Inequalities for the Moments of the Eigenvalues of the Schrodinger Hamiltonian and Their Relation to Sobolev Inequalities

By Elliott H. Lieb, W. Thirring. 2002

607 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/2a4800a35554f6c269746cb8e4964b18883191eb

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

Sum rules for Jacobi matrices and their applications to spectral theory (2001, unknown): “Remarks.”
Lieb-Thirring inequalities with improved constants (2007, unknown): “The constant 2/3 √ 3 should be compared with the Lieb–Thirring constant found in [7] for a class of single eigenvalue potentials and with the constant obtained in [5] which is twice as large as the semi-classical one, 4 3 √ 3π < 2 3 √ 3 < 2× 2 3π = 2× 1 2π ∫ R (1− ξ(2))+ dξ.”
Stability of Matter (2005, background): “A second, highly nontrivial consequence, is that the thermodynamic functions exist.”
The Stability of Matter in Quantum Mechanics (2009, methodology): “It is conjectured [135] thatL1,3 = Lcl 1,3.”
Low-Rank Matrix Recovery via Efficient Schatten p-Norm Minimization (2012, background): “To prove it, we need the following lemmas: Lemma 1 (Araki-Lieb-Thirring (Lieb and Thirring 1976; Araki 1990; Audenaert 2008)).”
Hardy-Sobolev-Maz'ya inequalities for arbitrary domains (2011, methodology): “When the term (2DΩ)−2 is absent, these inequalities go back to Lieb and Thirring [20].”
Rigidity versus symmetry breaking via nonlinear flows on cylinders and Euclidean spaces (2015, methodology): “0 if d3, >0 if d= 2, and >1=2 if d= 1, the lowest negative eigenvalue, Rd 1 [V], of the operator V satises Rd 1 [V] L1 ;dkV +k +d=2 L +d=2(Rd) 8V 2L q(Rd) with optimal constant L1 ;d . See [36,40,23] for details. Proposition 7.1. Let d2 and q2(d=2;+1). The function 7!( ) is convex, positive an”
TRACE INEQUALITIES AND QUANTUM ENTROPY: An introductory course (2009, background): “4 was first proved in [22], and has had many applications since then.”
Eigenvalue bounds for Schrödinger operators with complex potentials. II (2015, background): “For this bound, see [15, 19] and also [4] for optimal constants, optimal potentials and stability results.”
Additivity for unital qubit channels (2001, methodology): “That method uses the Lieb-Thirring bound [12], which in turn was proved using one of Epstein’s concavity results [6].”