The Olea europaea L. var. sylvestris (Mill.) Lehr. forests in the Mediterranean area

This paper examines the forest communities dominated by Olea europaea L. var. sylvestris (Mill.) Lehr. that have been described up until now in the Mediterranean Region (including other isolated extrazonal areas in the northwestern Iberian Peninsula and in Northern Turkey) as more or less evolved aspects of woods, microwoods and high maquis that principally tend to make up climacic and edapho-climacic “series heads”. These forma- tions maintain a significant large-scale distributive potential within the infra- and thermomediterranean bioclimate belts (with a few penetrations into the mesomediterranean) with a dry-subhumid (and sometimes humid) ombrotype; however, they are currently quite rare and fragmented in the wake of large-scale deforestation and the impoverishment of old-growth communities dominated by a species known to live for millennia. The study was conducted through the analysis of phytosociological data taken from the scientific literature and other unpublished data regarding North-Africa (Morocco, Algeria), the Iberian Peninsula, the Balearic Islands as well as other islands from the Tyrrhenian area (Sardinia, Corsica, Sicily and its minor islands), the Italian Peninsula, the Balkan Peninsula, the Aegean region, Turkey and the southern Anatolian coast. A comparison between the different communities has shown a high floristic and physiognomic-structural homogeneity that justifies their categorization in the Quercetea ilicis class. The biogeographic and ecologic vicariance shown by the same formations within the large Mediterranean distribution range makes it pos- sible to subdivide them into the following orders and alliances: 1) Pistacio-Rhamnetalia alaterni [A) all. Tetraclini articulatae-Pistacion atlanticae (suball. Pistacienion atlanticae); B) all. Asparago albi-Rhamnion oleoidis; C) all. Oleo sylvestris-Ceratonion siliquae]; 2) Quercetalia calliprini [D) all. Ceratonio-Pistacion lentisci]; 3) Quercetalia ilicis [E) all. Querco rotundifoliae-Oleion sylvestris; F) all. Fraxino orni-Quercion ilicis; G) all. Erico arboreae-Quercion ilicis; H) all. Arbuto unedonis-Laurion nobilis (suball. Arbuto-Laurenion nobilis)]. Regarding the syntaxonomical aspect: (i) two new associations are described [Hippocrepido emeroidis-Oleetum sylvestris and Junipero foetidissimae-Oleetum sylvestris]; (ii) two new associations [Phillyreo latifoliae-Oleetum sylvestris Barbero, Quézel & Rivas-Martínez ex Gianguzzi & Bazan ass. nova and Calicotomo intermediae-Oleetum sylvestris Quézel, Barbero, Benabid, Loisel & Rivas-Martínez 1988 ex Gianguzzi & Bazan ass. nova] and a new subassocia- tion [Aro neglecti-Oleetum sylvestris Rivas-Martínez & Cantò 2002 corr. Rivas-Martínez & Cantò fraxinetosum angustifoliae Pérez Latorre, Galán de Mera, Deil & Cabezudo ex Gianguzzi & Bazan subass. nova] are leptotypified; (iii) a nomen novum of the association is redefined [Rhamno laderoi-Oleastretum sylvestris (Cantò, Ladero, Perez-Chiscano & Rivas-Martínez 2011) Gianguzzi & Bazan nom. nov.]

Coexistence of different scaling laws for the entanglement entropy in a periodically driven system

The out-of-equilibrium dynamics of many body systems has recently received a burst of interest, also due to experimental implementations. The dynamics of both observables, such as magnetization and susceptibilities, and quantum information related quantities, such as concurrence and entanglement entropy, have been investigated under different protocols bringing the system out of equilibrium. In this paper we focus on the entanglement entropy dynamics under a sinusoidal drive of the transverse magnetic field in the 1D quantum Ising model. We find that the area and the volume law of the entanglement entropy coexist under periodic drive for an initial non-critical ground state. Furthermore, starting from a critical ground state, the entanglement entropy exhibits finite size scaling even under such a periodic drive. This critical-like behaviour of the out-of-equilibrium driven state can persist for arbitrarily long time, provided that the entanglement entropy is evaluated on increasingly subsystem sizes, whereas for smaller sizes a volume law holds. Finally, we give an interpretation of the simultaneous occurrence of critical and non-critical behaviour in terms of the propagation of Floquet quasi-particles.Comment: contribution to the 11th Italian Quantum Information Science conference (IQIS), September 17th-20th, 2018 - Catania, Italy, 4 page

A waiting time phenomenon for thin film equations

We prove the occurrence of a waiting time phenomenon for solutions to fourth order degenerate parabolic differential equations which model the evolution of thin films of viscous fluids. In space dimension less or equal to three, we identify a general criterion on the growth of initial data near the free boundary which guarantees that for sufficiently small times the support of strong solutions locally does not increase. It turns out that this condition only depends on the smoothness of the diffusion coefficient in its point of degeneracy. Our approach combines a new version of Stampacchia's iteration lemma with weighted energy or entropy estimates. On account of numerical experiments, we conjecture that the aforementioned growth criterion is optimal

On Nilcompactifications of Prime Spectra of Commutative Rings

Given a ring R and S one of its ideals, we obtain a compactification of the prime spectrum of S through a mainly algebraic process. We name it the R-nilcompactification of SpecS. We study some categorical properties of this construction.Comment: 12 pages, 8 Tikz figure

Class of exact memory-kernel master equations

A well-known situation in which a non-Markovian dynamics of an open quantum system $S$ arises is when this is coherently coupled to an auxiliary system $M$ in contact with a Markovian bath. In such cases, while the joint dynamics of $S$-$M$ is Markovian and obeys a standard (bipartite) Lindblad-type master equation (ME), this is in general not true for the reduced dynamics of $S$. Furthermore, there are several instances (\eg the dissipative Jaynes-Cummings model) in which a {\it closed} ME for the $S$'s state {\it cannot} even be worked out. Here, we find a class of bipartite Lindblad-type MEs such that the reduced ME of $S$ can be derived exactly and in a closed form for any initial product state of $S$-$M$. We provide a detailed microscopic derivation of our result in terms of a mapping between two collision modelsComment: 9 pages, 1 figur