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PubblicazioneClifford-dressed variational principles for precise Loschmidt echoes( 2025)We extend the recently introduced Clifford-dressed time-dependent variational principle (TDVP) to efficiently compute many-body wave-function amplitudes in the computational basis. This advancement enhances the study of Loschmidt echoes, which generally require accurate calculations of the overlap between the evolved state and the initial wave function. By incorporating Clifford-disentangling gates during TDVP evolution, our method effectively controls entanglement growth while keeping the computation of these amplitudes accessible. Specifically, it reduces the problem to evaluating the overlap between a matrix product state (MPS) and a stabilizer state, a task that remains computationally feasible within the proposed framework. To demonstrate the effectiveness of this approach, we first benchmark it on the one-dimensional transverse-field Ising model. We then apply it to more challenging scenarios, including a nonintegrable next-to-nearest-neighbor Ising chain and a two-dimensional Ising model. Our results highlight the versatility and efficiency of the Clifford-augmented MPS, showcasing its capability to go beyond the evaluation of simple expectation values. This makes it a powerful tool for exploring various aspects of many-body quantum dynamics.
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PubblicazioneExploring RNA destabilization mechanisms in biomolecular condensates through atomistic simulations( 2025): Biomolecular condensates are currently recognized to play a key role in organizing cellular space and in orchestrating biochemical processes. Despite an increasing interest in characterizing their internal organization at the molecular scale, not much is known about how the densely crowded environment within these condensates affects the structural properties of recruited macromolecules. Here, we adopted explicit-solvent all-atom simulations based on a combination of enhanced sampling approaches to investigate how the conformational ensemble of an RNA hairpin is reshaped in a highly concentrated peptide solution that mimics the interior of a biomolecular condensate. Our simulations indicate that RNA structure is greatly perturbed by this distinctive physico-chemical environment, which weakens RNA secondary structure and promotes extended nonnative conformations. The resulting high-resolution picture reveals that RNA unfolding is driven by the effective solvation of nucleobases through hydrogen bonding and stacking interactions with surrounding peptides. This solvent effect can be modulated by the amino acid composition of the model condensate as proven by the differential RNA behavior observed in the case of arginine-rich and lysine-rich peptides.
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PubblicazioneVisuo-spatial reasoning in the human brain(SISSA, 2024-11-25)This thesis explores the brain correlates and contextual factors influencing visuo-spatial reasoning through Mental Rotation (MR) tasks in men and women. Visuo-spatial reasoning, a critical cognitive function, underpins everyday activities and is often assessed through MR tasks, where previous studies have shown gender differences favoring men. The research addresses the ongoing nature-nurture debate by examining the contributions of top-down (strategy-related), bottom-up (stimulus-related), and cognitive traits to MR performance and neural activation. Four experiments are conducted to: (1) investigate gender-specific strategy preferences in MR tasks; (2) characterize the neural correlates of MR and their modulation by imagery strategies; (3) compare brain activations related to different MR stimuli (abstract, manipulable, and bodily); and (4) assess the impact of individual cognitive traits on MR performance and brain activity. This comprehensive approach aims to provide deeper insights into the cognitive and neural mechanisms underlying gender differences in MR, with implications for understanding disparities in STEM-related fields.
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PubblicazioneBallistic macroscopic fluctuation theory( 2023)We introduce a new universal framework describing fluctuations and correlations in quantum and classical many-body systems, at the Euler hydrodynamic scale of space and time. The framework adapts the ideas of the conventional macroscopic fluctuation theory (MFT) to systems that support ballistic transport. The resulting "ballistic MFT" (BMFT) is solely based on the Euler hydrodynamics data of the many-body system. Within this framework, mesoscopic observables are classical random variables depending only on the fluctuating conserved densities, and Euler-scale fluctuations are obtained by deterministically transporting thermodynamic fluctuations via the Euler hydrodynamics. Using the BMFT, we show that long-range correlations in space generically develop over time from long-wavelength inhomogeneous initial states in interacting models. This result, which we verify by numerical calculations, challenges the long-held paradigm that at the Euler scale, fluid cells may be considered uncorrelated. We also show that the Gallavotti-Cohen fluctuation theorem for non-equilibrium ballistic transport follows purely from time-reversal invariance of the Euler hydrodynamics. We check the validity of the BMFT by applying it to integrable systems, and in particular the hard-rod gas, with extensive simulations that confirm our analytical results.
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PubblicazioneAn elementary proof of existence and uniqueness for the Euler flow in localized Yudovich spaces( 2024)We revisit Yudovich's well-posedness result for the 2-dimensional Euler equations for an inviscid incompressible fluid on either a sufficiently regular (not necessarily bounded) open set Omega subset of R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega \subset \mathbb {R}<^>2$$\end{document} or on the torus Omega=T2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Omega =\mathbb {T}<^>2$$\end{document}. We construct global-in-time weak solutions with vorticity in L1 boolean AND Lulp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>1\cap L<^>p_{ul}$$\end{document} and in L1 boolean AND Yul Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>1\cap Y<^>\Theta _{ul}$$\end{document}, where Lulp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>p_{ul}$$\end{document} and Yul Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y<^>\Theta _{ul}$$\end{document} are suitable uniformly-localized versions of the Lebesgue space Lp\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>p$$\end{document} and of the Yudovich space Y Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$Y<^>\Theta $$\end{document} respectively, with no condition at infinity for the growth function Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document}. We also provide an explicit modulus of continuity for the velocity depending on the growth function Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document}.We prove uniqueness of weak solutions in L1 boolean AND Yul Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L<^>1\cap Y<^>\Theta _{ul}$$\end{document} under the assumption that Theta\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Theta $$\end{document} grows moderately at infinity. In contrast to Yudovich's energy method, we employ a Lagrangian strategy to show uniqueness. Our entire argument relies on elementary real-variable techniques, with no use of either Sobolev spaces, Calder & oacute;n-Zygmund theory or Littlewood-Paley decomposition, and actually applies not only to the Biot-Savart law, but also to more general operators whose kernels obey some natural structural assumptions.