Entanglement entropy in restricted integrable spin-chains

In questa tesi abbiamo presentato il calcolo dell’Entropia di Entanglement di un sistema quantistico unidimensionale integrabile la cui rappresentazione statistica é data dal modello RSOS, il cui punto critico é una realizzazione su reticolo di tutti i modelli conformi minimali. Sfruttando l’integrabilitá di questi modelli, abbiamo svolto il calcolo utilizzando la tecnica delle Corner Transfer Matrices (CTM). Il risultato ottenuto si discosta leggermente dalla previsione di J. Cardy e P. Calabrese ricavata utilizzando la teoria dei campi conformi descriventi il punto critico. Questa differenza é stata imputata alla non-unitarietá del modello studiato, in quanto la tecnica CTM studia il ground state, mentre la previsione di Cardy e Calabrese si focalizza sul vuoto conforme del modello: nel caso dei sistemi non-unitari questi due stati non coincidono, ma possono essere visti come eccitazioni l’uno dell’altro. Dato che l’Entanglement é un fenomeno genuinamente quantistico e il modello RSOS descrive un sistema statistico classico bidimensionale, abbiamo proposto una Hamiltoniana quantistica unidimensionale integrabile la cui rappresentazione statistica é data dal modello RSOS.

Implementation of network entropy algorithms on hpc machines, with application to high-dimensional experimental data

Network Theory is a prolific and lively field, especially when it approaches Biology. New concepts from this theory find application in areas where extensive datasets are already available for analysis, without the need to invest money to collect them. The only tools that are necessary to accomplish an analysis are easily accessible: a computing machine and a good algorithm. As these two tools progress, thanks to technology advancement and human efforts, wider and wider datasets can be analysed. The aim of this paper is twofold. Firstly, to provide an overview of one of these concepts, which originates at the meeting point between Network Theory and Statistical Mechanics: the entropy of a network ensemble. This quantity has been described from different angles in the literature. Our approach tries to be a synthesis of the different points of view. The second part of the work is devoted to presenting a parallel algorithm that can evaluate this quantity over an extensive dataset. Eventually, the algorithm will also be used to analyse high-throughput data coming from biology.

Horizon entropy from scratch

Scopo di questo lavoro di tesi è lo studio di alcune proprietà delle teorie generali della gravità in relazione alla meccanica e la termodinamica dei buchi neri. In particolare, la trattazione che seguirà ha lo scopo di fornire un percorso autoconsistente che conduca alla nozione di entropia di un orizzonte descritta in termini delle carica di Noether associata all'invarianza del funzionale d'azione, che descrive la teoria gravitazionale in considerazione, per trasformazioni di coordinate generali. Si presterà particolare attenzione ad alcune proprietà geometriche della Lagrangiana, proprietà che sono indipendenti dalla particolare forma della teoria che si sta prendendo in considerazione; trattasi cioè non di proprietà dinamiche, legate cioè alla forma delle equazioni del moto del campo gravitazionale, ma piuttosto caratteristiche proprie di qualunque varietà rappresentante uno spaziotempo curvo. Queste caratteristiche fanno sì che ogni teoria generale della gravità possieda alcune grandezze definite localmente sullo spaziotempo, in particolare una corrente di Noether e la carica ad essa associata. La forma esplicita della corrente e della carica dipende invece dalla Lagrangiana che si sceglie di adottare per descrivere il campo gravitazionale. Il lavoro di tesi sarà orientato prima a descrivere come questa corrente di Noether emerge in qualunque teoria della gravità invariante per trasformazioni generali e come essa viene esplicitata nel caso di Lagrangiane particolari, per poi identificare la carica ad essa associata come una grandezza connessa all' entropia di un orizzonte in qualunque teoria generale della gravità.

Evaluation of slope stability under water and seismic load through the Minimum Lithostatic Deviation method

The main objective of this thesis is to obtain a better understanding of the methods to assess the stability of a slope. We have illustrated the principal variants of the Limit Equilibrium (LE) method found in literature, focalizing our attention on the Minimum Lithostatic Deviation (MLD) method, developed by Prof. Tinti and his collaborators (e.g. Tinti and Manucci, 2006, 2008). We had two main goals: the first was to test the MLD method on some real cases. We have selected the case of the Vajont landslide with the objective to reconstruct the conditions that caused the destabilization of Mount Toc, and two sites in the Norwegian margin, where failures has not occurred recently, with the aim to evaluate the present stability state and to assess under which conditions they might be mobilized. The second goal was to study the stability charts by Taylor and by Michalowski, and to use the MLD method to investigate the correctness and adequacy of this engineering tool.

Entanglement entropy in 1-d quantum spin chains

In questa tesi abbiamo studiato il comportamento delle entropie di Entanglement e dello spettro di Entanglement nel modello XYZ attraverso delle simulazioni numeriche. Le formule per le entropie di Von Neumann e di Renyi nel caso di una catena bipartita infinita esistevano già, ma mancavano ancora dei test numerici dettagliati. Inoltre, rispetto alla formula per l'Entropia di Entanglement di J. Cardy e P. Calabrese per sistemi non critici, tali relazioni presentano delle correzioni che non hanno ancora una spiegazione analitica: i risultati delle simulazioni numeriche ne hanno confermato la presenza. Abbiamo inoltre testato l'ipotesi che lo Schmidt Gap sia proporzionale a uno dei parametri d'ordine della teoria, e infine abbiamo simulato numericamente l'andamento delle Entropie e dello spettro di Entanglement in funzione della lunghezza della catena di spin. Ciò è stato possibile solo introducendo dei campi magnetici ''ad hoc'' nella catena, con la proprietà che l'andamento delle suddette quantità varia a seconda di come vengono disposti tali campi. Abbiamo quindi discusso i vari risultati ottenuti.

Global Search for Minimum Energy (H2O)n Clusters, n = 3−5

The Gaussian-3 (G3) model chemistry method has been used to calculate the relative ΔG° values for all possible conformers of neutral clusters of water, (H2O)n, where n = 3−5. A complete 12-fold conformational search around each hydrogen bond produced 144, 1728, and 20 736 initial starting structures of the water trimer, tetramer, and pentamer. These structures were optimized with PM3, followed by HF/6-31G* optimization, and then with the G3 model chemistry. Only two trimers are present on the G3 potential energy hypersurface. We identified 5 tetramers and 10 pentamers on the potential energy and free-energy hypersurfaces at 298 K. None of these 17 structures were linear; all linear starting models folded into cyclic or three-dimensional structures. The cyclic pentamer is the most stable isomer at 298 K. On the basis of this and previous studies, we expect the cyclic tetramers and pentamers to be the most significant cyclic water clusters in the atmosphere.

Structure and thermodynamics of H3O+(H2O)8 clusters: A combined molecular dynamics and quantum mechanics approach

We have studied the structure and stability of (H3O+)(H2O)8 clusters using a combination of molecular dynamics sampling and high-level ab initio calculations. 20 distinct oxygen frameworks are found within 2 kcal/mol of the electronic or standard Gibbs free energy minimum. The impact of quantum zero-point vibrational corrections on the relative stability of these isomers is quite significant. The box-like isomers are favored in terms of electronic energy, but with the inclusion of zero-point vibrational corrections and entropic effects tree-like isomers are favored at higher temperatures. Under conditions from 0 to 298.15 K, the global minimum is predicted to be a tree-like structure with one dangling singly coordinated water molecule. Above 298.15 K, higher entropy tree-like isomers with two or more singly coordinated water molecules are favored. These assignments are generally consistent with experimental IR spectra of (H3O+)(H2O)8 obtained at 150 K.

Synovial sarcomas usually metastasize after >5 years: a multicenter retrospective analysis with minimum follow-up of 10 years for survivors

Synovial sarcoma (SS) is a malignant soft tissue sarcoma with a poor prognosis because of late local recurrence and distant metastases. To our knowledge, no studies have minimum follow-up of 10 years that evaluate long-term outcomes for survivors.

Effects of isoflurane upon minimum alveolar concentration and cerebral cortex depression in pigs and goats: an interspecies comparison

This study compared the effects of isoflurane in pigs (n=10 Yorkshire-Landrace cross) and dairy goats (n=10) by evaluation of electroencephalographic (EEG) burst suppression thresholds (BST) in the cerebral cortex and minimum alveolar concentration (MAC) values in the spinal cord. The study also investigated whether individual MAC values can predict the effects of isoflurane on the cerebral cortex. MAC values and BST/MAC ratios were significantly different between species. Inhibition of movement by isoflurane may be less effective in pigs than in goats. No significant correlation was found between individual MAC and BST values, indicating that in single animals the individual MAC poorly reflects the cerebrocortical depressant effect of isoflurane in pigs and goats.

The effects of isoflurane minimum alveolar concentration on withdrawal reflex activity evoked by repeated transcutaneous electrical stimulation in ponies

The aim of this study was to quantify the effects of isoflurane at approximately the minimum alveolar concentration (peri-MAC) on the temporal summation (TS) of reflex activity in ponies. TS was evoked by repeated electrical stimulations applied at 5 Hz for 2 s on the digital nerve of the left forelimb of seven ponies. Surface electromyographic activity was recorded from the deltoid and common digital extensor muscles. TS thresholds and amplitude of response to stimulations of increasing intensities were assessed during anaesthesia at 0.85, 0.95 and 1.05 times the individual MAC, and after anaesthesia in standing animals. Under isoflurane anaesthesia, TS thresholds increased significantly in a concentration-dependent fashion and at each isoflurane MAC, the responses increased significantly for increasing stimulation intensities. A concentration-dependent depression of evoked reflexes with a reduction in the slopes of the stimulus-response function was observed for both muscles. The results demonstrated that with this model it is possible to describe and quantify the effects of anaesthetics on spinal sensory-motor processing in ponies.