Post-Minkowskian Hamiltonians in modified theories of gravity

The aim of this note is to describe the computation of post-Minkwoskian Hamiltonians in modified theories of gravity. Exploiting a recent relation between amplitudes of massive scalars and Hamiltonians for relativistic point-particles, we define a post-Minkowskian potential at second order in Newton's constant arising from $\mathcal{R}^3$ modifications in General Relativity. Using this result we calculate the associated contribution to the scattering angle for binary black holes at second post-Minkowskian order, showing agreement in the non relativistic limit with previous results for the bending angle of a massless particle around a static massive source in $\mathcal{R}^3$ theories.Comment: 11 pages, new calculations added (v2. submitted to Physics Letter B

Analysis and Design of High Speed Serial Interfaces for Automotive Applications

The demand for an enriched end-user experience and increased performance in next generation electronic applications is never ending, and it is a common trend for a wide spectrum of applications owing to different markets, like computing, mobile communication and automotive. For this reason High Speed Serial Interface have become widespread components for nowadays electronics with a constant demand for power reduction and data rate increase. In the frame of gigabit serial systems, the work discussed in this thesis develops in two directions: on one hand, the aim is to support the continuous data rate increase with the development of novel link modeling approaches that will be employed for system level evaluation and as support in the design and characterization phases. On the other hand, the design considerations and challenges in the implementation of the transmitter, one of the most delicate blocks for the signal integrity performance of the link, are central. The first part of the activity regarding link performance predictions lead to the development of an enhanced statistical simulation approach, capable to account for the transmitter waveform shape in the ISI analysis, a characteristic that is missed by the available state-ofthe- art simulation approaches. The proposed approach has been extensively tested by comparison with traditional simulation approaches (Spice-like simulators) and validated against experimental characterization of a test system, with satisfactory results. The second part of the activity consists in the design of a high speed transmitter in a deeply scaled CMOS technology, spanning from the concept of the circuit, its implementation and characterization. Targets of the design are to achieve a data rate of 5 Gb/s with a minimum voltage swing of 800 mV, thus doubling the data rate of the current transmitter implementation, and reduce the power dissipation adopting a voltage mode architecture. The experimental characterization of the fabricated lot draws a twofold picture, with some of the performance figures showing a very good qualitative and quantitative agreement with pre-silicon simulations, and others revealing a poor performance level, especially for the eye diagram. Investigation of the root causes by the analysis of the physical silicon design, of the bonding scheme of the prototypes and of the pre-silicon simulations is reported. Guidelines for the redesign of the circuit are also given.Nel panorama delle applicazioni elettroniche il miglioramento delle performance di un prodotto da una generazione alla successiva ha lo scopo di offrire all\u2019utilizzatore finale nuove funzioni e migliorare quelle esistenti. Negli ultimi anni grazie al costante avanzamento della tecnologia integrata, si \ue8 assistito ad un enorme sviluppo della capacit\ue0 computazionale dei dispositivi in tutti i segmenti di mercato, quali ad esempio l\u2019information technology, la comunicazione mobile e l\u2019automotive. La conseguente necessit\ue0 di mettere in comunicazione dispostivi diversi all\u2019interno della stessa applicazione e di traferire grosse quantit\ue0 di dati ha provocato una capillare diffusione delle interfacce seriali ad alta velocit\ue0, o High Speed Serial Interfaces (HSSIs). La necessit\ue0 di ridurre il consumo di potenza e aumentare il bit rate per questo tipo di applicazioni \ue8 diventata dunque un ambito di ricerca di estremo interesse. Il lavoro discusso in questa tesi si colloca nell\u2019ambito della trasmissione di dati seriali a bit rate superiori ad 1Gb/s e si sviluppa in due direzioni: da un lato, a sostegno del continuo aumento del bit rate nelle nuove generazioni di interfacce, \ue8 stato affrontato lo sviluppo di nuovi approcci di modellazione del sistema, che possano essere impiegati nella valutazione delle prestazioni dell\u2019interfaccia e a supporto delle fasi di progettazione e di caratterizzazione. Dall\u2019altro lato, si \ue8 focalizzata l\u2019attenzione sulle sfide e sulle problematiche inerenti il progetto di uno dei blocchi pi\uf9 delicati per le prestazioni del sistema, il trasmettitore. La prima parte della tesi ha come oggetto lo sviluppo di un approccio di simulazione statistico innovativo, in grado di includere nell\u2019analisi degli effetti dell\u2019interferenza di intersimbolo anche la forma d\u2019onda prodotta all\u2019uscita del trasmettitore, una caratteristica che non \ue8 presente in altri approcci di simulazione proposti in letteratura. La tecnica proposta \ue8 ampiamente testata mediante il confronto con approcci di simulazione tradizionali (di tipo Spice) e mediante il confronto con la caratterizzazione sperimentale di un sistema di test, con risultati pienamente soddisfacenti. La seconda parte dell\u2019attivit\ue0 riguarda il progetto di un trasmettitore integrato high speed in tecnologia CMOS a 40nm e si estende dallo studio di fattibilit\ue0 del circuito fino alla sua realizzazione e caratterizzazione. Gli obiettivi riguardano il raggiungimento di un bit rate pari a 5 Gb/s, raddoppiando cos\uec il bit rate dell\u2019attuale implementazione, e di una tensione differenziale di uscita minima di 800mV (picco-picco) riducendo allo stesso tempo la potenza dissipata mediante l\u2019adozione di una architettura Voltage Mode. I risultati sperimentali ottenuti dal primo lotto fabbricato non delineano un quadro univoco: alcune performance mostrano un ottimo accordo qualitativo e quantitativo con le simulazioni pre-fabbricazione, mentre prestazioni non soddisfacenti sono state ottenute in particolare per il diagramma ad occhio. Grazie all\u2019analisi del layout del prototipo, del bonding tra silicio e package e delle simulazioni pre-fabbricazione \ue8 stato possibile risalire ai fattori responsabili del degrado delle prestazioni rispetto alla previsioni pre-fabbricazione, permettendo inoltre di delineare le linee guida da seguire nella futura progettazione di un nuovo prototipo

Gravitational shock waves and scattering amplitudes

We study gravitational shock waves using scattering amplitude techniques. After first reviewing the derivation in General Relativity as an ultrarelativistic boost of a Schwarzschild solution, we provide an alternative derivation by exploiting a novel relation between scattering amplitudes and solutions to Einstein's field equations. We prove that gravitational shock waves arise from the classical part of a three point function with two massless scalars and a graviton. The region where radiation is localized has a distributional profile and it is now recovered in a natural way, thus bypassing the introduction of singular coordinate transformations as used in General Relativity. The computation is easily generalized to arbitrary dimensions and we show how the exactness of the classical solution follows from the absence of classical contributions at higher loops. A classical double copy between gravitational and electromagnetic shock waves is also provided and for a spinning source, using the exponential form of three point amplitudes, we infer a remarkable relation between gravitational shock waves and spinning ones, also known as gyratons. Using this property, we infer a family of exact solutions describing gravitational shock waves with spin. We then compute the phase shift of a particle in a background of shock waves finding agreement with an earlier computation by Amati, Ciafaloni and Veneziano for particles in the high energy limit. Applied to a gyraton, it provides a result for the scattering angle to all orders in spin.Comment: 23 pages, published on JHE

All-order waveforms from amplitudes

Waveforms are classical observables associated with any radiative physical process. Using scattering amplitudes, these are usually computed in a weak-field regime to some finite order in the post-Newtonian or post-Minkowskian approximation. Here, we use strong field amplitudes to compute the waveform produced in scattering of massive particles on gravitational plane waves, treated as exact nonlinear solutions of the vacuum Einstein equations. Notably, the waveform contains an infinite number of post-Minkowskian contributions, as well as tail effects. We also provide, and contrast with, analogous results in electromagnetism.Comment: 14 pages + references, 1 figur

Post-Minkowskian Scattering Angle in Einstein Gravity

Using the implicit function theorem we demonstrate that solutions to the classical part of the relativistic Lippmann-Schwinger equation are in one-to-one correspondence with those of the energy equation of a relativistic two-body system. A corollary is that the scattering angle can be computed from the amplitude itself, without having to introduce a potential. All results are universal and provide for the case of general relativity a very simple formula for the scattering angle in terms of the classical part of the amplitude, to any order in the post-Minkowskian expansion.Comment: 24 pages, minor corrections, published version to appear in JHE

Second-order Post-Minkowskian scattering in arbitrary dimensions

We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.Comment: 51 pages, 1 figure, version to appear in JHE

Scalar-graviton amplitudes

Using the CHY-formalism and its extension to a double cover we provide covariant expressions for tree-level amplitudes with two massive scalar legs and an arbitrary number of gravitons in D dimensions. Using unitarity methods, such amplitudes are needed inputs for the computation of post-Newtonian and post-Minkowskian expansions in classical general relativity.Comment: 25 page

A Simple Modelling Tool for Fast Combined Simulation of Interconnections, Inter-Symbol Interference and Equalization in High-Speed Serial Interfaces for Chip-to-Chip Communications

We describe an effcient system-level simulator that, starting from the architecture of a well-specified transmissive medium (a channel modelled as single-ended or coupled differential microstrips plus cables) and including the system-level characteristics of transmitter and receiver (voltage swing, impedance, etc.), computes the eye diagram and the bit-error rate that is obtained in high-speed serial interfaces. Various equalization techniques are included, such as feed-forward equalization at the transmitter, continuous-time linear equalization and decision-feedback equalization at the receiver. The impact of clock and data jitter on the overall system performance can easily be taken into account and fully-adaptive equalization can be simulated without increasing the computational burden or the model\u2019s complexity

Towards a Long-Read Sequencing Approach for the Molecular Diagnosis of RPGRORF15 Genetic Variants

Sequencing of the low-complexity ORF15 exon of RPGR, a gene correlated with retinitis pigmentosa and cone dystrophy, is difficult to achieve with NGS and Sanger sequencing. False results could lead to the inaccurate annotation of genetic variants in dbSNP and ClinVar databases, tools on which HGMD and Ensembl rely, finally resulting in incorrect genetic variants interpretation. This paper aims to propose PacBio sequencing as a feasible method to correctly detect genetic variants in low-complexity regions, such as the ORF15 exon of RPGR, and interpret their pathogenicity by structural studies. Biological samples from 75 patients affected by retinitis pigmentosa or cone dystrophy were analyzed with NGS and repeated with PacBio. The results showed that NGS has a low coverage of the ORF15 region, while PacBio was able to sequence the region of interest and detect eight genetic variants, of which four are likely pathogenic. Furthermore, molecular modeling and dynamics of the RPGR Glu-Gly repeats binding to TTLL5 allowed for the structural evaluation of the variants, providing a way to predict their pathogenicity. Therefore, we propose PacBio sequencing as a standard procedure in diagnostic research for sequencing low-complexity regions such as RPGRORF15, aiding in the correct annotation of genetic variants in online databases