Quantum behavior in mesoscopic systems

In this thesis I present the work done during my PhD. The Thesis is divided into two parts; in the first one I present the study of mesoscopic quantum systems whereas in the second one I address the problem of the definition of Markov regime for quantum system dynamics. The first work presented is the study of vortex patterns in (quasi) two dimensional rotating Bose Einstein condensates (BECs). I consider the case of an anisotropy trapping potential and I shall show that the ground state of the system hosts vortex patterns that are unstable. In a second work I designed an experimental scheme to transfer entanglement from two entangled photons to two BECs. This work is meant to propose a feasible experimental set up to bring entanglement from microscopic to macroscopic systems for both the study of fundamental questions (quantum to classical transition) and technological applications. In the last work of the first part another experimental scheme is presented in order to detect coherences of a mechanical oscillator which is assumed to have been previously cooled down to the quantum regime. In this regime in fact the system can rapidly undergo decoherence so that new techniques have to be employed in order to detect and manipulate their states. In the scheme I propose a micro-mechanical oscillator is coupled to a BEC and the detection is performed by monitoring the BEC with a negligible back-action on the cantilever. In the second part of the thesis I give a definition of Markov regime for open quantum dynamics. The importance of such definition comes from both the mathematical description of the system dynamics and from the understanding of the role played by the environment in the evolution of an open system. In the Markov regime the mathematical description can be simplified and the role of the environment is a passive one.

Synthesis and reactivity of α-diazo-β-keto sulfoxides: scope and synthetic potential

The research described in this thesis focuses on the design and synthesis of stable α-diazosulfoxides and investigation of their reactivity under a variety of conditions (transition-metal catalysis, thermal, photochemical and microwave) with a particular emphasis on the synthesis of novel heterocyclic compounds with potential biological activity. The exclusive reaction pathway for these α-diazosulfoxides was found to be hetero-Wolff rearrangement to give α-oxosulfine intermediates. In the first chapter, a literature review of sulfines is presented, including a discussion of naturally occurring sulfines, and an overview of the synthesis and reactivity of sulfines. The potential of sulfines in organic synthesis and recent developments in particular are highlighted. The second chapter discusses the synthesis and reactivity of α-diazosulfoxides, building on earlier results in this research group. The synthesis of lactone-based α-diazosulfoxides and, for the first time, ketone-based benzofused and monocyclic α-diazosulfoxides is described. The reactivity of these α-diazosulfoxides is then explored under a variety of conditions, such as transition-metal catalysis, photochemical and microwave, generating labile α-oxosulfine intermediates, which are trapped using amines and dienes, in addition to the spontaneous reaction pathways which occur with α-oxosulfines in the absence of a trap. A new reaction pathway was explored with the lactone based α-oxosulfines, involving reaction with amines to generate novel 3-aminofuran-2(5H)-ones via carbophilic attack, in very good yields. The reactivity of ketone-based α-diazosulfoxides was explored for the first time, and once again, pseudo-Wolff rearrangement to the α-oxosulfines was the exclusive reaction pathway observed. The intermediacy of the α-oxosulfines was confirmed by trapping as cycloadducts, with the stereochemical features dependant on the reaction conditions. In the absence of a diene trap, a number of reaction fates from the α-oxosulfines were observed, including complete sulfinyl extrusion to give indanones, sulfur extrusion to give indanediones, and, to a lesser extent, dimerisation. The indanediones were characterised by trapping as quinoxalines, to enable full characterisation. One of the overriding outcomes of this thesis was the provision of new insights into the behaviour of α-oxosulfines with different transition metal catalysts, and under thermal, microwave and photolysis conditions. A series of 3-aminofuran-2(5H)-ones and benzofused dihydro-2H-thiopyran S-oxides were submitted for anticancer screening at the U.S. National Cancer Institute. A number of these derivatives were identified as hit compounds, with excellent cell growth inhibition. One 3-aminofuran-2(5H)-one derivative has been chosen for further screening. The third chapter details the full experimental procedures, including spectroscopic and analytical data for the compounds prepared during this research. The data for the crystal structures are contained in the attached CD.