arXiv subjects

Francesco Gargano

Publications and source records attributed to Francesco Gargano.

At least 19 recordsLinked to original sources

arXiv2026

Turing mechanisms in a multimode open quantum system

We investigate pattern formation in a finite chain of bosonic modes whose dynamics is governed by a Gorini-Kossakowski-Sudarshan-Lindblad (GKSL) master equation. The model combines local parametric driving and nonlinear damping with nonlocal dissipative couplings between modes that work on different discrete spatial scales. In the classical limit, these mechanisms generate a reaction-diffusion-like dynamics, allowing the emergence of Turing-type instabilities. The key aspect of the analysis is the coexistence and competition of different unstable spatial modes. Depending on the range of parameters, the system may select different stationary nonuniform configurations, oscillatory wave-like states, or regimes in which multiple modes interact before a dominant pattern is established, thus providing a mechanism for pattern selection. We compare the deterministic bifurcation scenario, generated by a reaction-diffusion-like system derived from semiclassical drift dynamics, with the quantum dynamics, derived via the GKSL master equation, using phase-space methods and reduced Wigner functions. The results show how Turing instabilities, mode competition, and pattern selection can be extended to multimode open quantum systems, providing a bridge between nonlinear dynamical systems, dissipative quantum mechanics, and spatial self-organization.

quant-ph↗

arXiv2026

A Damage-Driven Model for Duchenne Muscular Dystrophy: Early-Stage Dynamics and Invasion Thresholds

We introduce a spatially extended mathematical model for Duchenne muscular dystrophy based on a damage-driven paradigm, in which immune recruitment is triggered by tissue injury. The model is formulated as a reaction--diffusion--chemotaxis system describing the interaction between healthy tissue, damaged fibers, immune cells and inflammatory signals. We establish the global well-posedness of the system and investigate the early-stage dynamics through linearization around the healthy equilibrium. Our analysis shows that diffusion does not induce Turing instabilities, so that spatial heterogeneity cannot arise from diffusion-driven mechanisms. Instead, disease progression occurs through invasion processes. We derive explicit conditions for the onset of invasion, interpreted as an effective damage reproduction threshold and characterize the minimal propagation speed of pathological fronts, showing that the dynamics is governed by a pulled-front mechanism. Numerical simulations support the analytical results and confirm the transition between decay and invasion. These results provide a mathematical framework for early-stage disease progression and indicate that spatial spreading arise from the expansion of localized damage rather than from intrinsic pattern-forming mechanisms.

math-ph↗

arXiv2025

From Classical Rationality to Contextual Reasoning: Quantum Logic as a New Frontier for Human-Centric AI in Finance

We consider state of the art applications of artificial intelligence (AI) in modelling human financial expectations and explore the potential of quantum logic to drive future advancements in this field. This analysis highlights the application of machine learning techniques, including reinforcement learning and deep neural networks, in financial statement analysis, algorithmic trading, portfolio management, and robo-advisory services. We further discuss the emergence and progress of quantum machine learning (QML) and advocate for broader exploration of the advantages provided by quantum-inspired neural networks.

q-fin.CP↗

arXiv2025

Modeling Epidemics with Memory Effects: an Open Quantum System Approach

In this work, we introduce a quantum-inspired epidemic model to study the dynamics of an infectious disease in a population divided into compartments. By treating the healthy population as a large reservoir, we construct a framework based on open quantum systems and a Hilbert space formalism to model the spread of the infection. This approach allows for a mathematical framework that captures both Markovian and semi-Markovian dynamics in the evolution equations. Through numerical experiments, we examine the impact of varying memory parameters on the epidemic evolution, focusing in particular on the conditions under which the model remains physically admissible.

q-bio.PE↗

arXiv2025

Density matrices and entropy operator for non-Hermitian quantum mechanics

In this paper we consider density matrices operator related to non-Hermitian Hamiltonians. In particular, we analyse two natural extensions of what is usually called a density matrix operator (DM), of pure states and of the entropy operator: we first consider those {\em operators} which are simply similar to a standard DM, and then we discuss those which are intertwined with a DM by a third, non invertible, operator, giving rise to waht we call Riesz Density Matrix operator (RDM). After introducing the mathematical framework, we apply the framework to a couple of applications. The first application is related to a non-Hermitian Hamiltonian describing gain and loss phenomena, widely considered in the context of $PT$-quantum mechanics. The second application is related to a finite-dimensional version of the Swanson Hamiltonian, never considered before, and addresses the problem of deriving a milder version of the RDM when exceptional points form in the system.

math-ph↗

arXiv2024

Coherent States of Graphene Layer with and without a PT-symmetric Chemical Potential

In this paper we construct different classes of coherent and bicoherent states for the graphene tight-binding model in presence of a magnetic field, and for a deformed version where we include a $\mathcal{P}\mathcal{T}$-symmetric chemical potential $V$. In particular, the problems caused by the absence of a suitable ground state for the system is taken into account in the construction of these states, for $V=0$ and for $V\neq0$. We introduce ladder operators which work well in our context, and we show, in particular, that there exists a choice of these operators which produce a factorization of the Hamiltonian. The role of broken and unbroken $\mathcal{P}\mathcal{T}$-symmetry is discussed, in connection with the strength of $V$.

math-ph↗

arXiv2022

Bi-coherent states as generalized eigenstates of the position and the momentum operators

In this paper we show that the position and the derivative operators, $\hat q$ and $\hat D$, can be treated as ladder operators connecting the various vectors of two biorthonormal families, $\mathcal{F}_φ$ and $\mathcal{F}_ψ$. In particular, the vectors in $\mathcal{F}_φ$ are essentially monomials in $x$, $x^k$, while those in $\mathcal{F}_ψ$ are weak derivatives of the Dirac delta distribution, $δ^{(m)}(x)$, times some normalization factor. We also show how bi-coherent states can be constructed for these $\hat q$ and $\hat D$, both as convergent series of elements of $\mathcal{F}_φ$ and $\mathcal{F}_ψ$, or using two different displacement-like operators acting on the two vacua of the framework. Our approach generalizes well known results for ordinary coherent states.

quant-ph↗

arXiv2020

Eigenvalues of non-hermitian matrices: a dynamical and an iterative approach. Application to a truncated Swanson model

We propose two different strategies to find eigenvalues and eigenvectors of a given, not necessarily Hermitian, matrix $A$. Our methods apply also to the case of complex eigenvalues, making the strategies interesting for applications to physics, and to pseudo-hermitian quantum mechanics in particular. We first consider a {\em dynamical} approach, based on a pair of ordinary differential equations defined in terms of the matrix $A$ and of its adjoint $A^\dagger$. Then we consider an extension of the so-called power method, for which we prove a fixed point theorem for $A\neq A^\dagger$ useful in the determination of the eigenvalues of $A$ and $A^\dagger$. The two strategies are applied to some explicit problems. In particular, we compute the eigenvalues and the eigenvectors of the matrix arising from a recently proposed quantum mechanical system, the {\em truncated Swanson model}, and we check some asymptotic features of the Hessenberg matrix.

math-ph↗

arXiv2019

A no-go result for the quantum damped harmonic oscillator

In this letter we show that it is not possible to set up a canonical quantization for the damped harmonic oscillator using the Bateman lagrangian. In particular, we prove that no square integrable vacuum exists for the {\em natural} ladder operators of the system, and that the only vacua can be found as distributions. This implies that the procedure proposed by some authors is only formally correct, and requires a much deeper analysis to be made rigorous.

quant-ph↗

arXiv2018

Two-dimensional non commutative Swanson model and its bicoherent states

We introduce an extended version of the Swanson model, defined on a two-dimensional non commutative space, which can be diagonalized exactly by making use of pseudo-bosonic operators. Its eigenvalues are explicitly computed and the biorthogonal sets of eigenstates of the Hamiltonian and of its adjoint are explicitly constructed. We also show that it is possible to construct two displacement-like operators from which a family of bi-coherent states can be obtained. These states are shown to be eigenstates of the deformed lowering operators, and their projector allows to produce a suitable resolution of the identity in a dense subspace of $\Lc^2(\Bbb R^2)$.

math-ph↗

arXiv2018

Bi-squeezed states arising from pseudo-bosons

Extending our previous analysis on bi-coherent states, we introduce here a new class of quantum mechanical vectors, the \emph{bi-squeezed states}, and we deduce their main mathematical properties. We relate bi-squeezed states to the so-called regular and non regular pseudo-bosons. We show that these two cases are different, from a mathematical point of view. Some physical examples are considered.

math-ph↗

arXiv2016

Exceptional Points in a non-Hermitian extension of the Jaynes-Cummings Hamiltonian

We consider a generalization of the non-Hermitian ${\mathcal PT}$ symmetric Jaynes-Cummings {Hamiltonian, recently introduced for studying optical phenomena with time-dependent physical parameters, that includes environment-induced decay}. In particular, we investigate the interaction of a two-level fermionic system (such as a two-level atom) with a single bosonic field mode in a cavity. The states of {the} two-level system are allowed to decay because of the interaction with the environment, {and this is included phenomenologically in our non-Hermitian Hamiltonian by introducing complex energies for the fermion system. We focus our attention} on the occurrence of exceptional points in the spectrum of the Hamiltonian, clarifying its mathematical and physical meaning.

quant-ph↗

arXiv2016

Projector operators in clustering

In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which generates different clusters from a set of input data. Also, we consider what happens when the orthonormal bases first used in the definition of the projectors are replaced by frames, and how these can be useful when trying to connect some noised signal to a given cluster.

math.FA↗

arXiv2014

A Phenomenological Operator Description of Dynamics of Crowds: Escape Strategies

We adopt an operatorial method, based on creation, annihilation and number operators, to describe one or two populations mutually interacting and moving in a two--dimensional region. In particular, we discuss how the two populations, contained in a certain two-dimensional region with a non--trivial topology, react when some alarm occurs. We consider the cases of both low and high densities of the populations, and discuss what is changing as the strength of the interaction increases. We also analyze what happens when the region has either a single exit or two ways out.

physics.soc-ph↗

arXiv2014

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective.

math-ph↗

arXiv2014

A spectral approach to a constrained optimization problem for the Helmholtz equation in unbounded domains

We study some convergence issues for a recent approach to the problem of transparent boundary conditions for the Helmholtz equation in unbounded domains. The approach is based on the minimization on an integral functional which arises from an integral formulation of the radiation condition at infinity. In this Letter, we implement a Fourier-Chebyschev collocation method and show that this approach reduce the computational cost significantly. As a consequence, we give numerical evidence of some convergence estimates available in literature and we study the robustness of the algorithm at low and mid-high frequencies.

math.NA↗

arXiv2013

High Reynolds number Navier-Stokes solutions and boundary layer separation induced by a rectilinear vortex

We compute the solutions of Prandtl's and Navier-Stokes equations for the two dimensional flow induced by a rectilinear vortex interacting with a boundary in the half plane. For this initial datum Prandtl's equation develops, in a finite time, a separation singularity. We investigate the different stages of unsteady separation for Navier-Stokes solution at different Reynolds numbers $Re=10^3-10^5$, and we show the presence of a large-scale interaction between the viscous boundary layer and the inviscid outer flow. We also see a subsequent stage, characterized by the presence of a small-scale interaction, which is visible only for moderate-high Re numbers $Re=10^4-10^5$. We also investigate the asymptotic validity of boundary layer theory by comparing Prandtl's solution to Navier-Stokes solutions during the various stages of unsteady separation.

math-ph↗

arXiv2013

Singularity formation for Prandtl's equations

We consider Prandtl's equations for the impulsively started disk and follow the process of the formation of the singularity in the complex plane using the singularity tracking method. We classify Van Dommelen and Shen's singularity as a cubic root singularity. We introduce a class of initial data which have a dipole singularity in the complex plane. These data are uniformly bounded in $H^1$ and lead to an earlier singularity formation. The presence of a small viscosity in the streamwise direction changes the behavior of the singularities.

math-ph↗