[PDF][PDF] The Lieb-Thirring inequalities: recent results and open problems
RL Frank - arxiv preprint arxiv:2007.09326, 2020 - arxiv.org
arxiv:2007.09326v1 [math-ph] 18 Jul 2020 Page 1 arxiv:2007.09326v1 [math-ph] 18 Jul 2020
THE LIEB–THIRRING INEQUALITIES: RECENT RESULTS AND OPEN PROBLEMS RUPERT …
THE LIEB–THIRRING INEQUALITIES: RECENT RESULTS AND OPEN PROBLEMS RUPERT …
Universal functionals in density functional theory
In this chapter we first review the Levy–Lieb functional, which gives the lowest kinetic and
interaction energy that can be reached with all possible quantum states having a given …
interaction energy that can be reached with all possible quantum states having a given …
The nonlinear Schrödinger equation for orthonormal functions II: Application to Lieb–Thirring Inequalities
In this paper we disprove part of a conjecture of Lieb and Thirring concerning the best
constant in their eponymous inequality. We prove that the best Lieb–Thirring constant when …
constant in their eponymous inequality. We prove that the best Lieb–Thirring constant when …
The state of the Lieb--Thirring conjecture
L Schimmer - arxiv preprint arxiv:2203.06051, 2022 - arxiv.org
In 1976 Lieb and Thirring established upper bounds on sums of powers of the negative
eigenvalues of a Schr\" odinger operator in terms of semiclassical phase-space integrals …
eigenvalues of a Schr\" odinger operator in terms of semiclassical phase-space integrals …
[HTML][HTML] Lieb–Thirring inequality with semiclassical constant and gradient error term
PT Nam - Journal of Functional Analysis, 2018 - Elsevier
Abstract In 1975, Lieb and Thirring derived a semiclassical lower bound on the kinetic
energy for fermions, which agrees with the Thomas–Fermi approximation up to a constant …
energy for fermions, which agrees with the Thomas–Fermi approximation up to a constant …
Methods of modern mathematical physics: Uncertainty and exclusion principles in quantum mechanics
D Lundholm - arxiv preprint arxiv:1805.03063, 2018 - arxiv.org
These are lecture notes for a master-level course given at KTH, Stockholm, in the spring of
2017, with the primary aim of proving the stability of matter from first principles using modern …
2017, with the primary aim of proving the stability of matter from first principles using modern …
Optimizers for the finite-rank Lieb-Thirring inequality
The finite-rank Lieb-Thirring inequality provides an estimate on a Riesz sum of the $ N $
lowest eigenvalues of a Schr\" odinger operator $-\Delta-V (x) $ in terms of an $ L^ p …
lowest eigenvalues of a Schr\" odinger operator $-\Delta-V (x) $ in terms of an $ L^ p …
[PDF][PDF] The periodic Lieb–Thirring inequality
Abstract We discuss the Lieb-Thirring inequality for periodic systems, which has the same
optimal constant as the original inequality for finite systems. This allows us to formulate a …
optimal constant as the original inequality for finite systems. This allows us to formulate a …
[PDF][PDF] METHODS OF MODERN MATHEMATICAL PHYSICS
D LUNDHOLM - mathematik.uni-muenchen.de
These are lecture notes for a master-level course with the primary aim of proving the stability
of matter from first principles using modern mathematical methods in many-body quantum …
of matter from first principles using modern mathematical methods in many-body quantum …
NOTES TO APPENDIX D
IM Sigal - Doing Mathematics: Convention, Subject, Calculation …, 2015 - books.google.com
9 (1983): 129–206. 4. See note 33 of chapter 3. 5. Technically, phase space is the realm of
Hamilton's equations, which preserve phase space volume (Liouville's theorem). And …
Hamilton's equations, which preserve phase space volume (Liouville's theorem). And …