• Keine Ergebnisse gefunden

First, we prove that for any eigenstate of a harmonic system each of itsM-particle reduced density operators ρM obeys a duality condition

N/A
N/A
Info
Herunterladen
Protected

Academic year: 2021

Aktie "First, we prove that for any eigenstate of a harmonic system each of itsM-particle reduced density operators ρM obeys a duality condition"

Copied!
1
0
0

Wird geladen.... (Jetzt Volltext ansehen)

Jetzt herunterladen ( 1 Seite )

Volltext

(1)

Harmonic N-particle systems: reduced density operators and their properties

Solving analytically theN-particle Schr¨odinger equation for interacting parti- cles is typically impossible. One exception is given by harmonic models which are also relevant from a physical viewpoint since they arise as an effective de- scription of lattice systems. We present two results. First, we prove that for any eigenstate of a harmonic system each of itsM-particle reduced density operators ρM obeys a duality condition. This condition implies duality relations for the eigenvaluesλk ofρM and relates a harmonic model with length scalesl1, . . . , lN

with another one with inverse lengths 1/l1, . . . ,1/lN. Entanglement entropies and correlation functions inherit duality fromρM. Second, for the specific case of N identical particles we explore the influence of the exchange statistics on the 1-particle properties obtained fromρ1. Although the (natural) occupation numbers for fermions and bosons differ significantly the fermionic and bosonic natural orbitals are very similar.

1

Referenzen

Jetzt herunterladen ( PDF - 1 Seite - 12.23 KB )

ÄHNLICHE DOKUMENTE

(b) Harmonic Oscillator [3 points] Show that e−iαNa†eiαN =e−iαa†, (1) where a† and a are the ladder-operators of the harmonic oscillator with [a, a

We consider an electron in a molecule, which consists of three atoms A,

Thermodynamics of a Colloidal Particle in a Time-Dependent Non-Harmonic Potential

In particular, we identify applied work, exchanged heat, and change in internal energy along a single trajectory and thus test the consistency of these notions on this level, or,

Harmonic lattice behavior of two-dimensional colloidal crystals

Using positional data from videomicroscopy and applying the equipartition theorem for harmonic Hamiltonians, we determine the wave-vector-dependent normal mode spring constants of

As cause we often specify an event the occurrence of which first guaranteed that of the effect

We mostly talk about necessary circumstances at a time when the cause is already completed and it is certain that the effect thas occurred or will occur.. Then every

a We of an be and & the and of of a the To a to a a ( & a by way to a in and In at are as AS A COMPONENT FOR

Previous experimental research has shown that such models can account for the information processing of dimensionally described and simultaneously presented choice

A construction of conformal-harmonic maps

Conformal harmonic maps from a 4-dimensional con- formal manifold to a Riemannian manifold are maps satisfying a certain conformally invariant fourth order equation.. We prove a

a) Since(E, τ) is a locally convex Hausdorff t.v.s, we know thatτ is generated by

Fachbereich Mathematik und

We are sorry that

 We are sorry to note that the goods (ordered) have not arrived yet..  We are