• Corpus ID: 229348723

Direct methods to Lieb-Thirring kinetic inequalities

@inproceedings{Nam2020DirectMT,
  title={Direct methods to Lieb-Thirring kinetic inequalities},
  author={Phan Th{\`a}nh Nam},
  year={2020}
}
  • P. T. Nam
  • Published 22 December 2020
  • Mathematics
We review some recent progress on Lieb-Thirring inequalities, focusing on direct methods to kinetic estimates for orthonormal functions and applications for many-body quantum systems. 
A proof of the Lieb-Thirring inequality via the Besicovitch covering lemma
. We give a proof of the Lieb–Thirring inequality on the kinetic energy of orthonormal functions by using a microlocal technique, in which the uncertainty and exclusion principles are combined
Mathematical Elements of Density Functional Theory
We review some of the basic mathematical results about density functional theory.
The state of the Lieb--Thirring conjecture
Estimates on the bound states of a Hamiltonian are of importance in quantum mechanics. For a Schrödinger operator −∆ + V on L(R) with decaying potential V : R → R of particular interest are bounds on

References

SHOWING 1-10 OF 75 REFERENCES
Lieb-Thirring Inequalities
This is a brief review of Lieb-Thirring inequalities for eigenvalues of the Schroedinger operator and lower bounds for the quantum mechanical kinetic energy (and some generalizations) in R^n.
The Lieb–Thirring inequality revisited
We provide new estimates on the best constant of the Lieb-Thirring inequality for the sum of the negative eigenvalues of Schr\"odinger operators, which significantly improve the so far existing
Lieb–Thirring inequalities for wave functions vanishing on the diagonal set
We propose a general strategy to derive Lieb-Thirring inequalities for scale-covariant quantum many-body systems. As an application, we obtain a generalization of the Lieb-Thirring inequality to wave
New bounds on the Lieb-Thirring constants
Abstract.Improved estimates on the constants Lγ,d, for 1/2<γ<3/2, d∈N, in the inequalities for the eigenvalue moments of Schrödinger operators are established.
The Lieb–Thirring Inequality for Interacting Systems in Strong-Coupling Limit
We consider an analogue of the Lieb-Thirring inequality for quantum systems with homogeneous repulsive interaction potentials, but without the antisymmetry assumption on the wave functions. We show
Fractional Hardy–Lieb–Thirring and Related Inequalities for Interacting Systems
We prove analogues of the Lieb–Thirring and Hardy–Lieb–Thirring inequalities for many-body quantum systems with fractional kinetic operators and homogeneous interaction potentials, where no
Lieb-Thirring inequalities with improved constants
Following Eden and Foias we obtain a matrix version of a generalised Sobolev inequality in one-dimension. This allows us to improve on the known estimates of best constants in Lieb-Thirring
On Lieb-Thirring inequalities for higher order operators with critical and subcritical powers
Let ϰi(Hl(V)) denote the negative eigenvalues of the operatorHlu≔(−Δ)lu−V≧0,x ℝd onL2(ℝd). We prove the two-sided estimate. We discuss bounds on the Riesz means.
On Lieb-Thirring Inequalities for Schrödinger Operators with Virtual Level
We consider the operator H=−Δ−V in L2(ℝd), d≥3. For the moments of its negative eigenvalues we prove the estimate Similar estimates hold for the one-dimensional operator with a Dirichlet condition at
Sharp Lieb-Thirring inequalities in high dimensions
We show how a matrix version of the Buslaev-Faddeev-Zakharov trace formulae for a one-dimensional Schr\"odinger operator leads to Lieb-Thirring inequalities with sharp constants $L^{cl}_{\gamma,d}$
...
...