Dynamical Casimir effect and the structure of vacuum in quantum field theory

Some of the most interesting phenomena that arise from the developments of the modern physics are surely vacuum fluctuations. They appear in different branches of physics, such as Quantum Field Theory, Cosmology, Condensed Matter Physics, Atomic and Molecular Physics, and also in Mathematical Physics. One of the most important of these vacuum fluctuations, sometimes called "zero-point energy", as well as one of the easiest quantum effect to detect, is the so-called Casimir effect. The purposes of this thesis are: - To propose a simple retarded approach for dynamical Casimir effect, thus a description of this vacuum effect when we have moving boundaries. - To describe the behaviour of the force acting on a boundary, due to its self-interaction with the vacuum.

Nuovi coniugati fra acido azelaico ed azaeterocicli: sintesi e valutazione dell'attività biologica

The well-known antiproliferative properties of the 9-hydroxystearic acid (9-HSA) on human colon cancer cells (HT-29 cell line) have inspired this thesis work in order to obtain new derivatives maintaining the C1-C8 chain of the HSA linked to an heterocyclic moiety at the C-9 carbon atom and to investigate their biological activity. First, thiazoles, thiadiazoles and benzothiazoles, that are compounds of interest in many fields for their biological activities, have been introduced through an amide bond starting from their 2-amino precursors. The products have been obtained by treatment with methyl 9-chloro-9-oxononanoate according to a Schotten-Baumann type reaction. The acylation reaction occurred at the endocyclic nitrogen atom of the heterocycle, as ascertained through NOESY-1D experiment. After, methyl 9-chloro-9-oxononanoate was reacted with indole, N-methylindole, and triptamine giving a serie of new indole derivatives. Finally, the biological activity of some compounds has been tested through assays on HT-29 cancer cells and bacterial and fungal microorganisms; docking calculations have also been performed to evaluate the possible interactions with the active site of histone deacetylase, which are molecular targets of the 9-HSA.

Black holes as quantum bound states

We present a new quantum description for the Oppenheimer-Snyder model of gravitational collapse of a ball of dust. Starting from the geodesic equation for dust in spherical symmetry, we introduce a time-independent Schrödinger equation for the radius of the ball. The resulting spectrum is similar to that of the Hydrogen atom and Newtonian gravity. However, the non-linearity of General Relativity implies that the ground state is characterised by a principal quantum number proportional to the square of the ADM mass of the dust. For a ball with ADM mass much larger than the Planck scale, the collapse is therefore expected to end in a macroscopically large core and the singularity predicted by General Relativity is avoided. Mathematical properties of the spectrum are investigated and the ground state is found to have support essentially inside the gravitational radius, which makes it a quantum model for the matter core of Black Holes. In fact, the scaling of the ADM mass with the principal quantum number agrees with the Bekenstein area law and the corpuscular model of Black Holes. Finally, the uncertainty on the size of the ground state is interpreted within the framework of an Uncertainty Principle.

La metrica di Agmon ed il decadimento esponenziale delle soluzioni di equazioni alle derivate parziali

The aim of this master thesis is to study the exponential decay of solutions of elliptic partial equations. This work is based on the results obtained by Agmon. To this purpose, first, we define the Agmon metric, that plays an important role in the study of exponential decay, because it is related to the rate of decay. Under some assumptions on the growth of the function and on the positivity of the quadratic form associated to the operator, a first result of exponential decay is presented. This result is then applied to show the exponential decay of eigenfunctions with eigenvalues whose real part lies below the bottom of the essential spectrum. Finally, three examples are given: the harmonic oscillator, the hydrogen atom and a Schrödinger operator with purely discrete spectrum.