25 papers
Self-adjoint extensions of -photon light-matter Hamiltonians
Felix Fischer, Felix Knapp, Daniel Burgarth +1
Multiphoton light-matter interactions, in which a bosonic mode exchanges excitations at a time with a quantum system, are a source of genuine nonlinearity in quantum optics and…
The Floquet-Magnus expansion of unbounded operators
Daniel Burgarth, Robin Hillier, Davide Lonigro +1
The Floquet-Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamilto…
Essentially singular limits of Jacobi operators and applications to higher-order squeezing
Felix Fischer, Daniel Burgarth, Davide Lonigro
We study a family of Jacobi operators in which the diagonal entries are multiplied by a coupling parameter . Under suitable conditions, the operator is self-adjoint for ev…
Wandering range of robust quantum symmetries
Daniel Burgarth, Paolo Facchi, Marilena Ligabò +2
This paper introduces the concept of the wandering range of a robust symmetry of a Hamiltonian . This quantity measures how the perturbed time evolution $\mathrm{e}^{\mathrm…
Rotating-Wave and Secular Approximations for Open Quantum Systems
Daniel Burgarth, Paolo Facchi, Giovanni Gramegna +1
We derive a nonperturbative bound on the distance between evolutions of open quantum systems described by time-dependent generators. We show how this result can be employed to prov…
The quantum harmonic oscillator on a circle -- fragmentation of the algebraic method
Daniel Burgarth, Paolo Facchi
A quantum particle on a circle in a quadratic potential exhibits a spectrum that is not harmonic, despite having all algebraic properties of the quantum harmonic oscillator. This r…