Implicit density-functional theory

Liu, Bin; Percus, J. K.

doi:10.1103/physreva.74.012508

Cited by 14 publications

(4 citation statements)

References 13 publications

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“…It has been argued that the mechanism behind selftrapping in a bosonic Josephson junction can be viewed as a quantum Zeno effect; the atom-atom interaction acts as an effective measurement in which the state of single atoms is measured by the remaining ones [75] (external measurement induced Zeno effects on self-trapping have also been discussed [76]). The question then arises as to whether in the present self-trapping set-up the bosons perform an effective measurement on the impurity (or vice versa)?…”

Section: Impurity Induced Self-trappingmentioning

confidence: 99%

Impurity in a bosonic Josephson junction: Swallowtail loops, chaos, self-trapping, and Dicke model

2014

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We study a model describing N identical bosonic atoms trapped in a double-well potential together with a single impurity atom, comparing and contrasting it throughout with the Dicke model. As the boson-impurity coupling strength is varied, there is a symmetry-breaking pitchfork bifurcation which is analogous to the quantum phase transition occurring in the Dicke model. Through stability analysis around the bifurcation point, we show that the critical value of the coupling strength has the same dependence on the parameters as the critical coupling value in the Dicke model. We also show that, like the Dicke model, the mean-field dynamics go from being regular to chaotic above the bifurcation and macroscopic excitations of the bosons are observed. Overall, the boson-impurity system behaves like a poor man's version of the Dicke model.

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Section: Impurity Induced Self-trappingmentioning

confidence: 99%

Impurity in a bosonic Josephson junction: Swallowtail loops, chaos, self-trapping, and Dicke model

2014

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“…One has to be, however, extremely careful in the construction because of the N-representability problem. 10,15,[30][31][32][33][34][35][36][37][38][39][40][41][42][43] Dal Ri et al 19 derived density matrices from Jastrowtype trial wave functions. The pair density used in this work can be considered as the lowest-order approximation to the general N-representable pair density presented by Dal Ri et al Consequently, our pair density is, at least approximately, N-representable.…”

Section: Discussionmentioning

confidence: 99%

Modeling the Pauli potential in the pair density functional theory

Amovilli

Nagy

2008

The Journal of Chemical Physics

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In the ground state the pair density can be determined by solving a single auxiliary equation of a two-particle problem. A novel method for determining the Pauli potential entering this equation is presented and, starting from a reliable description of the pair density, an analytical expression is derived for atomic systems. Test calculations are presented for Be and isoelectronic C 2+ and O 4+ions.

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“…A fundamental problem in the density matrix theory is the N-representability problem. 7,8,[10][11][12][13][14][15][16][17][18][19][20][21][22] An approximate functional does not generally satisfy N-representability. It is supposed that the fulfillment of the above mentioned exact relations is important from the point of view of N-representability, too.…”

Section: Discussionmentioning

confidence: 99%