Quantum Variance and Ergodicity for the baker's map

We prove a Egorov theorem, or quantum-classical correspondence, for the quantised baker's map, valid up to the Ehrenfest time. This yields a logarithmic upper bound for the decay of the quantum variance, and, as a corollary, a quantum ergodic theorem for this map

Follow the fugitive: an application of the method of images to open dynamical systems

Borrowing and extending the method of images we introduce a theoretical framework that greatly simplifies analytical and numerical investigations of the escape rate in open dynamical systems. As an example, we explicitly derive the exact size- and position-dependent escape rate in a Markov case for holes of finite size. Moreover, a general relation between the transfer operators of closed and corresponding open systems, together with the generating function of the probability of return to the hole is derived. This relation is then used to compute the small hole asymptotic behavior, in terms of readily calculable quantities. As an example we derive logarithmic corrections in the second order term. Being valid for Markov systems, our framework can find application in information theory, network theory, quantum Weyl law and via Ulam's method can be used as an approximation method in more general dynamical systems.Comment: 9 pages, 1 figur

Exploring TV Seriality and Television Studies through Data-Driven Approaches

The chapter discusses the use of data-driven approaches in television studies, which has become possible due to the increasing availability of digital data. Computational techniques can be used to analyze cultural artifacts, gain insights into audience reactions to specific shows or episodes, and investigate patterns and trends in television programming over time. The chapter also highlights the challenges of analyzing television series, which are complex open systems that interact with external factors such as the production process, audience feedback, and cultural and social context. Content analysis, which involves qualitative and quantitative methods based on the coding process and data collection, can be used to analyze various elements of a TV series. Generative AI is also discussed, which refers to the use of deep multi-modal algorithms to generate new content such as images, speech, and text. Generative methods like Generative Adversarial Networks (GANs) and Stable Diffusion can create new content that is almost indistinguishable from real data. While generating videos is more challenging, Recurrent Neural Networks (RNNs) like LSTMs can capture the temporal dynamics of the scenes to create interesting and promising applications for complex, but short-duration videos

Entropic measures of individual mobility patterns

Understanding human mobility from a microscopic point of view may represent a fundamental breakthrough for the development of a statistical physics for cognitive systems and it can shed light on the applicability of macroscopic statistical laws for social systems. Even if the complexity of individual behaviors prevents a true microscopic approach, the introduction of mesoscopic models allows the study of the dynamical properties for the non-stationary states of the considered system. We propose to compute various entropy measures of the individual mobility patterns obtained from GPS data that record the movements of private vehicles in the Florence district, in order to point out new features of human mobility related to the use of time and space and to define the dynamical properties of a stochastic model that could generate similar patterns. Moreover, we can relate the predictability properties of human mobility to the distribution of time passed between two successive trips. Our analysis suggests the existence of a hierarchical structure in the mobility patterns which divides the performed activities into three different categories, according to the time cost, with different information contents. We show that a Markov process defined by using the individual mobility network is not able to reproduce this hierarchy, which seems the consequence of different strategies in the activity choice. Our results could contribute to the development of governance policies for a sustainable mobility in modern cities

Programma del Corso A.A. 14/15

Lista sommaria degli argomenti svolti a lezione. I riferimenti sono alla seconda edizione del libro. A disposizione per chiarimenti o altro

The d'-dibaryon in a colored cluster model

We calculate the mass and structure of a J^P=0^-, T=0 six-quark system using a colored diquark-tetraquark cluster wave function and a nonrelativistic quark model Hamiltonian. The calculated mass is some 350 MeV above the empirical value if the same confinement strength as in the nucleon is used. If the effective two-body confinement strength is weaker in a compound six-quark system than in a single baryon, as expected from a simple harmonic oscillator model, one obtains M_d' = 2092 MeV close to experiment.Comment: 6 pages, Revtex, 2 ps-figures included, to appear in the Proceedings of the '6th Conference on the Intersections of Particle and Nuclear Physics' Big Sky, 199

Dynamics of transposable elements generates structure and symmetries in genetic sequences

Genetic sequences are known to possess non-trivial composition together with symmetries in the frequencies of their components. Recently, it has been shown that symmetry and structure are hierarchically intertwined in DNA, suggesting a common origin for both features. However, the mechanism leading to this relationship is unknown. Here we investigate a biologically motivated dynamics for the evolution of genetic sequences. We show that a metastable (long-lived) regime emerges in which sequences have symmetry and structure interlaced in a way that matches that of extant genomes.Comment: 6 pagesm 4 figure

Egorov property in perturbed cat map

We study the time evolution of the quantum-classical correspondence (QCC) for the well known model of quantised perturbed cat maps on the torus in the very specific regime of semi-classically small perturbations. The quality of the QCC is measured by the overlap of classical phase-space density and corresponding Wigner function of the quantum system called quantum-classical fidelity (QCF). In the analysed regime the QCF strongly deviates from the known general behaviour in particular it decays faster then exponential. Here we study and explain the observed behavior of the QCF and the apparent violation of the QCC principle.Comment: 12 pages, 7 figure

On a waiting-time result of Kontoyiannis: mixing or decoupling?

We introduce conditions of lower decoupling to the study of waiting-time estimations of the cross entropy between two mutually independent stationary stochastic processes. Although similar decoupling conditions have been used in the literature on large deviations and statistical mechanics, they appear largely unexplored in information theory. Building on a result of Kontoyiannis, namely Theorem 4 in [Kontoyiannis, J. Theor. Probab., 1998], and replacing the $\psi$-mixing condition in this result with a lower decoupling condition, we considerably extend the validity of waiting-time estimation of cross entropy