Scarring in open chaotic systems: The local density of states

Chaotic Hamiltonians are known to follow Random Matrix Theory (RMT) ensembles in the apparent randomness of their spectra and wavefunction statistics. Deviations form RMT also do occur, however, due to system-specific properties, or as quantum signatures of classical chaos. Scarring, for instance, is the enhancement of wavefunction intensity near classical periodic orbits, and it can be characterized by a local density of states (or local spectrum) that clearly deviates from RMT expectations, by exhibiting a peaked envelope, which has been described semiclassically. Here, the system is connected to an opening, the local density of states is introduced for the resulting non-Hermitian chaotic Hamiltonian, and estimated a priori in terms of the Green's function of the closed system and the open channels. The predictions obtained are tested on quantum maps coupled both to a single-channel opening and to a Fresnel-type continuous opening. The main outcome is that strong coupling to the opening gradually suppresses the energy dependence of the local density of states due to scarring, and restores RMT behavior.Comment: 9 pages, 3 figure

Neighborhoods of periodic orbits and the stationary distribution of a noisy chaotic system

The finest state space resolution that can be achieved in a physical dynamical system is limited by the presence of noise. In the weak-noise approximation the neighborhoods of deterministic periodic orbits can be computed as distributions stationary under the action of a local Fokker-Planck operator and its adjoint. We derive explicit formulae for widths of these distributions in the case of chaotic dynamics, when the periodic orbits are hyperbolic. The resulting neighborhoods form a basis for functions on the attractor. The global stationary distribution, needed for calculation of long-time expectation values of observables, can be expressed in this basis.Comment: 6 pages, 3 figure

Teoria di campo conforme

In questa trattazione si introduce e si sviluppa la teoria di campo conforme. Dal principale riferimento bibliografico si è voluto estrarre ed elaborare un testo che, più che sull'esaustività della trattazione, si concentra sulle particolari proprietà della teoria date proprio dall'imposta invarianza sotto trasformazioni conformi. Partendo da una breve introduzione storica seguita dall'esposizione di alcune nozioni preliminari utili (Capitolo 1) si passa successivamente allo sviluppo della teoria in d >2 dimensioni (Capitolo 2) con particolare attenzione alla struttura di gruppo delle trasformazioni conformi e alle correnti conservate ottenute dalla presenza di tali simmetrie della teoria (Paragrafo 2.4). Inoltre particolare enfasi è data alle condizioni imposte sulle funzioni di correlazione dalle simmetrie (Paragrafo 2.5). Successivamente (Capitolo 3) si procede con lo studio della teoria conforme in due dimensioni, dove essa possiede particolari proprietà che la distinguono dal caso di background a più alte dimensioni. In tale contesto si considera l'algebra di Virasoro (Paragrafo 3.2) e si espongono brevemente i casi del bosone libero (Paragrafo 3.5) e del fermione libero (Paragrafo 3.6). Si ha infine (Capitolo 4) un'introduzione alla teoria nel caso di spazi con topologie non banali, in particolare il toro, concentrandosi sulla costruzione del background e sul gruppo modulare (Paragrafo 4.2)

Alcune osservazioni sull’uso e sulla diffusione della coroplastica rituale nei depositi dell’Italia meridionale: il caso di Locri Epizefiri

In the last decades, research on the coroplastica and the votive deposits in Italy has significantly developed; in particular the findings from Locri Epizefiri represent an excellent opportunity to investigate the archaeological expressions of worship, and to begin decoding their ritual traces. The important deposit excavated by P. Orsi in the Mannella’s site is a very well-known and composite example, characterized by the presence of pinakes, the clay tablets which have allowed researchers to investigate the most peculiar ceremonies of the greek colony. We present a case study to investigate the expressive grammar of rituality, to discuss methodological and interpretative problems, and to try and read the Mannella’s deposit within the worship system of the local community. The problem of the recognition of the main sanctuary of Persephone is faced, and also the meaning and function of the pinakes and their role in the behavior-system of the sacred polis. We offer a new interpretation, primarily based on a functional-type research, which starts from the different levels of context that can be reconstructed

Statistics of Chaotic Resonances in an Optical Microcavity

Distributions of eigenmodes are widely concerned in both bounded and open systems. In the realm of chaos, counting resonances can characterize the underlying dynamics (regular vs. chaotic), and is often instrumental to identify classical-to-quantum correspondence. Here, we study, both theoretically and experimentally, the statistics of chaotic resonances in an optical microcavity with a mixed phase space of both regular and chaotic dynamics. Information on the number of chaotic modes is extracted by counting regular modes, which couple to the former via dynamical tunneling. The experimental data are in agreement with a known semiclassical prediction for the dependence of the number of chaotic resonances on the number of open channels, while they deviate significantly from a purely random-matrix-theory-based treatment, in general. We ascribe this result to the ballistic decay of the rays, which occurs within Ehrenfest time, and importantly, within the timescale of transient chaos. The present approach may provide a general tool for the statistical analysis of chaotic resonances in open systems.Comment: 5 pages, 5 figures, and a supplemental informatio

Zinc(II)-methimazole complexes: synthesis and reactivity

The tetrahedral S-coordinated complex [Zn(MeImHS)(4)](ClO4)(2), synthesised from the reaction of [Zn(ClO4)(2)] with methimazole (1-methyl-3H-imidazole-2-thione, MeImHS), reacts with triethylamine to yield the homoleptic complex [Zn(MeImS)(2)] (MeImS = anion methimazole). ESI-MS and MAS C-13-NMR experiments supported MeImS acting as a (N, S)-chelating ligand. The DFT-optimised structure of [Zn(MeImS)(2)] is also reported and the main bond lengths compared to those of related Zn-methimazole complexes. The complex [Zn(MeImS)(2)] reacts under mild conditions with methyl iodide and separates the novel complex [Zn(MeImSMe)(2)I-2] (MeImSMe = S-methylmethimazole). X-ray diffraction analysis of the complex shows a ZnI2N2 core, with the methyl thioethers uncoordinated to zinc. Conversely, the reaction of [Zn( MeImS)(2)] with hydroiodic acid led to the formation of the complex [Zn(MeImHS)(2)I-2] having a ZnI2S2 core with the neutral methimazole units S-coordinating the metal centre. The Zn-coordinated methimazole can markedly modify the coordination environment when changing from its thione to thionate form and vice versa. The study of the interaction of the drug methimazole with the complex [Zn(MeIm)(4)](2+) (MeIm = 1-methylimidazole) - as a model for Zn-enzymes containing a N-4 donor set from histidine residues shows that methimazole displaces only one of the coordinated MeIm molecules; the formation constant of the mixed complex [Zn(MeIm)(3)(MeImHS)](2+) was determined