On reduced density matrices for disjoint subsystems

Reduced density matrices and Bose-Einstein condensation

Emergence and applications of the ubiquitous tool of reduced density matrices in the rigorous analysis of Bose Einstein condensation is reviewed, and new related results are added. The need and the nature of scaling limits of infinitely many particles is discussed, which imposes that a physically meaningful and mathematically well-posed definition of asymptotic condensation is placed at the lev...

Compact forms of reduced density matrices

The objective of this paper is to identify the necessary and sufficient minimum information carried by Reduced Density Matrices ~RDMs!. This minimum of essential information determines a set of equivalent compact-form matrices that are devoid of the redundant information present in the original RDMs when the system possesses symmetry invariances. The basic properties and algebra operations of t...

Dynamics of reduced density matrices: Classical memory versus quantum nonlocality

The nonlocality in the path integral description of the reduced density matrix for a system interacting with a classical harmonic bath can be eliminated through the introduction of auxiliary variables, leading to Markovian equations. By contrast, the presence of an imaginary part in quantum mechanical response functions appears to prohibit similar approaches, necessitating explicit treatment of...

Calculation of reduced density matrices from correlation functions

Reduced density matrices and entanglement entropy in free lattice models

We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a certain free-particle Hamiltonian. We discuss the derivation of this result, the character of the Hamiltonian and its eigenstates, the single-particle spectra and...