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

AuthorsNagy, Istvan; Aldazabal, Íñigo ; Rubio, Angel
Issue Date2012
PublisherAmerican Physical Society
CitationPhysical Review A 86: 022512 (2012)
AbstractBased on the correlated ground-state wave function of an exactly solvable interacting one-dimensional two-electron 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(x 1,x 2,t)n 2(x 1,x 2,t)/[n(x 1,t)n(x 2,t)] 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 Λ 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(Λ,t), the von Neumann entropy S(Λ,t)=-k=0P k(t)lnP k(t) is calculated as well. The such-defined information entropy is zero at t *(Λ) and its maximum in time is S(Λ,t=)= S(Λ,t=0). © 2012 American Physical Society.
Publisher version (URL)http://dx.doi.org/10.1103/PhysRevA.86.022512
Identifiersdoi: 10.1103/PhysRevA.86.022512
issn: 1050-2947
e-issn: 1094-1622
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