The quantum time-dependent harmonic oscillator

La presente tesi si propone di mostrare che l’oscillatore armonico quantistico dipendente dal tempo è un sistema risolvibile in maniera esatta. La trattazione è articolata in tre capitoli: nel primo viene richiamata la teoria dell’oscillatore armonico quantistico indipendente dal tempo, al fine di recuperare i concetti e le metodologie che sono comuni anche alla sua controparte dipendente dal tempo. Nel secondo capitolo viene fornita una breve introduzione alla teoria degli operatori invarianti dipendenti dal tempo, di cui ci interessa la loro relazione con le soluzioni dell’equazione di Schrödinger. Infine, nel terzo capitolo viene presentato il problema dell’oscillatore armonico quantistico dipendente dal tempo e discussa la sua soluzione esatta. In aggiunta se ne individuano gli stati coerenti.

Caratterizzazione e generazione di segnali PWM per amplificatori in classe D ad alta efficienza

The convergence of information technology and consumer electronics towards battery powered portable devices has increased the interest in high efficiency, low dissipation amplifiers. Class D amplifiers are the state of the art in low power consumption and high performance amplification. In this thesis we explore the possibility of exploiting nonlinearities introduced by the PWM modulation, by designing an optimized modulation law which scales its carrier frequency adaptively with the input signal's average power while preserving the SNR, thus reducing power consumption. This is achieved by means of a novel analytical model of the PWM output spectrum, which shows how interfering harmonics and their bandwidth affect the spectrum. This allows for frequency scaling with negligible aliasing between the baseband spectrum and its harmonics. We performed low noise power spectrum measurements on PWM modulations generated by comparing variable bandwidth, random test signals with a variable frequency triangular wave carrier. The experimental results show that power-optimized frequency scaling is both feasible and effective. The new analytical model also suggests a new PWM architecture that can be applied to digitally encoded input signals which are predistorted and compared with a cosine carrier, which is accurately synthesized by a digital oscillator. This approach has been simulated in a realistic noisy model and tested in our measurement setup. A zero crossing search on the obtained PWM modulation law proves that this approach yields an equivalent signal quality with respect to traditional PWM schemes, while entailing the use of signals whose bandwidth is remarkably smaller due to the use of a cosine instead of a triangular carrier.

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.

Excited state energy surfaces of flexible emitters for thermally activated delayed fluorescence

Organic Light-Emitting Diodes (OLEDs) technology has matured over recent years, reaching the commercialization level and being used in various applications. The required efficiency can be achieved by transforming triplet excitons into singlet states via Reverse InterSystem Crossing (RISC), which a general mechanism called thermally activated delayed fluorescence (TADF). Two prototypical molecules in the field, 2CzBN and 4CzBN, Carbazole Benzonitrile (donor-acceptor) derivatives, possess similar energy gap between singlet and triplet (∆EST, a key parameter in the RISC rate), but different TADF performance. In this sense, other parameter must be considered to explain these different behaviors. In this work, we theoretically investigate 2CzBN and 4CzBN and address the problem of how flexible donor-acceptor (D-A) or donor-acceptor-donor (D-A-D) molecular architectures affect the nature of excited state, and the oscillator strength. Furthermore, we analyze the RISC rates as a function of the conformation of the carbazole side groups, considering the S0, S1, T1 and T2 states. The oscillator strength of 4CzBN is higher than of 2CzBN, which, in turn, is almost vanishing, resulting in only 4CzBN being a TADF active molecule. We also note the presence of a second triplet state T2 lower in energy than S1, and that the reorganization energies, associated to the RISC processes involving T1 and T2, are both important factor in differentiating the rates in 2CzBN and 4CzBN. However, the 4CzBN RISC rate from T2 to S1 is surprisingly high with respect to the one from T1 to S1, although, according to EL-Sayed rules, since T2 (CT/LE) is more similar to S1 (CT) than in 2CzBN (LE, CT), this transition should be less favored. These insights are important to understand the photophysics of the TADF process and to design novel TADF emitters based on the benzo-carbazole architecture.

Computational characterization of carbazole-benzonitrile derivatives for applications in Organic Light Emitting Diodes

The technology of Organic Light-Emitting Diodes has reached such a high level of reliability that it can be used in various applications. The required light emission efficiency can be achieved by transforming the triplet excitons into singlet states through Reverse InterSystem Crossing (RISC), which is the main process of a general mechanism called thermally activated delayed fluorescence (TADF). In this thesis, we theoretically analyzed two carbazole-benzonitrile (donor-acceptor) derivatives, 2,5-di(9H-carbazol-9-yl)benzonitrile (p-2CzBN) and 2,3,4,5,6-penta(9H-carbazol-9-yl)benzonitrile (5CzBN), and addressed the problem of how donor-acceptor (D-A) or donor-acceptor-donor (D-A-D) flexible molecular architectures influence the nature of the excited states and the emission intensity. Furthermore, we analyzed the RISC rates as a function of the conformation of the carbazole lateral groups, considering the first electronic states, S0, S1, T1 and T2, involved in TADF process. The two prototype molecules, p-2CzBN and 5CzBN, have a similar energy gap between the first singlet and triplet states (∆EST, a key parameter in the RISC rate), but different TADF performances. Therefore, other parameters must be considered to explain their different behavior. The oscillator strength of p-2CzBN, never tested as emitter in OLEDs, is similar to that of 5CzBN, which is an active TADF molecule. We also note that the presence of a second T2 triplet state, lower in energy than S1 only in 5CzBN, and the reorganization energies, associated with RISC processes involving T1 and T2, are important factors in differentiating the rates in p-2CzBN and 5CzBN. For p-2CzBN, the RISC rate from T2 to S1 is surprisingly higher than that from T1 to S1, in disagreement with El-Sayed rules, due to a large reorganization energy associated to the T1 to S1, process; while the contrary occurs for 5CzBN. These insights are important for designing new TADF emitters based on the benzo-carbazole architecture.

Stochastic physics and representation of El Niño Southern Oscillation in climate models

El Niño-Southern Oscillation (ENSO) è il maggiore fenomeno climatico che avviene a livello dell’Oceano Pacifico tropicale e che ha influenze ambientali, climatiche e socioeconomiche a larga scala. In questa tesi si ripercorrono i passi principali che sono stati fatti per tentare di comprendere un fenomeno così complesso. Per prima cosa, si sono studiati i meccanismi che ne governano la dinamica, fino alla formulazione del modello matematico chiamato Delayed Oscillator (DO) model, proposto da Suarez e Schopf nel 1988. In seguito, per tenere conto della natura caotica del sistema studiato, si è introdotto nel modello lo schema chiamato Stochastically Perturbed Parameterisation Tendencies (SPPT). Infine, si sono portati due esempi di soluzione numerica del DO, sia con che senza l’introduzione della correzione apportata dallo schema SPPT, e si è visto in che misura SPPT porta reali miglioramenti al modello studiato.