Search results for " Modelli e Metodi Matematici"

Critical reflections on asymptotically safe gravity

2020

Asymptotic safety is a theoretical proposal for the ultraviolet completion of quantum field theories, in particular for quantum gravity. Significant progress on this program has led to a first characterization of the Reuter fixed point. Further advancement in our understanding of the nature of quantum spacetime requires addressing a number of open questions and challenges. Here, we aim at providing a critical reflection on the state of the art in the asymptotic safety program, specifying and elaborating on open questions of both technical and conceptual nature. We also point out systematic pathways, in various stages of practical implementation, towards answering them. Finally, we also take…

Oh, wait, O8 de Sitter may be unstable!

2021

We analyze the stability of four-dimensional de Sitter vacua constructed by compactifying massive Type IIA supergravity in the presence of two O8 sources [1]. When embedded in String Theory the first source has a clear interpretation as an O8$_-$ plane, but the second one could correspond to either an O8$_+$ plane or to an O8$_-$ plane with 16 D8-branes on top. We find that this latter solution has a tachyonic instability, corresponding to the D8-branes moving away from the O8$_-$ plane. We comment on the possible ways of distinguishing between these sources.

Multi-boson block factorization of fermions

2017

The numerical computations of many quantities of theoretical and phenomenological interest are plagued by statistical errors which increase exponentially with the distance of the sources in the relevant correlators. Notable examples are baryon masses and matrix elements, the hadronic vacuum polarization and the light-by-light scattering contributions to the muon g-2, and the form factors of semileptonic B decays. Reliable and precise determinations of these quantities are very difficult if not impractical with state-of-the-art standard Monte Carlo integration schemes. I will review a recent proposal for factorizing the fermion determinant in lattice QCD that leads to a local action in the g…

Study of the Effects of Nuclear Motion on High Harmonic Generation in Simple Molecules

2010

Universality of Schmidt decomposition and particle identity

2017

Schmidt decomposition is a widely employed tool of quantum theory which plays a key role for distinguishable particles in scenarios such as entanglement characterization, theory of measurement and state purification. Yet, it is held not to exist for identical particles, an open problem forbidding its application to analyze such many-body quantum systems. Here we prove, using a newly developed approach, that the Schmidt decomposition exists for identical particles and is thus universal. We find that it is affected by single-particle measurement localization and state overlap. We study paradigmatic two-particle systems where identical qubits and qutrits are located in the same place or in sep…

Radon transform as a set of probability distributions

2009

It is proved that the Radon transform of the Wigner function gives the probability distributions related to measuring the observable operators obtained as linear combinations of position and momentum of the relevant particle. The generalization to an arbitrary number of degrees of freedom is given.

Learning, regularization and ill-posed inverse problems

2005

Many works have shown that strong connections relate learning from examples to regularization techniques for ill-posed inverse problems. Nevertheless by now there was no formal evidence neither that learning from examples could be seen as an inverse problem nor that theoretical results in learning theory could be independently derived using tools from regularization theory. In this paper we provide a positive answer to both questions. Indeed, considering the square loss, we translate the learning problem in the language of regularization theory and show that consistency results and optimal regularization parameter choice can be derived by the discretization of the corresponding inverse prob…

Voltage drop across Josephson junctions for L\'evy noise detection

2020

We propose to characterize L\'evy-distributed stochastic fluctuations through the measurement of the average voltage drop across a current-biased Josephson junction. We show that the noise induced switching process in the Josephson washboard potential can be exploited to reveal and characterize L\'evy fluctuations, also if embedded in a thermal noisy background. The measurement of the average voltage drop as a function of the noise intensity allows to infer the value of the stability index that characterizes L\'evy-distributed fluctuations. An analytical estimate of the average velocity in the case of a L\'evy-driven escape process from a metastable state well agrees with the numerical calc…

Enhancement of stability in systems with metastable states

2007

The investigation of noise‐induced phenomena in far from equilibrium systems is one of the approach used to understand the behaviour of physical and biological complex systems. Metastability is a generic feature of many nonlinear systems, and the problem of the lifetime of metastable states involves fundamental aspects of nonequilibrium statistical mechanics. The enhancement of the life‐time of metastable states through the noise enhanced stability effect and the role played by the resonant activation phenomenon will be discussed in models of interdisciplinary physics: (i) Ising model (ii) Josephson junction; (iii) stochastic FitzHugh‐Nagumo model; (iv) a population dynamics model, and (v) …

Noise stabilization effects in models of interdisciplinary physics

2009

Metastability is a generic feature of many nonlinear systems, and the problem of the lifetime of metastable states involves fundamental aspects of nonequilibrium statistical mechanics. The investigation of noise-induced phenomena in far from equilibrium systems is one of the approaches used to understand the behaviour of physical and biological complex systems. The enhancement of the lifetime of metastable states through the noise enhanced stability effect and the role played by the resonant activation phenomenon will be discussed in models of interdisciplinary physics: (i) polymer translocation dynamics; (ii) transient regime of FitzHugh-Nagumo model; (iii) market stability in a nonlinear …