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Thesis (M.A.)--Boston Universit

Entanglement spectrum of random-singlet quantum critical points

The entanglement spectrum, i.e., the full distribution of Schmidt eigenvalues of the reduced density matrix, contains more information than the conventional entanglement entropy and has been studied recently in several many-particle systems. We compute the disorder-averaged entanglement spectrum, in the form of the disorder-averaged moments of the reduced density matrix, for a contiguous block of many spins at the random-singlet quantum critical point in one dimension. The result compares well in the scaling limit with numerical studies on the random XX model and is also expected to describe the (interacting) random Heisenberg model. Our numerical studies on the XX case reveal that the dependence of the entanglement entropy and spectrum on the geometry of the Hilbert space partition is quite different than for conformally invariant critical points.Comment: 11 pages, 10 figure

Asymptotics of Harish-Chandra expansions, bounded hypergeometric functions associated with root systems, and applications

A series expansion for Heckman-Opdam hypergeometric functions $\varphi_\lambda$ is obtained for all $\lambda \in \mathfrak a^*_{\mathbb C}.$ As a consequence, estimates for $\varphi_\lambda$ away from the walls of a Weyl chamber are established. We also characterize the bounded hypergeometric functions and thus prove an analogue of the celebrated theorem of Helgason and Johnson on the bounded spherical functions on a Riemannian symmetric space of the noncompact type. The $L^p$-theory for the hypergeometric Fourier transform is developed for $0<p<2$. In particular, an inversion formula is proved when $1\leq p <2$

Strong thermal leptogenesis and the absolute neutrino mass scale

We show that successful strong thermal leptogenesis, where the final asymmetry is independent of the initial conditions and in particular a large pre-existing asymmetry is efficiently washed-out, favours values of the lightest neutrino mass $m_1 \gtrsim 10\,{\rm meV}$ for normal ordering (NO) and $m_1 \gtrsim 3\,{\rm meV}$ for inverted ordering (IO) for models with orthogonal matrix entries respecting $|\Omega_{ij}^2| \lesssim 2$. . We show analytically why lower values of $m_1$ require a high level of fine tuning in the seesaw formula and/or in the flavoured decay parameters (in the electronic for NO, in the muonic for IO). We also show how this constraint exists thanks to the measured values of the neutrino mixing angles and can be tighten by a future determination of the Dirac phase. Our analysis also allows to place more stringent constraint for a specific model or class of models, such as $SO(10)$-inspired models, and shows that some models cannot realise strong thermal leptogenesis for any value of $m_1$. A scatter plot analysis fully supports the analytical results. We also briefly discuss the interplay with absolute neutrino mass scale experiments concluding that they will be able in the coming years to either corner strong thermal leptogenesis or find positive signals pointing to a non-vanishing $m_1$. Since the constraint is much stronger for NO than for IO, it is very important that new data from planned neutrino oscillation experiments will be able to solve the ambiguity.Comment: 22 pages; 7 figures; v2: matches JCAP versio

Antigen-presenting cells and antigen presentation in tertiary lymphoid organs

Tertiary lymphoid organs (TLOs) form in territorialized niches of peripheral tissues characterized by the presence of antigens; however, little is known about mechanism(s) of antigen handling by ectopic lymphoid structures. In this mini review, we will discuss the role of antigen-presenting cells and mechanisms of antigen presentation in TLOs, summarizing what is currently known about this facet of the formation and function of these tissues as well as identifying questions yet to be addressed

Preoperative digital three-dimensional planning for rhinoplasty

BACKGROUND: This report describes preoperative digital planning for rhinoplasty using a new three-dimensional (3D) radiologic viewer that allows both patients and surgeons to visualize on a common monitor the 3D real aspect of the nose in its inner and outer sides. METHODS: In the period 2002 to 2008, 210 patients underwent rhinoplasty procedures in the authors' clinic. The patients were randomly divided into three groups according to the type of preoperative planning used: photos only, a simulated result by Adobe Photoshop, or the 3D radiologic viewer. The parameters evaluated included the number of patients that underwent surgery after the first consultation, the number of patients who asked for a reintervention, patient satisfaction (according to a test given to the patients 12 months postoperatively), the surgical time required for a functional intervention, and the improvement in nasal function by postoperative rhinomanometry and subjective evaluation. RESULTS: Computer-aided technologies led to a higher number of patients deciding to undergo a rhinoplasty. Simulation of the postoperative results was not as useful in the postoperative period due to the higher number of reintervention requests. CONCLUSION: The patients undergoing rhinoplasties preferred new technologies in the preoperative period. The advantages of using the 3D radiologic viewer included improved preoperative planning, reduction in intraoperative stress, a higher number of patients undergoing surgery, reduction in postoperative surgical corrections, reduction in surgical time for the functional intervention, a higher rate of improvement in nasal function, a higher percentage of postoperative satisfaction, and reduced costs

On the equipartition of thermal and non-thermal energy in clusters of galaxies

Clusters of galaxies are revealing themselves as powerful sources of non thermal radiation in a wide range of wavelengths. In order to account for these multifrequency observations equipartition of cosmic rays (CRs) with the thermal gas in clusters of galaxies is often invoked. This condition might suggest a dynamical role played by cosmic rays in the virialization of these large scale structures and is now testable through gamma ray observations. We show here, in the specific case of the Coma and Virgo clusters, for which upper limits on the gamma ray emission exist, that equipartition implies gamma ray fluxes that are close or even in excess of the EGRET limit, depending on the adopted model of CR injection. We use this bound to limit the validity of the equipartition condition. We also show that, contrary to what claimed in previous calculations, the equipartition assumption implies gamma ray fluxes in the TeV range which can be detectable even by currently operating gamma ray observatories if the injection cosmic ray spectrum is flatter than $E^{-2.4}$.Comment: 20 pages + 2 figures. To appear in the Astrophysical Journa