Eigenvalue asymptotics for the one-particle density matrix
Alexander V. Sobolev
Abstract
The one-particle density matrix γ(x,y) for a bound state of an atom or molecule is one of the key objects in the quantum-mechanical approximation schemes. We prove the asymptotic formula λk∼(Ak)−8∕3, A≥0, as k→∞, for the eigenvalues λk of the self-adjoint operator Γ≥0 with kernel γ(x,y).
Topics & Concepts
Eigenvalues and eigenvectorsMathematicsDensity matrixOperator (biology)Matrix (chemical analysis)Mathematical physicsQuantumKernel (algebra)Self-adjoint operatorUpper and lower boundsPure mathematicsMathematical analysisQuantum mechanicsPhysicsHilbert spaceChemistryGeneTranscription factorBiochemistryChromatographyRepressorSpectral Theory in Mathematical PhysicsAdvanced Chemical Physics StudiesMatrix Theory and Algorithms