Rupert L. Frank

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20162026

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math-ph2024

Lieb-Thirring inequality for the 2D Pauli operator

Rupert L. Frank, Hynek Kovařík

By the Aharonov-Casher theorem, the Pauli operator $P$ has no zero eigenvalue when the normalized magnetic flux $α$ satisfies $∣ α ∣ < 1$ , but it does have a zero energy resonance. We…

math-ph2023

Cwikel-Lieb-Rozenblum type inequalities for Hardy-Schrödinger operator

Giao Ky Duong, Rupert L. Frank, Thi Minh Thao Le +2

We prove a Cwikel-Lieb-Rozenblum type inequality for the number of negative eigenvalues of the Hardy-Schrödinger operator $- Δ - (d - 2)^{2} / (4∣ x ∣^{2}) - W (x)$ on $L^{2} (R^{d})$ . The b…

math-ph2016

The ionization conjecture in Thomas-Fermi-Dirac-von Weizsäcker theory

Rupert L. Frank, Phan Thành Nam, Hanne Van Den Bosch

We prove that in Thomas-Fermi-Dirac-von Weizsäcker theory, a nucleus of charge $Z > 0$ can bind at most $Z + C$ electrons, where $C$ is a universal constant. This result is obtained th…