QBind · Quantum Nature of Binding

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Project objective

In my project Quantum Nature of Binding (QBind), I will develop rigorous methods to fully capture the quantum nature of particles in the process of binding. I aim to determine precise criteria under which Schrödinger operators with critical potentials produce binding in many-particle systems.I will develop tools to treat two long-standing challenges at the interface of mathematics and physics: the formation of negatively charged ions (the Ionization Conjecture), and the Efimov effect, a striking quantum phenomenon predicted in 1970 but only partially understood mathematically. In particular, I will provide analytic proofs for the confinement-induced Efimov effect. This effect was predicted by Nishida and Tan due to advancements in experiments with ultracold atoms.Methodologically, I will restore the quantum structure in the Benguria–Lieb Argument by replacing mean-field arguments with a semiclassical expression that retains quantum information of the electronic hull. The result will open new perspectives on the Ionization Conjecture, one of Barry Simon’s famous 1984 problems.The project is structured around three objectives: 1. Determine exact decay properties of quantum states under critical Schrödinger operators in various dimensions. 2. Transfer the binding mechanism due to quantum tunneling from three dimensions to geometrically constrained configurations, proving the confinement-induced Efimov effect. 3. Prove a weighted Lieb–Oxford inequality using my results on Coulomb kernels, with direct application to the Ionization Conjecture.QBind will bridge mathematics and physics by providing experimentalists with rigorous criteria to design laboratory tests of the Efimov effect. With recent advances in ultracold atom experiments, interest has surged. Efimov’s 1970 article has received more than twice as many citations in the past five years as in the three decades after publication, yet few in mathematical journals. This project will close that gap.

Original text from CORDIS.

Participants

• KOBENHAVNS UNIVERSITET · KOBENHAVNCoordinatorDenmark

Links

• View on CORDIS
• DOI: 10.3030/101274746