Project description DEENESFRITPL New computational approaches to reduce the complexity of quantum mechanics The EU-funded COCONUT project plans to derive quantitative estimates of the computational complexity of spectral problems in quantum mechanics. The theoretical framework supporting this study will be the so-called solvability complexity index, which is the number of successive limits needed to solve the computational problem. The project will also combine numerical analysis methods and modern methods from spectral approximation theory to study two particular subjects: the spectral problem for Schrödinger operators with various types of potentials and the computation of scattering resonances in quantum mechanics. The findings will also be investigated for relativistic settings: in this case, the Schrödinger operator will be replaced by a Dirac operator. Show the project objective Hide the project objective Objective The goal of this Fellowship is to derive quantitative estimates on the computational complexity of spectral problems in quantum mechanics. The theoretical framework for this task is provided by the so-called Solvability Complexity Index, which roughly speaking, is the number of successive limits needed to solve the computational problem. I will approach this task by combining techniques from numerical analysis with modern methods from spectral approximation theory.The project is divided into three concise work projects:WP1: NONRELATIVISTIC QUANTUM SYSTEMS.In this project, the spectral problem for Schrödinger operators with various types of potentials is studied. New sharp estimates on the computational complexity are derived. This will contribute to a comprehensive understanding of the nonrelativistic theory.WP2: RESONANCES.In this second project, complexity issues are considered for the computation of scattering resonances in quantum mechanics. I will introduce new mathematical tools, which have not been used in complexity theory before to construct algorithms which compute the set of resonances of Schrödinger operators in one limit.WP3: EXTENSION TO RELATIVISTIC THEORY.The purpose of the final project is to extend the above results to the relativistic setting, in which the Schrödinger operator is replaced by a Dirac operator. This task is far from trivial, as methods from the Schrödinger case are generally not useful for Dirac operators.I also have robust career development and public outreach agendas, to complement the scientific aspects of this proposal. Combined, all these elements will establish me as a prominent research leader upon my return to Germany, with extensive links throughout Europe and the US. Fields of science natural sciencesphysical sciencesquantum physicsnatural sciencesmathematicsapplied mathematicsnumerical analysis Keywords Spectral Theory Approximation Computational Complexity Quantum Mechanics Schrödinger Operator Dirac Operator Resonances Programme(s) H2020-EU.1.3. - EXCELLENT SCIENCE - Marie Skłodowska-Curie Actions Main Programme H2020-EU.1.3.2. - Nurturing excellence by means of cross-border and cross-sector mobility Topic(s) MSCA-IF-2019 - Individual Fellowships Call for proposal H2020-MSCA-IF-2019 See other projects for this call Funding Scheme MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF) Coordinator CARDIFF UNIVERSITY Net EU contribution € 212 933,76 Address Newport road 30 36 CF24 0DE Cardiff United Kingdom See on map Region Wales East Wales Cardiff and Vale of Glamorgan Activity type Higher or Secondary Education Establishments Links Contact the organisation Opens in new window Website Opens in new window Participation in EU R&I programmes Opens in new window HORIZON collaboration network Opens in new window Other funding € 0,00
