arXiv subjects

Marcello Malagutti

Publications and source records attributed to Marcello Malagutti.

5 recordsLinked to original sources

arXiv2026

Perturbation Theory and the Quantum Rabi-model

In the first part of the paper we study a perturbative model of the Rabi system of Quantum Optics. We are therefore able to describe, through Rellich's theory, an analytic expansion of finite families of eigenvalues, of arbitrary fixed length. In particular, we prove that for finite families of eigenvalues the Braak conjecture holds. In the second part we study the asymptotics of the Weyl spectral counting function of a class of systems that generalize the Quantum Rabi Model to an $N$-level atom ($N\geq3$) with $n=N-1$ cavity modes of the electromagnetic field, with particular interest in the case $N=3$ and $n=2$.

quant-ph↗

arXiv2025

Propagation of Shubin-Sobolev singularities of Weyl-quantizations of complex quadratic forms

The aim of this work is to develop the Hörmander microlocal theory in the isotropic framework and use the results we obtain to study the propagation of singularities for an evolution problem, with diffusive part given by a Weyl-quantization of a complex quadratic form on the phase space.

math.AP↗

arXiv2023

Semialgebraic and Continuous Solution of Linear Equations with Semialgebraic Coefficients

Starting from the results of Charles Fefferman and Janos Kollár in \texit{Continuous Solutions of Linear Equations} [1], we adopt a new approach based on Fefferman's techniques of Glaeser refinement to show a more general result than the one proved by Kollár by using techniques from algebraic geometry. Considering a system of linear equations with semialgebraic (not only polynomial as in [1]) coefficients on $\mathbb{R}^{n}$, we get a necessary and sufficient condition for the existence of a continuous and semialgebraic solution on $\mathbb{R}^{n}$. This is different from what Fefferman and Luli obtained in \textit{Semialgebraic Sections Over the Plane} since they stated their result for solutions of regularity $C^m$ on the plane $\mathbb{R}^2$. More in depth, we prove that a continuous and semialgebraic solution on $\mathbb{R}^{n}$ exists if and only if there is a continuous solution i.e., if the Glaeser-stable bundle associated to the system has no empty fiber.

math.AG↗

arXiv2023

On The Spectral Zeta Function Of Second Order Semiregular Non-Commutative Harmonic Oscillators

In this paper we give a meromorphic continuation of the spectral zeta function for semiregular Non-Commutative Harmonic Oscillators (NCHO). By ``semiregular system'' we mean systems with terms with degree of homogeneity scaling by $1$ in their asymptotic expansion. As an application of our results, we first compute the meromorphic continuation of the Jaynes-Cummings (JC) model spectral zeta function. Then we compute the spectral zeta function of the JC generalization to a 3-level atom in a cavity. For both of them we show that it has only one pole in 1.

math.AP↗

arXiv2022

Semialgebraic Solutions of Linear Equations with Continuous Semialgebraic Coefficients

Starting from the results of Charles Fefferman and Janos Kollàr in Continuous Solutions of Linear Equations [1], we adopt a new approach based on Fefferman's techniques of Glaeser refinement to show a more general result than the one proved by Kollàr by using techniques from algebraic geometry. Considering a system of linear equations with semialgebraic (not only polynomial as in [1]) coefficients on R^n, we get a necessary and sufficient condition for the existence of a continuous and semialgebraic solution on R^n. This is different from what Fefferman and Luli obtained in Semialgebraic Sections Over the Plane [3] since they stated their result for solutions of regularity C^m on the plane R^2. More in depth, we prove that a continuous and semialgebraic solution on Rn exists if and only if there is a continuous solution i.e., if the Glaeser-stable bundle associated to the system has no empty fiber.

math.AG↗