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.

The collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counter ions?

The collapse of linear polyelectrolyte chains in a poor solvent: When does a collapsing polyelectrolyte collect its counter ions? The collapse of polyions in a poor solvent is a complex system and is an active research subject in the theoretical polyelectrolyte community. The complexity is due to the subtle interplay between hydrophobic effects, electrostatic interactions, entropy elasticity, intrinsic excluded volume as well as specific counter-ion and co-ion properties. Long range Coulomb forces can obscure single molecule properties. The here presented approach is to use just a small amount of screening salt in combination with a very high sample dilution in order to screen intermolecular interaction whereas keeping intramolecular interaction as much as possible (polyelectrolyte concentration cp ≤ 12 mg/L, salt concentration; Cs = 10^-5 mol/L). This is so far not described in literature. During collapse, the polyion is subject to a drastic change in size along with strong reduction of free counterions in solution. Therefore light scattering was utilized to obtain the size of the polyion whereas a conductivity setup was developed to monitor the proceeding of counterion collection by the polyion. Partially quaternized PVP’s below and above the Manning limit were investigated and compared to the collapse of their uncharged precursor. The collapses were induced by an isorefractive solvent/non-solvent mixture consisting of 1-propanol and 2-pentanone, with nearly constant dielectric constant. The solvent quality for the uncharged polyion could be quantified which, for the first time, allowed the experimental investigation of the effect of electrostatic interaction prior and during polyion collapse. Given that the Manning parameter M for QPVP4.3 is as low as lB / c = 0.6 (lB the Bjerrum length and c the mean contour distance between two charges), no counterion binding should occur. However the Walden product reduces with first addition of non solvent and accelerates when the structural collapse sets in. Since the dielectric constant of the solvent remains virtually constant during the chain collapse, the counterion binding is entirely caused by the reduction in the polyion chain dimension. The collapse is shifted to lower wns with higher degrees of quaternization as the samples QPVP20 and QPVP35 show (M = 2.8 respectively 4.9). The combination of light scattering and conductivity measurement revealed for the first time that polyion chains already collect their counter ions well above the theta-dimension when the dimensions start to shrink. Due to only small amounts of screening salt, strong electrostatic interactions bias dynamic as well as static light scattering measurements. An extended Zimm formula was derived to account for this interaction and to obtain the real chain dimensions. The effective degree of dissociation g could be obtained semi quantitatively using this extrapolated static in combination with conductivity measurements. One can conclude the expansion factor a and the effective degree of ionization of the polyion to be mutually dependent. In the good solvent regime g of QPVP4.3, QPVP20 and QPVP35 exhibited a decreasing value in the order 1 > g4.3 > g20 > g35. The low values of g for QPVP20 and QPVP35 are assumed to be responsible for the prior collapse of the higher quaternized samples. Collapse theory predicts dipole-dipole attraction to increase accordingly and even predicts a collapse in the good solvent regime. This could be exactly observed for the QPVP35 sample. The experimental results were compared to a newly developed theory of uniform spherical collapse induced by concomitant counterion binding developed by M. Muthukumar and A. Kundagrami. The theory agrees qualitatively with the location of the phase boundary as well as the trend of an increasing expansion with an increase of the degree of quaternization. However experimental determined g for the samples QPVP4.3, QPVP20 and QPVP35 decreases linearly with the degree of quaternization whereas this theory predicts an almost constant value.

Life Cycle Assessment of Peach Nectar: a comparative analysis between conventional and bioenergy-from-waste integrated food chains

Modern food systems are characterized by a high energy intensity as well as by the production of large amounts of waste, residuals and food losses. This inefficiency presents major consequences, in terms of GHG emissions, waste disposal, and natural resource depletion. The research hypothesis is that residual biomass material could contribute to the energetic needs of food systems, if recovered as an integrated renewable energy source (RES), leading to a sensitive reduction of the impacts of food systems, primarily in terms of fossil fuel consumption and GHG emissions. In order to assess these effects, a comparative life cycle assessment (LCA) has been conducted to compare two different food systems: a fossil fuel-based system and an integrated system with the use of residual as RES for self-consumption. The food product under analysis has been the peach nectar, from cultivation to end-of-life. The aim of this LCA is twofold. On one hand, it allows an evaluation of the energy inefficiencies related to agro-food waste. On the other hand, it illustrates how the integration of bioenergy into food systems could effectively contribute to reduce this inefficiency. Data about inputs and waste generated has been collected mainly through literature review and databases. Energy balance, GHG emissions (Global Warming Potential) and waste generation have been analyzed in order to identify the relative requirements and contribution of the different segments. An evaluation of the energy “loss” through the different categories of waste allowed to provide details about the consequences associated with its management and/or disposal. Results should provide an insight of the impacts associated with inefficiencies within food systems. The comparison provides a measure of the potential reuse of wasted biomass and the amount of energy recoverable, that could represent a first step for the formulation of specific policies on the integration of bioenergies for self-consumption.

Su(3) lattice gauge theories and spin chains

I modelli su reticolo con simmetrie SU(n) sono attualmente oggetto di studio sia dal punto di vista sperimentale, sia dal punto di vista teorico; particolare impulso alla ricerca in questo campo è stato dato dai recenti sviluppi in campo sperimentale per quanto riguarda la tecnica dell’intrappolamento di atomi ultrafreddi in un reticolo ottico. In questa tesi viene studiata, sia con tecniche analitiche sia con simulazioni numeriche, la generalizzazione del modello di Heisenberg su reticolo monodimensionale a simmetria SU(3). In particolare, viene proposto un mapping tra il modello di Heisenberg SU(3) e l’Hamiltoniana con simmetria SU(2) bilineare-biquadratica con spin 1. Vengono inoltre presentati nuovi risultati numerici ottenuti con l’algoritmo DMRG che confermano le previsioni teoriche in letteratura sul modello in esame. Infine è proposto un approccio per la formulazione della funzione di partizione dell’Hamiltoniana bilineare-biquadratica a spin-1 servendosi degli stati coerenti per SU(3).

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.

Assessment of right ventricular systolic function: Comparison between cardiac magnetic resonance derived ejection fraction and pulsed-wave tissue Doppler imaging of the tricuspid annulus

Systolic right ventricular (RV) function is an important predictor in the course of various congenital and acquired heart diseases. Its practical determination by echocardiography remains challenging. We compared routine assessment of lateral tricuspid annular systolic motion velocity (TV(lat), cm/s) using pulsed-wave tissue Doppler imaging from the apical 4-chamber view with cardiac magnetic resonance (CMR) as reference method.

Clinical outcome of high-risk patients with severe aortic stenosis and reduced left ventricular ejection fraction undergoing medical treatment or TAVI

Introduction Reduced left ventricular function in patients with severe symptomatic valvular aortic stenosis is associated with impaired clinical outcome in patients undergoing surgical aortic valve replacement (SAVR). Transcatheter Aortic Valve Implantation (TAVI) has been shown non-inferior to SAVR in high-risk patients with respect to mortality and may result in faster left ventricular recovery. Methods We investigated clinical outcomes of high-risk patients with severe aortic stenosis undergoing medical treatment (n = 71) or TAVI (n = 256) stratified by left ventricular ejection fraction (LVEF) in a prospective single center registry. Results Twenty-five patients (35%) among the medical cohort were found to have an LVEF≤30% (mean 26.7±4.1%) and 37 patients (14%) among the TAVI patients (mean 25.2±4.4%). Estimated peri-interventional risk as assessed by logistic EuroSCORE was significantly higher in patients with severely impaired LVEF as compared to patients with LVEF>30% (medical/TAVI 38.5±13.8%/40.6±16.4% versus medical/TAVI 22.5±10.8%/22.1±12.8%, p <0.001). In patients undergoing TAVI, there was no significant difference in the combined endpoint of death, myocardial infarction, major stroke, life-threatening bleeding, major access-site complications, valvular re-intervention, or renal failure at 30 days between the two groups (21.0% versus 27.0%, p = 0.40). After TAVI, patients with LVEF≤30% experienced a rapid improvement in LVEF (from 25±4% to 34±10% at discharge, p = 0.002) associated with improved NYHA functional class at 30 days (decrease ≥1 NYHA class in 95%). During long-term follow-up no difference in survival was observed in patients undergoing TAVI irrespective of baseline LVEF (p = 0.29), whereas there was a significantly higher mortality in medically treated patients with severely reduced LVEF (log rank p = 0.001). Conclusion TAVI in patients with severely reduced left ventricular function may be performed safely and is associated with rapid recovery of systolic left ventricular function and heart failure symptoms.

Value of age, creatinine, and ejection fraction (ACEF score) in assessing risk in patients undergoing percutaneous coronary interventions in the 'All-Comers' LEADERS trial

Background— The age, creatinine, and ejection fraction (ACEF) score (age/left ventricular ejection fraction+1 if creatinine >2.0 mg/dL) has been established as an effective predictor of clinical outcomes in patients undergoing elective coronary artery bypass surgery; however, its utility in “all-comer” patients undergoing percutaneous coronary intervention is yet unexplored. Methods and Results— The ACEF score was calculated for 1208 of the 1707 patients enrolled in the LEADERS trial. Post hoc analysis was performed by stratifying clinical outcomes at the 1-year follow-up according to ACEF score tertiles: ACEFlow ≤1.0225, 1.0225< ACEFmid ≤1.277, and ACEFhigh >1.277. At 1-year follow-up, there was a significantly lower number of patients with major adverse cardiac event–free survival in the highest tertile of the ACEF score (ACEFlow=92.1%, ACEFmid=89.5%, and ACEFhigh=86.1%; P=0.0218). Cardiac death was less frequent in ACEFlow than in ACEFmid and ACEFhigh (0.7% vs 2.2% vs 4.5%; hazard ratio=2.22, P=0.002) patients. Rates of myocardial infarction were significantly higher in patients with a high ACEF score (6.7% for ACEFhigh vs 5.2% for ACEFmid and 2.5% for ACEFlow; hazard ratio=1.6, P=0.006). Clinically driven target-vessel revascularization also tended to be higher in the ACEFhigh group, but the difference among the 3 groups did not reach statistical significance. The rate of composite definite, possible, and probable stent thrombosis was also higher in the ACEFhigh group (ACEFlow=1.2%, ACEFmid=3.5%, and ACEFhigh=6.2%; hazard ratio=2.04, P<0.001). Conclusions— ACEF score may be a simple way to stratify risk of events in patients treated with percutaneous coronary intervention with respect to mortality and risk of myocardial infarction.

Varying spin state composition by the choice of capping ligand in a family of molecular chains: detailed analysis of magnetic properties of chromium(III) horseshoes

We report a detailed physical analysis on a family of isolated, antiferro-magnetically (AF) coupled, chromium(III) finite chains, of general formula (Cr(RCO(2))(2)F)(n) where the chain length n = 6 or 7. Additionally, the chains are capped with a selection of possible terminating ligands, including hfac (= 1,1,1,5,5,5-hexafluoropentane-2,4-dionate(1-)), acac (= pentane-2,4-dionate(1-)) or (F)(3). Measurements by inelastic neutron scattering (INS), magnetometery and electron paramagnetic resonance (EPR) spectroscopy have been used to study how the electronic properties are affected by n and capping ligand type. These comparisons allowed the subtle electronic effects the choice of capping ligand makes for odd member spin 3/2 ground state and even membered spin 0 ground state chains to be investigated. For this investigation full characterisation of physical properties have been performed with spin Hamiltonian parameterisation, including the determination of Heisenberg exchange coupling constants and single ion axial and rhombic anisotropy. We reveal how the quantum spin energy levels of odd or even membered chains can be modified by the type of capping ligand terminating the chain. Choice of capping ligands enables Cr-Cr exchange coupling to be adjusted by 0, 4 or 24%, relative to Cr-Cr exchange coupling within the body of the chain, by the substitution of hfac, acac or (F)(3) capping ligands to the ends of the chain, respectively. The manipulation of quantum spin levels via ligands which play no role in super-exchange, is of general interest to the practise of spin Hamilton modelling, where such second order effects are generally not considered of relevance to magnetic properties.