A two-body study of dynamical expansion in the XXZ spin chain and equivalent interacting fermion models

Lo scopo di questa tesi è studiare l'espansione dinamica di due fermioni interagenti in una catena unidimensionale cercando di definire il ruolo degli stati legati durante l'evoluzione temporale del sistema. Lo studio di questo modello viene effettuato a livello analitico tramite la tecnica del Bethe ansatz, che ci fornisce autovalori ed autovettori dell'hamiltoniana, e se ne valutano le proprietà statiche. Particolare attenzione è stata dedicata alle caratteristiche dello spettro al variare dell'interazione tra le due particelle e alle caratteristiche degli autostati. Dalla risoluzione dell'equazione di Bethe vengono ricercate le soluzioni che danno luogo a stati legati delle due particelle e se ne valuta lo spettro energetico in funzione del momento del centro di massa. Si è studiato inoltre l'andamento del numero delle soluzioni, in particolare delle soluzioni che danno luogo ad uno stato legato, al variare della lunghezza della catena e del parametro di interazione. La valutazione delle proprietà dinamiche del modello è stata effettuata tramite l'utilizzo dell'algoritmo t-DMRG (time dependent - Density Matrix Renormalization Group). Questo metodo numerico, che si basa sulla decimazione dello spazio di Hilbert, ci permette di avere accesso a quantità che caratterizzano la dinamica quali la densità e la velocità di espansione. Da queste sono stati estratti i proli dinamici della densità e della velocità di espansione al variare del valore del parametro di interazione.

Prokaryotic community structure in ultra-slow spreading Southwest Indian Ridge.

The Southwest Indian Ridge segment that extends between 10° and 16° E has the slowest spreading rate of any other oceanic ridge (about 8.4 mm/year). In 2013 during the expedition ANTXXIX/8 seismology, geology, microbiology, heat flow analyses were carried out. Here, no hydrothermal plumes or black smoker systems were found but the results of the survey allowed to identify areas with peculiar characteristics: Area 1 with higher heat flux bsf; Area 2 where in 2002 the presence of hydrothermal emissions was hypothesized (Bach et al., 2002); Area 3 with anomalies of methane, ammonium, sulphide and dissolved inorganic carbon in pore water sediment profiles, and recovery of fauna vents. All these aspects suggest the presence of a hydrothermal circulation. Using Illumina 16S gene tag, statistical tools and phylogenetic trees, I provided a biological proof of the presence of hydrothermal circulation in this ridge segment. At Area 3, alpha and beta diversity indexes showed similarities with those described for venting microbial communities and about 40-70% of the dominant microbial community was found phylogenetically related to clones isolated hydrothermal-driven environments. Although the majority of chemosynthetic environment related taxa were not classified like autotrophic prokaryotes, some of them are key taxa in support of the presence of hydrothermal circulation, since they are partners of consortia or mediate specific reaction typically described for hydrothermal and seep environments, or are specialized organisms in exploiting labile organic substrates. Concluding, these results are remarkable because support the importance of ultra slow spreading ridge systems in contributing to global geochemical cycles and larval dispersion of vent fauna.

Alternative derivative expansion in Functional RG and application

We give a brief review of the Functional Renormalization method in quantum field theory, which is intrinsically non perturbative, in terms of both the Polchinski equation for the Wilsonian action and the Wetterich equation for the generator of the proper verteces. For the latter case we show a simple application for a theory with one real scalar field within the LPA and LPA' approximations. For the first case, instead, we give a covariant "Hamiltonian" version of the Polchinski equation which consists in doing a Legendre transform of the flow for the corresponding effective Lagrangian replacing arbitrary high order derivative of fields with momenta fields. This approach is suitable for studying new truncations in the derivative expansion. We apply this formulation for a theory with one real scalar field and, as a novel result, derive the flow equations for a theory with N real scalar fields with the O(N) internal symmetry. Within this new approach we analyze numerically the scaling solutions for N=1 in d=3 (critical Ising model), at the leading order in the derivative expansion with an infinite number of couplings, encoded in two functions V(phi) and Z(phi), obtaining an estimate for the quantum anomalous dimension with a 10% accuracy (confronting with Monte Carlo results).