Exact time evolution of the pair distribution function for an entangled two-electron initial state

Abstract

Based on the correlated ground-state wave function of an exactly solvable interacting one-dimensional twoelectron model Hamiltonian we address the switch-off of confining and interparticle interactions to calculate the exact time-evolving wave function from a prescribed correlated initial state. Using this evolving wave function, the time-dependent pair probability function R(is determined via the pair density n 2 (x 1 ,x 2 ,t) and single-particle density n(x,t). It is found that R(0,0,t = ∞) = R(0,0,t = 0) > 1, and R(x 1 ,x 2 ,t * ) = 1 at a finite t * for = 0 interparticle interaction strength in the initial two-electron model. By expanding n(x,t) in an infinite sum of closed-shell products of time-dependent normalized single-particle states and time-dependent occupation numbers P k ( ,t), the von Neumann entropy S( ,t) = − ∞ k=0 P k (t)lnP k (t) is calculated as well. The such-defined information entropy is zero at t * ( ) and its maximum in time is S( ,t = ∞) = S( ,t = 0).

Quantum entanglement in strong-field ionization

“…Most of the papers on quantum entanglement in light induced atomic processes study the correlations between the emitted photon and the emitting atomic system [31][32][33]. Papers on entanglement between a charged particle and a photon [34,35], entanglement in two particles' collision [36][37][38][39][40][41] and on the temporal change of the correlation potential during electron tunneling from a molecule [42] give valuable insight into the quantum features of problems related to our present paper. Entanglement between the fragments of an atomic system due to a light-induced break-up process, like photoionization and photodissociation, was studied by Fedorov and coworkers [43,44] in the framework of Gaussian states.…”

“…Because these Neumann entropies are actually correlation entropies in this case, we expect them look really similar to the respective quantum mutual entropies. For sake of completeness, we note that the entropies(38) and(39) are also entanglement entropies of two special bipartitions of the six coordinate quantum system, namely x c against all the other coordinates and z c against all the other coordinates, respectively.Electron entropies per direction: these are also of importance related to the conditional entropies, and the distinction of quantum versus classical correlations. Similarly, they are also special entanglement entropies of two bipartitions of the six coordinate quantum system in similar manner as the core entropies per direction.…”

One-particle Green’s function of interacting two electrons using analytic solutions for a three-body problem: comparison with exact Kohn–Sham system

“…This model has been studied intensively. [19][20][21][22] The variable transformation for the center-of-mass coordinate x + ≡ (x 1 + x 2 )/2 and the scaled relative coordinate x − ≡ (x 1 − x 2 )/ √ 2 decouples the interacting Hamiltonian into two Hamiltonians for independent harmonic oscillators as…”

Quantum Singwi-Tosi-Land-Sjölander approach for interacting inhomogeneous systems under electromagnetic fields: Comparison with exact results

“…We assume that 0 ≦ Λ ≦ 1/2 as in the previous works. [29][30][31] V 0σ (x) = mω 2 0 x 2 /2 and v(x) = −mΛω 2 0 x 2 /2 correspond to those in eqs. (3) and (2) , respectively, for this system.…”

“…al. [29][30][31], since it enables us to compare the various quantities within the inhomogeneous STLS approximation and those calculated exactly from their definitions. We focus on the comparison between the exact and the STLS-approximated density response functions since they are directly related to the formulation of inhomogeneous STLS approach.…”