ORCID Profile
0000-0002-7547-4804
Current Organisation
Group of Mathematical Physics of Lisbon University
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Publisher: Springer Science and Business Media LLC
Date: 17-09-2016
Publisher: IOP Publishing
Date: 03-2021
Publisher: Elsevier BV
Date: 02-2015
Publisher: Springer Science and Business Media LLC
Date: 06-05-2023
Publisher: Springer Netherlands
Date: 2009
Publisher: Elsevier BV
Date: 06-2007
Publisher: Springer Science and Business Media LLC
Date: 02-2021
Abstract: We study the large momentum limit of the monster potentials of Bazhanov-Lukyanov-Zamolodchikov, which — according to the ODE/IM correspondence — should correspond to excited states of the Quantum KdV model. We prove that the poles of these potentials asymptotically condensate about the complex equilibria of the ground state potential, and we express the leading correction to such asymptotics in terms of the roots of Wronskians of Hermite polynomials. This allows us to associate to each partition of N a unique monster potential with N roots, of which we compute the spectrum. As a consequence, we prove — up to a few mathematical technicalities — that, fixed an integer N , the number of monster potentials with N roots coincides with the number of integer partitions of N , which is the dimension of the level N subspace of the quantum KdV model. In striking accordance with the ODE/IM correspondence.
Publisher: Springer Science and Business Media LLC
Date: 04-01-2022
DOI: 10.1007/S00208-021-02337-W
Abstract: We study a second-order linear differential equation known as the deformed cubic oscillator, whose isomonodromic deformations are controlled by the first Painlevé equation. We use the generalised monodromy map for this equation to give solutions to the Riemann-Hilbert problems of (Bridgeland in Invent Math 216(1):69–124, 2019) arising from the Donaldson-Thomas theory of the A $$_2$$ 2 quiver. These are the first known solutions to such problems beyond the uncoupled case. The appendix by Davide Masoero contains a WKB analysis of the asymptotics of the monodromy map.
Publisher: IOP Publishing
Date: 09-02-2010
Publisher: Springer Science and Business Media LLC
Date: 19-05-2016
Publisher: IOP Publishing
Date: 20-08-2010
Publisher: Springer Science and Business Media LLC
Date: 25-06-2020
Publisher: IOP Publishing
Date: 30-12-2016
Publisher: Springer Science and Business Media LLC
Date: 23-09-2010
Publisher: Oxford University Press (OUP)
Date: 20-11-2013
DOI: 10.1093/IMRN/RNT223
Publisher: Springer Science and Business Media LLC
Date: 07-03-2014
Publisher: Springer Science and Business Media LLC
Date: 24-01-2013
Publisher: SIGMA (Symmetry, Integrability and Geometry: Methods and Application)
Date: 06-01-2018
Location: Germany
Location: Portugal
Start Date: 2016
End Date: 2019
Funder: Fundação para a Ciência e a Tecnologia
View Funded ActivityStart Date: 2017
End Date: 2021
Funder: Fundação para a Ciência e a Tecnologia
View Funded ActivityStart Date: 2022
End Date: 2021
Funder: Fundação para a Ciência e a Tecnologia
View Funded ActivityStart Date: 2012
End Date: 2018
Funder: Fundação para a Ciência e Tecnologia (FCT)
View Funded ActivityStart Date: 2018
End Date: 2021
Funder: Fundação para a Ciência e a Tecnologia
View Funded Activity