Symmetries of L\'evy processes on compact quantum groups, their Markov semigroups and potential theory

Strongly continuous semigroups of unital completely positive maps (i.e. quantum Markov semigroups or quantum dynamical semigroups) on compact quantum groups are studied. We show that quantum Markov semigroups on the universal or reduced C${}^*$-algebra of a compact quantum group which are translation invariant (w.r.t. to the coproduct) are in one-to-one correspondence with L\'evy processes on its $*$-Hopf algebra. We use the theory of L\'evy processes on involutive bialgebras to characterize symmetry properties of the associated quantum Markov semigroup. It turns out that the quantum Markov semigroup is GNS-symmetric (resp. KMS-symmetric) if and only if the generating functional of the L\'evy process is invariant under the antipode (resp. the unitary antipode). Furthermore, we study L\'evy processes whose marginal states are invariant under the adjoint action. In particular, we give a complete description of generating functionals on the free orthogonal quantum group $O_n^+$ that are invariant under the adjoint action. Finally, some aspects of the potential theory are investigated. We describe how the Dirichlet form and a derivation can be recovered from a quantum Markov semigroup and its L\'evy process and we show how, under the assumption of GNS-symmetry and using the associated Sch\"urmann triple, this gives rise to spectral triples. We discuss in details how the above results apply to compact groups, group C$^*$-algebras of countable discrete groups, free orthogonal quantum groups $O_n^+$ and the twisted $SU_q (2)$ quantum group.Comment: 54 pages, thoroughly revised, to appear in the Journal of Functional Analysi

Sinestesia in architettura. Parole e musica. Progetto architettonico e studio illuminotecnico e acustico di una biblioteca e auditorium a Pontassieve (Firenze)

La presente Tesi di Laurea ha come oggetto la progettazione architettonica, integrata da uno studio illuminotecnico e acustico, di una biblioteca di quartiere, con annesso auditorium, nel Comune di Pontassieve (Firenze). Il tema scaturisce dalla proposta progettuale avanzata dal Comune per la sistemazione del Parco comunale adiacente a Piazza della Libertà , situato nel quartiere denominato “I Villini”, a sud – est di Pontassieve capoluogo. Lo scopo essenziale della Tesi è quello di realizzare un progetto che assuma il ruolo di nuovo centro propulsore della vita culturale del quartiere e che sia dotato di una portata innovativa, pur nella continuità e nel dialogo con le preesistenze e l’ambiente circostante. La multidisciplinarità dell’intero iter progettuale, ovvero il continuo dialogo tra la materia compositivo-architettonica e quella illuminotecnico-acustica, si accorda coerentemente con l’ispirazione alla base del progetto, derivata dalla figura retorica della sinestesia, un fenomeno percettivo che unisce diversi campi semantici e sensoriali

The Italian Retranslations of Virginia Woolf's To the Lighthouse: A Corpus-based Literary Analysis

The research goal is to clarify how and to what degree the modernist style and features of Virginia Woolf’s To the Lighthouse are rendered in the eleven retranslations into Italian of this novel and whether these can be characterised as modernist novels themselves. A suitable methodology has been developed, which is drawn on the existing corpus methods for descriptive translation studies. Empirical evidence of the differences between target texts have been found, which in many cases have been interpreted as due to the translators’ voice or thumb-prints. The present research uses a systematic literary comparison of the retranslations by adopting a mixed-method and bottom-up (inductive) approach by developing an empirical corpus approach. This corpus is specifically tailored to identify and study both linguistic and non-linguistic modernist features throughout the texts such as stream of consciousness-indirect interior monologue and free indirect speech. All occurrences will be analysed in this thesis in the computations of inferential and comparative statistics such as lexical variety and lexical frequency. The target texts were digitised, and the resulting text files were then analysed by using a bespoke, novel computer program, which is capable of the mentioned functions not provided by commercially available software such as WordSmith Tools and WMatrix. Not only did this methodology enable performing in-depth explorations of micro- and macro-textual features, but it also allowed a mixed-method approach combining close-reading qualitative analysis with systematic quantitative comparisons. The obtained empirical results identify a progressive source-text orientation of the retranslations of Woolf’s style in a few aspects of a few target texts. The translators’ presence affected all the eleven target texts in register and style under the influence of the Italian translation norms usually attributed to the translation of literary classics

Retranslating Virginia Woolf's To the Lighthouse in Modernist and Post-modernist Italy: A Corpus-based Study

A corpus-based analysis is employed to study the literary style's evolution in eleven Italian retranslations of Virginia Woolf's To the Lighthouse. The aim is to examine how and to what degree the literary movements have affected the target texts. During the twentieth century, increasing criticism, scepticism, and distance concerning the world's traditional vision and life were reflected in post-modernist literature, although in different ways across the European countries. New literary forms took place also in Italian literature. Woolf's novel's modernist features are a case in point to test Berman's Retranslation Hypothesis, which states that further retranslations tend to be text-source-oriented. This close-reading analysis partially confirms the proposed theory and indicates that the examined retranslations also remain relatively distant from the modernist and post-modernist experiments in Italy

Mantle-Crust Isotopic Relationships along Mid Ocean Ridges: Constraints from the Analysis of Time Series

Isotopic relationships between parent mantle and daughter MORBs have been used to reveal the composite nature of the source tracking the missing components in their isotopic fingerprints. An opportunity to address this issue is given by temporal sections of single ridge segments where MORB and residual parent mantle peridotites can be assessed together. The possibility has been offered by the flexured and uplifted lithospheric slab that exposes, on the sea floor along a seafloor spreading flow line, a zero to 26 Ma relatively undisturbed lithospheric section (Vema Lithospheric Section or VLS) generated at the 80 km long Mid Atlantic ridge segment (EMAR) at 11°N. Temporal variations of the Nd isotopic composition of crustal basalts and parental mantle along the VLS reveal a large dispersion of residual isotopic composition with respect to the melt products. Equilibration with partially mixed melts can account for the observed relationships in the mantle rocks. The mean MORB isotopic composition and the average composition of the residues do not match because of the preferential extraction of the low-melting component. The compositional difference in both isotopic and elemental distribution is a function of the average degree of melting of the mantle. This observation can only be justified by progressive melting of composite lithologies where mantle potential temperature and amount of dispersed low-melting lithologies control the relative extent of melting of the mantle host and that of the dispersed heterogeneities resulting in differential fractions of mixed melts in the final products. This observation is confirmed by global correlations in Nd isotopes and chemical indicators of degree of melting from other portions of the mid ocean ridge system

Pyroxenites sow discord between parent mantle and daughter MORB

Mantle rocks and MORBs sampled along the 26 Ma record of the Vema Lithospheric Section or VLS (Mid Atlantic 11\ub0N) reveal a profound divergence between parent and daughter rocks in their compositional evolution. Finding the cause of this discordance requires comparing the evolution through time of the extent of melting with the produced crustal thickness and changes in the chemistry and isotopic composition of the sampled rocks. Mantle rocks show a progressive increase of their degree of melting during time, as if the potential temperature had increased in the last 26 Ma. However, plate kinematics reveal a significant decrease of the spreading rate that should sensibly lower the average degree of melting. MORB inferred degree of melting decreases through time while their isotopic fingerprint becomes more depleted. The observed variations can be reconciled by considering that a variable amount of lowmelting lithologies entered the melting region. The observed decoupling of the degree of melting of mantle and MORB is attributed to the effect of undercooling exerted by lowmelting heterogeneities due to heat diffusion before the host mantle starts melting itself. The observed temporal evolution is matched by a decreasing amount of low-melting, isotopically enriched, lithologies (pyroxenites) dispersed in a DMM-type host mantle. Approaching the present day setting, the amount of pyroxenites has become negligible restoring harmony between parent mantle and MORB daughters in terms of degree of melting and integrated melt production. This observation can be extended to the entire MOR system revealing the sensitivity of the spreading system to the amount of low-melting lithologies dispersed in the depleted mantle host. At limit conditions of the mantle potential temperature, heat diffusion into the low-solidus melting lithology prevents the host mantle from reaching its solidus

Nonchondritic 142Nd in suboceanic mantle peridotites

The discovery that several solid Earth reservoirs have a superchondritic 142Nd/144Nd ratio led to the hypothesis that either the bulk silicate Earth is not chondritic or that a subchondritic reservoir lies hidden somewhere within the Earth's interior. One important reservoir, i.e., mid-ocean ridge peridotites representing the main component of the upper oceanic mantle and the source of mid-ocean ridge basalt, has never been tested for 142Nd/144Nd. We determined the 142Nd/144Nd ratio in clinopyroxene separated from two peridotites and a pyroxenite from the SW Indian Ridge and one peridotite from the northern Mid-Atlantic Ridge. All samples analyzed have superchondritic 142Nd/144Nd ratios in line with mantle-derived material measured to date, except for some ancient cratonic rocks

Water-rich basalts at mid-ocean-ridge cold spots

Although water is only present in trace amounts in the suboceanic upper mantle, it is thought to play a significant role in affecting mantle viscosity, melting and the generation of crust at mid-ocean ridges. The concentration of water in oceanic basalts has been observed to stay below 0.2wt%, except for water-rich basalts sampled near hotspots and generated by 'wet' mantle plumes. Here, however, we report unusually high water content in basaltic glasses from a cold region of the mid-ocean-ridge system in the equatorial Atlantic Ocean. These basalts are sodium-rich, having been generated by low degrees of melting of the mantle, and contain unusually high ratios of light versus heavy rare-earth elements, implying the presence of garnet in the melting region. We infer that water-rich basalts from such regions of thermal minima derive from low degrees of 'wet' melting greater than 60 km deep in the mantle, with minor dilution by melts produced by shallower 'dry' melting—a view supported by numerical modelling. We therefore conclude that oceanic basalts are water-rich not only near hotspots, but also at 'cold spots'