Duality of reduced density matrices and their eigenvalues
Abstract
For states of quantum systems of N particles with harmonic interactions we prove that each reduced density matrix ρ obeys a duality condition. This condition implies duality relations for the eigenvalues λ_{k} of ρ and relates a harmonic model with length scales {{\ell }_{1}},{{\ell }_{2}},\ldots ,{{\ell }_{N}} with another one with inverse lengths 1/{{\ell }_{1}},1/{{\ell }_{2}},\ldots ,1/{{\ell }_{N}}. Entanglement entropies and correlation functions inherit duality from ρ. Selfduality can only occur for noninteracting particles in an isotropic harmonic trap.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 October 2014
 DOI:
 10.1088/17518113/47/41/415305
 arXiv:
 arXiv:1408.3128
 Bibcode:
 2014JPhA...47O5305S
 Keywords:

 Quantum Physics;
 Mathematical Physics
 EPrint:
 J. Phys. A: Math. Theor. 47 (2014) 415305