Davide Lonigro
Researcher in quantum mechanics
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Research interests
My research sits at the intriguing boundary between theoretical and mathematical physics. I focus on infinite-dimensional quantum systems, paying particular attention to the often-overlooked interplay between abstract properties—such as self-adjointness, domain issues, and notions of convergence—and the underlying physical phenomena. A central theme in my work is the development of rigorous models of matter–field interaction, their spectral analysis, and their role in understanding key processes in quantum optics and the theory of open quantum systems.
Below is an overview of my main research directions—though research rarely fits neatly into boxes, nor should it.
Taming UV divergences in light–matter interaction
Even the simplest models of light–matter interaction, like spin–boson models, can already run into mathematical difficulties. Their Hamiltonians, as they appear in real-world applications, often come with divergences that prevent them from directly generating a valid dynamics. In my research, I explore how to tame these ultraviolet divergences and make sense of the models by developing renormalization schemes. Depending on how severe the divergence is, these schemes allow one to recover a unique, well-defined dynamics in a carefully chosen limiting process.
Some relevant papers:
D. Lonigro, J. Math. Phys. 63 (2022), 072105.
D. Lonigro, Math. Phys. Anal. Geom. 26 (2023), 15.
B. Alvarez, S. Lill, D. Lonigro, J. Valentín Martín, arXiv:2508.00803.
Dynamics of infinite-dimensional systems: approximations and effective models
Most realistic quantum systems cannot be solved exactly, and one must rely on approximations and effective models. For infinite-dimensional systems, however, approximations require special care: their validity depends on subtle mathematical choices, and even when justified, one still needs precise error bounds. My research has addressed this challenge by quantifying the accuracy of widely used approximations—such as the rotating-wave approximation in quantum optics, the Trotter error in dynamical decoupling, and finite-dimensional truncations. In the latter case, I have shown how mathematical issues like essential self-adjointness can directly affect the convergence of numerical simulations—or even cause them to fail.
Some relevant papers:
A. Hahn, D. Burgarth, D. Lonigro, SciPost Phys. 19 (2025), 035.
Z. Szabó, S. Gehr, P. Facchi, K. Yuasa, D. Burgarth, D. Lonigro, Phys. Rev. A, in press (2025).
F. Fischer, D. Burgarth, D. Lonigro, arXiv:2412.15889 & arXiv:2508.09044.
Quantum foundations: non-Markovianity, non-classicality, and bi-probabilities
Realistic models of quantum systems are never isolated: they inevitably interact with an external environment, such as a bosonic field. This interaction not only complicates their description but also gives rise to striking phenomena, including quantum non-Markovianity. In my early work, I explored these effects in spin–boson models, showing how the nature of the coupling shapes the emergence of non-Markovian and non-classical behavior. More recently, I broadened this line of research by developing a framework based on bi-probability distributions, which makes it possible to formulate a version of the Kolmogorov extension theorem that holds in the quantum setting.
Some relevant papers:
D. Burgarth, P. Facchi, M. Ligabò, D. Lonigro, Phy. Rev. A 103 (2021), 012203.
D. Lonigro, D. Chruściński, J. Phys. A: Math. Theor. 55 (2022), 225308.
D. Lonigro, F. Sakuldee, Ł. Cywiński, D. Chruściński, and P. Szańkowski, Quantum 8 (2024), 1447.
Infinite-dimensional quantum control and time-dependent Hamiltonians
Beyond simply describing how additional degrees of freedom influence quantum systems, one can also harness them to actively steer a system’s evolution. This idea lies at the heart of the mathematical theory of quantum control, which studies how quantum systems can be manipulated through time-dependent Hamiltonians. Many protocols of practical interest, however, are inherently infinite-dimensional, bringing new mathematical challenges. My work in this area has focused on quantum control at the boundary—where the system is driven by actions at its boundary rather than external fields—and on control through singular perturbations, such as point interactions.
Some relevant papers:
A. Balmaseda, D. Lonigro, J.M. Pérez-Pardo, SIAM J. Control Optim. 62 (2024), 826–852.
A. Balmaseda, D. Lonigro, J.M. Pérez-Pardo, J. Func. Anal. 287 (2024), 110563.
A. Balmaseda, D. Lonigro, J.M. Pérez-Pardo, SIAM J. Control Optim. 63 (2025), 1022–1050.
Low-dimensional quantum physics and waveguide QED
Spin–boson models also play a central role in quantum waveguide electrodynamics, where they describe artificial atoms (emitters) coupled to a photonic waveguide. In this setting, my research has focused on the emergence of bound states in the continuum—exotic states with energies above the propagation threshold, heuristically formed by trapped photons between resonant emitters. In certain regimes, such as evenly spaced emitter arrays, these bound states cannot be captured by standard perturbative methods, making a more refined mathematical treatment essential. More broadly, I have also studied the structure of low-dimensional physical theories and how dimensional reduction can both recover known models and reveal new ones.
Some relevant papers:
P. Facchi, D. Lonigro, S. Pascazio, F. V. Pepe, D. Pomarico, Phys. Rev. A 100 (2019), 023834.
D. Lonigro, P. Facchi, S. Pascazio, F. V. Pepe, D. Pomarico, New J. Phys. 23 (2021), 103033.
G. Angelone, E. Ercolessi, P. Facchi, D. Lonigro, R. Maggi, G. Marmo, S. Pascazio, F.V. Pepe, J. Phys. A: Math. Theor. 56 (2023), 065201.
Boundary conditions in quantum mechanics
The behavior of a quantum particle in a cavity is crucially influenced by the boundary conditions. These conditions can have a decisive impact on both the spectral and dynamical properties of the system. My research has explored this theme in several directions: from studying boundary effects in magnetic and quantum Hall systems, to developing quantum control schemes based on time-dependent boundaries. More recently, I have uncovered a surprising connection between boundary conditions and finite-dimensional truncations of quantum systems: for a particle in a box, certain mathematically valid truncation bases can lead to dynamics that converge to a system with incorrect boundary conditions—effectively placing the particle in the “wrong box”.
Some relevant papers:
G. Angelone, M. Asorey, P. Facchi, D. Lonigro, Y. Martinez, J. Phys. A: Math. Theor. 56 (2023), 025301.
A. Balmaseda, D. Lonigro, J.M. Pérez-Pardo, J. Phys. A: Math. Theor. 56 (2023), 325201.
F. Fischer, D. Burgarth, D. Lonigro, arXiv:2412.15889.
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