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Resonant systems emerge as weakly nonlinear approximations to problems with highly resonant linearized perturbations. Examples include nonlinear Schrödinger equations in harmonic potentials and nonlinear dynamics in antide Sitter spacetime. The classical dynamics within this class of systems can be very rich, ranging from fully integrable to chaotic as one changes the values of the mode coupling coefficients. Here, we initiate a study of quantum infinitedimensional resonant systems, which are mathematically a highly special case of twobody interaction Hamiltonians (extensively researched in condensed matter, nuclear and highenergy physics). Despite the complexity of the corresponding classical dynamics, the quantum version turns out to be remarkably simple: the Hamiltonian is blockdiagonal in the Fock basis, with all blocks of varying finite sizes. Being solvable in terms of diagonalizing finite numerical matrices, these systems are thus arguably the simplest interacting quantum field theories known to man. We demonstrate how to perform the diagonalization in practice, and study both numerical patterns emerging for the integrable cases, and the spectral statistics, which efficiently distinguishes the special integrable cases from generic (chaotic) points in the parameter space. We discuss a range of potential applications in view of the computational simplicity and dynamical richness of quantum resonant systems.
Originele taal2  English 

Artikelnummer  025102 
Aantal pagina's  20 
Tijdschrift  Journal of Physics. A, Mathematical and Theoretical 
Volume  52 
Nummer van het tijdschrift  2 
DOI's  
Status  Published  13 dec 2018 
Bibliografische nota
v2: slightly expanded published versionVingerafdruk
Duik in de onderzoeksthema's van 'Quantum resonant systems, integrable and chaotic'. Samen vormen ze een unieke vingerafdruk.Projecten
 1 Actief

SRP8: SRP (Zwaartepunt): HogeEnergiefysica
D'Hondt, J., Van Eijndhoven, N., Craps, B., Buitink, S., D'Hondt, J., Van Eijndhoven, N. & Craps, B.
1/11/12 → 31/10/22
Project: Fundamenteel