Uniqueness and Non-Degeneracy of Minimizers of the Pekar Functional on a Ball

We consider the Pekar functional on a ball in R^3. We prove uniqueness of minimizers, and a quadratic lower bound in terms of the distance to the minimizer. The latter follows from non-degeneracy of the Hessian at the minimum

Bound on four-dimensional Planck mass

In this note we derive a bound using data from cosmic rays physics on a model recently proposed to solve the hierarchy problem by lowering the Planck scale to the TeV region without the introduction of extra-dimensions. We show that the non observation of small black holes by AGASA implies a model independent limit for the four-dimensional reduced Planck mass of roughly 488 GeV.Comment: 5 page

Quantum black holes at LHC

I present a review of the state of the art of quantum black holes and of their possible phenomenology at the LHC following X. Calmet, S. D. H. Hsu and W. Gong, Phys. Lett. B, 668 (2008) 20-23. By quantum black holes I mean black holes of mass and Schwarzchild radius of the order of the quantum gravity scale, far below the semi-classical regime. These black holes inherit SU(3) and U(1) charges from their parton progenitors and decays in two-particles final states. The model is based on a minimal assumption: the conservation of local gauge charges, while no constraint is imposed on global symmetries. It is possible to identify in that way some interesting signature for quantum black holes decaying in two-particles backto-back final states such as jet + hard photon, jet + missing energy, jet + charged lepton and two charged leptons with different flavor. The phenomenology depends strongly on the symmetries imposed in the model

IST Austria Thesis

This thesis is the result of the research carried out by the author during his PhD at IST Austria between 2017 and 2021. It mainly focuses on the Fröhlich polaron model, specifically to its regime of strong coupling. This model, which is rigorously introduced and discussed in the introduction, has been of great interest in condensed matter physics and field theory for more than eighty years. It is used to describe an electron interacting with the atoms of a solid material (the strength of this interaction is modeled by the presence of a coupling constant α in the Hamiltonian of the system). The particular regime examined here, which is mathematically described by considering the limit α →∞, displays many interesting features related to the emergence of classical behavior, which allows for a simplified effective description of the system under analysis. The properties, the range of validity and a quantitative analysis of the precision of such classical approximations are the main object of the present work. We specify our investigation to the study of the ground state energy of the system, its dynamics and its effective mass. For each of these problems, we provide in the introduction an overview of the previously known results and a detailed account of the original contributions by the author

A Non-Commutative Entropic Optimal Transport Approach to Quantum Composite Systems at Positive Temperature

This paper establishes new connections between many-body quantum systems, One-body Reduced Density Matrices Functional Theory (1RDMFT) and Optimal Transport (OT), by interpreting the problem of computing the ground-state energy of a finite dimensional composite quantum system at positive temperature as a non-commutative entropy regularized Optimal Transport problem. We develop a new approach to fully characterize the dual-primal solutions in such non-commutative setting. The mathematical formalism is particularly relevant in quantum chemistry: numerical realizations of the many-electron ground state energy can be computed via a non-commutative version of Sinkhorn algorithm. Our approach allows to prove convergence and robustness of this algorithm, which, to our best knowledge, were unknown even in the two marginal case. Our methods are based on careful a priori estimates in the dual problem, which we believe to be of independent interest. Finally, the above results are extended in 1RDMFT setting, where bosonic or fermionic symmetry conditions are enforced on the problem

The effective mass problem for the Landau-Pekar equations

We provide a definition of the effective mass for the classical polaron described by the Landau-Pekar equations. It is based on a novel variational principle, minimizing the energy functional over states with given (initial) velocity. The resulting formula for the polaron's effective mass agrees with the prediction by Landau and Pekar [10].Comment: 14 page

Persistence of the spectral gap for the Landau–Pekar equations

The Landau–Pekar equations describe the dynamics of a strongly coupled polaron. Here, we provide a class of initial data for which the associated effective Hamiltonian has a uniform spectral gap for all times. For such initial data, this allows us to extend the results on the adiabatic theorem for the Landau–Pekar equations and their derivation from the Fröhlich model obtained in previous works to larger times

Ecological Niche Modeling of Seventeen Sandflies Species (Diptera, Psychodidae, Phlebotominae) from Venezuela

The purpose of this study is to create distribution models of seventeen Lutzomyia species in Venezuela. Presence records were obtained from field collections over 30 years by several research teams. We used maximum entropy method for model construction based on 30 arc-second resolution environmental layers: 19 bioclimatic variables, elevation, and land cover. Three species were distributed throughout north-central Venezuelan, two restricted to northern Venezuelan coast, and three throughout the west; five were restricted mainly to the Andean and finally two species within sparse pattern. The most important variables that contributed were related to precipitation. The environmental niche model of sandflies might be a useful tool to contribute to the understanding of the ecoepidemiological complexity of the transmission dynamics of the leishmaniases

Stochastic compartmental models and CD8+ T cell exhaustion

In this PhD thesis, mathematical models for cell differentiation are presented. Cell differentiation is a widely observed process in cellular biology allowing a small pool of not specialised cells to develop and maintain a bigger population of cells with a specific function. Different mathematical techniques are employed in this thesis, to study cell differentiation process. We propose a time-independent stochastic mathematical model to represent a general differentiation process via a sequence of compartments. Since we are interested in the ultimate fate of the system, we define a discrete-time branching processes and consider the impact, on the final population, of cells passing through only one or multiple compartments. Further, we include time dependency and define a continuous-time Markov chain to analyse cells dynamics along the sequence of compartments over time. Also, we focus on the journey of a single cell over time and compute a number of summary statistics of interest. Moreover, the impact of different types of differentiation events is considered and numerical results inspired by biological applications, mainly related to immunology, are summarised to illustrate our theoretical approach and methods. In the last Chapter, we focus on a specific cell differentiation process: cells of the immune system have been observed to differentiate towards a dysfunctional state, called exhaustion, during a chronic infection or cancer. One of the aims of this PhD thesis is to shed light into the exhaustion-differentiation process of CD8+ T cells and its reversibility which is a topic of interest for the current and future development of immunotherapies. In particular, based on data collected by the Kaech Lab, several deterministic mathematical models are defined to investigate cells’ trajectory towards the exhausted state as well as the duration of the antigen signal at early time point of stimulation