Browsing by Author "De Nittis, Giuseppe"
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- ItemA new light on the FKMM invariant and its consequences(2023) De Nittis, Giuseppe; Kiyonori Gomi
- ItemAbout the notion of eigenstates for C*-algebras and some application in quantum mechanics(AIP Publishing, 2023) De Nittis, Giuseppe; Polo Ojito, Danilo JoséThis work is concerned with the notion of eigenstates for C*-algebras. After reviewing some basic and structural results, we explore the possibility of reinterpreting certain typical concepts of quantum mechanics (e. g. dynamical equilibrium states, ground states, gapped states, Fermi surfaces) in terms of (algebraic) eigenstates.
- ItemC*-algebric methods for transport phenomena(2023) Polo Ojito, Danilo; De Nittis, Giuseppe; Pontificia Universidad Católica de Chile. Facultad de Matemáticas
- ItemChiral vector bundles(2018) De Nittis, Giuseppe; Gomi, Kiyonori
- ItemCorrigendum to “Spectral continuity for aperiodic quantum systems I. General theory” [J. Funct. Anal. 275 (11) (2018) 2917–2977](2019) Siegfried Beckus; Jean Bellissard; De Nittis, Giuseppe
- ItemDerivation of Ray Optics Equations in Photonic Crystals via a Semiclassical Limit(2017) De Nittis, Giuseppe; Lein, M
- ItemDifferential geometric invariants for time-reversal symmetric Bloch bundles II: The low-dimensional "quaternionic" case(2023) De Nittis, Giuseppe; Gomi, KiyonoriThis paper is devoted to the construction of differential geometric invariants for the classification of "quaternionic" vector bundles. Provided that the base space is a smooth manifold of dimension two or three endowed with an involution that leaves fixed only a finite number of points, it is possible to prove that the Wess-Zumino term and the Chern-Simons invariant yield topological invariants able to distinguish between inequivalent realizations of "quaternionic" structures. This is a nontrivial generalization of results previously known only in the case of tori with time-reversal involution.
- ItemDifferential geometric invariants for time-reversal symmetric Bloch-bundles : the "Real" case(2016) De Nittis, Giuseppe; Gomi, K.
- ItemDixmier trace and the DOS of magnetic operators(2022) Fabian Belmonte; De Nittis, Giuseppe
- ItemErratum: “Exponentially localized Wannier functions in periodic zero flux magnetic fields” [J. Math. Phys. 52, 112103 (2011)](2020) De Nittis, Giuseppe; Max Lein
- ItemExplicit spectral analysis for operators representing the unitary group U (d) and its Lie algebra u (d) through the Metaplectic representation and Weyl quantization(World Scientific Publishing, ) Belmonte, Fabián; De Nittis, GiuseppeIn this paper, we compute and analyze the spectrum of operators defined by the metaplectic representation μ on the unitary group U (d) and operators defined by the corresponding induced representation d μ of the Lie algebra u (d). We will show that the point spectrum of both types of operators can be expressed in terms of the eigenvalues of the corresponding matrices. For each A ∈ u (d), we will give conditions to guarantee that H A = −i d μ (A) has discrete spectrum. Under these conditions, using a known result in combinatorics, we show that the multiplicity of the eigenvalues of H A is (up to some explicit translation and scalar multiplication) a quasi-olynomial of degree d−1. Moreover, we show that the counting of eigenvalues function behaves as an Ehrhart polynomial. Using the latter result, we prove Weyl’s law for the operators H A.
- ItemGeometrical approach for quantum control : the qubit case(2021) Mendizábal Pico, Mauro Javier; De Nittis, Giuseppe; Spehner, Dominique; Pontificia Universidad Católica de Chile. Instituto de FísicaEn esta tesis presentamos un modelo de control cuántico para transiciones de estados puros y mixtos, aplicado a un qubit. El modelo está basado en la geometría del espacio de los estados cuánticos dada por la métrica de Bures y la ecuación de Liouville-von Neumann, la cual contiene información sobre los parámetros de los campos de control. Además, hacemos una revisión y simulación de los modelos o algoritmos de control cuántico que están bien establecidos en el área de control cuántico. Hemos llegado a concluir que nuestro trabajo supera a los modelos CRAB y GRAPE cuando se desea llegar al estado final en menos pasos; es decir, haciendo evolucionar al estado inicial lo menos posible, cumpliendo con un rango de valor de infidelidad deseado.
- ItemHilbert Grassmannians as classifying spaces(2025) De Nittis, Giuseppe; Gomi, Kiyonori; González Rendel, SantiagoIn this short work we prove that the Hilbert Grassmannians endowed with the weak topology are models for the classifying spaces of the unitary groups. As application of this result one can use Hilbert Grassmannians for the presentation of the $K$-theory of topological spaces by computing equivalences classes of homotopy equivalent maps.
- ItemLearning from insulators: New trends in the study of conductivity of metals(American Institute of Physics, 2024) De Nittis, Giuseppe; Lein M.; Rojas-Molina C.; Seri M.
- ItemLieb-Robinson Bounds in the Continuum Via Localized Frames(2024) Bachmann, Sven; De Nittis, GiuseppeWe study the dynamics of interacting fermions in the continuum. Our approach uses the concept of lattice-localized frames, which we introduce here. We first prove a Lieb-Robinson bound that is valid for a general class of local interactions, which implies the existence of the dynamics at the level of the CAR algebra. We then turn to the physical situation relevant to the (fractional) quantum Hall effect, namely the quasi-free second quantized Landau Hamiltonian to which electron-electron interactions can be added.
- ItemLinear Response Theory(2017) De Nittis, Giuseppe; Max Lein
- ItemOn the K-theoretic classification of dynamically stable systems(2019) De Nittis, Giuseppe; Kiyonori Gomi
- ItemPerturbation Theory for the Thermal Hamiltonian: 1D Case(SPRINGER, 2021) De Nittis, Giuseppe; Lenz, VicenteThis work continues the study of the thermal Hamiltonian, initially proposed by J. M. Luttinger in 1964 as a model for the conduction of thermal currents in solids. The previous work (De Nittis and Lenz in Spectral theory of the thermal Hamiltonian, 1D case, 2020) contains a complete study of the "free" model in one spatial dimension along with a preliminary scattering result for convolution-type perturbations. This work complements the results obtained in De Nittis and Lenz (2020) by providing a detailed analysis of the perturbation theory for the one-dimensional thermal Hamiltonian. In more detail, the following results are established: the regularity and decay properties for elements in the domain of the unperturbed thermal Hamiltonian; the determination of a class of self-adjoint and relatively compact perturbations of the thermal Hamiltonian; the proof of the existence and completeness of wave operators for a subclass of such potentials.
- ItemSpectral continuity for aperiodic quantum systems I. General theory(2018) Beckus, Siegfried; Bellissard, Jean; De Nittis, Giuseppe
- ItemSpectral continuity for aperiodic quantum systems: Applications of a folklore theorem(2020) Siegfried Beckus; Jean Bellissard; De Nittis, Giuseppe