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

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

An Assyrian King in Turin

At the Museum of Antiquity in Turin (Italy) is now again exhibited the famous portrait of Sargon II (donated by P.E. Botta to his hometown, along with another portrait of a courtier) together with a few small fragments of other lesser-known Assyrian wall reliefs, from Khorsabad and Nineveh. In this paper we present some considerations on the two Botta’s reliefs, considering in particular the representational codes used by artists in the composition of the Assyrian royal portraitsEn el museo de Antigüedades de Turín (Italia), actualmente se exhibe de nuevo el famoso retrato de Sargón II (donado por P.E. Botta a su ciudad natal a la par que otro retrato de un cortesano) junto con unos cuantos fragmentos pequeños de otros relieves murales asirios menos conocidos de Jorsabad y Nínive. En el presente artículo exponemos algunas consideraciones sobre los dos relieves de Botta, valorando en particular los códigos de representación utilizados por los artistas en la composición de los retratos asirios reale