Guest Lecture: Dr. Andrea Richaud obtained his PhD in Physics with honors in 2020 from the Politecnico di Torino. He subsequently worked as a postdoctoral researcher at SISSA (International School for Advanced Studies) in the Condensed Matter group (2020–2022) and as a Marie Sklodowska-Curie Fellow at the UPC in Barcelona (2023–2025). He is currently a Junior Leader Fellow at the same university, thanks to a prestigious fellowship funded by the “la Caixa” Foundation. Dr. Richaud is also co-leader within the COST Action SCALES. He holds the Italian National Scientific Qualification as Associate Professor in Theoretical Condensed Matter Physics and has obtained the corresponding academic qualifications in Spain and France. Quantized vortices are central excitations of quantum fluids and are traditionally described as massless defects governed by first-order dynamics. In many real systems, however, vortex cores are filled with tracer particles or other superfluid components, giving rise to an effective inertial mass. This fundamentally modifies the dynamical and collective properties of vortex systems. This doctoral course presents a unified theoretical framework for the dynamics of such massive vortices in two-dimensional quantum fluids. Starting from binary mixtutres of Bose–Einstein condensates, we derive the Massive Point Vortex model from a two-component Gross–Pitaevskii Lagrangian using time-dependent variational methods, highlighting the emergence of second-order dynamics and its formal analogy with that of charged particles in electromagnetic fields. We analyse the dynamical regimes offered by single- and few-vortex systems in ex-perimentally-realistic confining potentials, exploring phenomena as radial oscillations, precession reversal, and collision processes unique to massive vortices. Extensions to non-trivial domains via conformal mapping, vortex arrays and necklaces, ghost vor-tices, and Kelvin–Helmholtz instabilities are also discussed. Analytical derivations are complemented by a computational tutorial on massive point-vortex models. Beyond its specific focus, the course addresses themes that are central to ongoing research in superfluidity, quantum many-body physics, nonlinear dynamics with direct relevance to cold-atom experiments, superconductivity, and emerging quantum tech-nologies. The course aims to provide doctoral students with a rigorous theoretical framework to describe and analyze inertial effects in superfluid vortex dynamics. Participants will develop the tools needed to derive effective models from microscopic theories, investigate the stability and collective regimes of vortex systems, and critically connect analytical predictions with numerical simulations and experimental contexts.

Classical and Quantum Mechanics

1) Introduction: Massive vortices in Quantum Fluids: Superfluid liquid helium with tracers, Two-component BECs, One-component BECs at finite temperature, Fermi superfluids, 2) The Massive Point Vortex model and its derivation, within the time-dependent variational approximation, from a two-component Gross-Pitaevskii field Lagrangian. 3) Dynamical regimes of one- and few- vortex systems. Analysis of stable and unstable modes. 4) The case of non-trivial confining geometries: from the disk to the annulus and the ellipse. The importance of conformal maps. 5) Electromagnetic analogy between massive point vortices and electrical charges in 2D domains. 6) Hands-on-tutorial on the numerical simulation of Massive Point Vortex Models with Mathematica. 7) Beyond the standard Model Point-Vortex model: i) the possible relative dynamics of vortices and massive cores; ii) Designing the collision of massive vortices. 8) Kelvin Helmholtz instability in counterflowing superfluids: formation and disgregation of regular vortex arrays. 9) Ghost vortices: analytical study of their equilibrium configurations. 10) Vortex necklaces and Leggett bounds.

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Presentazione orale

P.D.2-2 - Giugno