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Mauro Spera

Publications and source records attributed to Mauro Spera.

8 recordsLinked to original sources
arXiv2026

Geometric Phases and Holonomy in Structured Optical Fields

Geometric phases are widely used in modern optics, yet their meaning and underlying geometry depend on the actual physical settings, which can substantially differ from one another. This tutorial article introduces geometric phases in nanophotonic systems, focusing on the interaction of structured light with nanostructures or metaatoms. We compare the present setting with conventional geometric phases of structured-light optics and show that similar phase laws may correspond to genuinely different underlying geometries. Our aim is to provide a pedagogical bridge between the mathematical language of geometric phases and experimentally relevant examples from nanophotonics.

physics.optics↗
arXiv2025

Generalized theta functions, projectively flat vector bundles and noncommutative tori

In this paper, the well-known relationship between theta functions and Heisenberg group actions thereon is resumed by combining complex algebraic and noncommutative geometric techniques in that we describe Hermitian-Einstein vector bundles on 2-tori via representations of noncommutative tori, thereby reconstructing Matsushima's setup and elucidating the ensuing Fourier-Mukai-Nahm (FMN) aspects. We prove the existence of noncommutative torus actions on the space of smooth sections of Hermitian-Einstein vector bundles on 2-tori preserving the eigenspaces of a natural Laplace operator. Motivated by the Coherent State Transform approach to theta functions, we extend the latter to vector valued thetas and develop an additional algebraic reinterpretation of Matsushima's theory making FMN-duality manifest again.

math.QA↗
arXiv2024

Mott resistive switching initiated by topological defects

Resistive switching is the fundamental process that triggers the sudden change of the electrical properties in solid-state devices under the action of intense electric fields. Despite its relevance for information processing, ultrafast electronics, neuromorphic devices, resistive memories and brain-inspired computation, the nature of the local stochastic fluctuations that drive the formation of metallic nuclei out of the insulating state has remained hidden. Here, using operando X-ray nano-imaging, we have captured the early-stages of resistive switching in a V2O3-based device under working conditions. V2O3 is a paradigmatic Mott material, which undergoes a first-order metal-to-insulator transition coupled to a lattice transformation that breaks the threefold rotational symmetry of the rhombohedral metal phase. We reveal a new class of volatile electronic switching triggered by nanoscale topological defects of the lattice order parameter of the insulating phase. Our results pave the way to the use of strain engineering approaches to manipulate topological defects and achieve the full control of the electronic Mott switching. The concept of topology-driven reversible electronic transition is of interest for a broad class of quantum materials, comprising transition metal oxides, chalcogenides and kagome metals, that exhibit first-order electronic transitions coupled to a symmetry-breaking order.

cond-mat.str-el↗
arXiv2023

Diffeological Symplectic Frobenius Reciprocity

In this note we prove that the symplectic Frobenius Reciprocity established in the paper "Symplectic Induction, Prequantum Induction and Prequantum Multiplicities" as a set bijection is indeed a diffeological diffeomorphism, as conjectured by its authors Ratiu and Ziegler. The same holds in the prequantum space context.

math.SG↗
arXiv2019

A hydrodynamical homotopy co-momentum map and a multisymplectic interpretation of higher order linking numbers

In this article a homotopy co-momentum map (à la Callies-Frégier-Rogers-Zambon) trangressing to the standard hydrodynamical co-momentum map of Arnol'd, Marsden and Weinstein and others is constructed and then generalized to a special class of Riemannian manifolds. Also, a covariant phase space interpretation of the coadjoint orbits associated to the Euler evolution for perfect fluids and in particular of Brylinski's manifold of smooth oriented knots is discussed. As an application of the above homotopy co-momentum map, a reinterpretation of the (Massey) higher order linking numbers in terms of conserved quantities within the multisymplectic framework is provided and knot theoretic analogues of first integrals in involution are determined.

math.DG↗
arXiv2009

On some hydrodynamical aspects of quantum mechanics

In this note we first set up an analogy between spin and vorticity of a perfect 2d-fluid flow, based on the Borel-Weil contruction of the irreducible unitary representations of SU(2), and looking at the Madelung-Bohm velocity attached to the ensuing spin wave functions. We also show that, in the framework of finite dimensional geometric quantum mechanics, the Schrödinger velocity field on projective Hilbert space is divergence-free (being Killing with respect to the Fubini-Study metric) and fulfils the stationary Euler equation, with pressure proportional to the Hamiltonian uncertainty (squared). We explicitly compute the pressure gradient of this "Schrödinger fluid" and determine its critical points. Its vorticity is also calculated and shown to depend on the spacings of the energy levels. These results follow from hydrodynamical properties of Killing vector fields valid in any (finite dimensional) Riemannian manifold, of possible independent interest.

math-ph↗