A Jensen inequality for partial traces and applications to partially semiclassical limits
Journal article, 2025
We prove a matrix inequality for convex functions of a Hermitian matrix on a bipartite space. As an application, we reprove and extend some theorems about eigenvalue asymptotics of Schr & ouml;dinger operators with homogeneous potentials. The case of main interest is where the Weyl expression is infinite and a partially semiclassical limit occurs.
Jensen's inequality
Semiclassical limits
Partial traces
Author
Eric A. Carlen
Rutgers University
Rupert L. Frank
Ludwig Maximilian University of Munich (LMU)
MCQST
Simon Larson
University of Gothenburg
Chalmers, Mathematical Sciences, Analysis and Probability Theory
Letters in Mathematical Physics
0377-9017 (ISSN) 1573-0530 (eISSN)
Vol. 115 3 52Subject Categories (SSIF 2025)
Mathematical Analysis
DOI
10.1007/s11005-025-01938-9