arXiv subjects

Alessandro Pignedoli

Publications and source records attributed to Alessandro Pignedoli.

4 recordsLinked to original sources

arXiv2026

Topological Classification of Non-Normalizable Vector Fields

Topological classification of physical vector fields conventionally relies on field normalization and homotopy-based invariants. However, when field amplitudes vanish, normalization becomes ill-defined, preventing a direct topological characterization. Here, we introduce a general framework for the topological classification of non-normalizable $n$-dimensional vector fields with compactifiable base spaces by transforming them into $(n+1)$-dimensional normalized vector fields. This construction extends homotopy-based classification to fields containing amplitude zeros. We explicitly demonstrate the approach for one-, two-, and three-dimensional non-normalized vector fields and derive the corresponding topological invariants. The resulting topological charges are robust under continuous deformations and can change only when the embedding structure becomes singular. Our framework provides a unified route to the topological characterization of non-normalizable fields and opens the door to the study of topological phenomena in a broad range of systems, including magnetic textures, ferroelectrics, electromagnetic fields, and wave systems.

cond-mat.other↗

arXiv2026

Leveraging Interactions for Efficient Swarm-Based Brownian Computing

Drawing inspiration from swarm intelligence, we show that short-range attractive interactions between thermally driven Brownian quasiparticles enable energy-efficient optimization. As quasiparticles can be generated directly within a material, the swarm size can be adjusted with minimal energy overhead. Using an optimization task defined by a spatially varying temperature landscape, we quantitatively show that interacting swarms reliably identify global optima and significantly outperform non-interacting searchers within a well-defined regime of interaction strength and swarm size. This improvement arises from emergent cooperative behavior, where local interactions guide the swarm toward high-quality solutions without central coordination. To link our physical model to experimental realizations, we coarse-grain the quasiparticle dynamics onto a sensor lattice and generate trajectories emulating particle-tracking measurements. We further show that the interacting swarm adapts robustly to landscapes that evolve over time. These findings establish interacting Brownian quasiparticles as a physical platform for scalable and energy-efficient unconventional computing.

cond-mat.stat-mech↗

arXiv2024

3D Magnetic Textures with Mixed Topology: Unlocking the Tunable Hopf Index

Knots and links play a crucial role in understanding topology and discreteness in nature. In magnetic systems, twisted, knotted and braided vortex tubes manifest as Skyrmions, Hopfions, or screw dislocations. These complex textures are characterized by topologically non-trivial quantities, such as a Skyrmion number, a Hopf index $H$, a Burgers vector (quantified by an integer $\nu$), and linking numbers. In this work, we introduce a discrete geometric definition of $H$ for periodic magnetic textures, which can be separated into contributions from the self-linking and inter-linking of flux tubes. We show that fractional Hopfions or textures with non-integer values of $H$ naturally arise and can be interpreted as states of ``mixed topology" that are continuously transformable to one of the multiple possible topological sectors. Our findings demonstrate a solid physical foundation for the Hopf index to take integer, non-integer, or specific fractional values, depending on the underlying topology of the system.

cond-mat.mes-hall↗

arXiv2024

Numerical Calculation of the Hopf Index for 3D Magnetic Textures

To gain deeper insight into the complex, stable, and robust configurations of magnetic textures, topological characterisation has proven essential. In particular, while the skyrmion number is a well-established topological invariant for 2D magnetic textures, the Hopf index serves as a key topological descriptor for 3D magnetic structures. In this work, we present and compare various methods for numerically calculating the Hopf index, provide implementations, and offer a detailed analysis of their accuracy and computational efficiency. Additionally, we identify and address common pitfalls and challenges associated with the numerical computation of the Hopf index, offering insights for improving the robustness of these techniques.

cond-mat.mes-hall↗