband electromagnetic field reservoir. The frequency of modulation is selected to be of the order of the bare-state spontaneous decay rate. In this way, one can induce quantum interference effects and, consequently, quantum coherences among multiple decaying transition pathways. Depending on the modulation depth and its absolute phase, both the spontaneous emission and the frequency shift may be conveniently modified and controlled.Comment: 8 pages, 6 figure

Amplifying ultraweak transitions in collective systems via quantum interference

We investigate laser-induced quantum interference phenomena in superradiance processes and in an ensemble of initially excited $\Lambda-$type closely packed three-level emitters. The lower doublet levels are pumped with a coherent laser field. Due to constructive quantum interference effects, the superradiance occurs on a much weaker atomic transition which is not the case in the absence of the coherent driving. This result may be of visible relevance for enhancing ultraweak transitions in atomic or atomic-like systems, respectively, or for high-frequency lasing effects.Comment: 12 pages, 3 figure