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Chemical Physics Letters

Time-dependent rotated hartree approach

Jasna Kučar, Hans‐Dieter Meyer, Lorenz S. Cederbaum

Published Jan 1, 1987• 87 citations
Publisher
DOI
10.1016/0009-2614(87)80480-3

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We examine the complementary types of motion induced by the time-dependent mean field and the related residual interaction in the frame of quasispin systems. The time-dependent Hartree-Fock law of motion is used to generate an instantaneous basis, where the residual interaction induces transitions that deviate the exact motion with respect to the simple Slater determinant evolution. Geometric images of both kinds of dynamics are given and definite time scales are extracted for the validity of the time-dependent Hartree-Fock description, its second order correction, and the building up of a noticeable relative polarization of the exact wave function. It is seen that in addition to the time-dependent Hartree-Fock motion over the Bloch sphere, the exact dynamics contains an "inwards" component as well as additional rotations.NUCLEAR STRUCTURE Time-dependent Hartree-Fock; moving basis; residual interaction; complementary motions; quasispin systems; Slater determinant; time scales; rotations and nonrotations on Bloch sphere; polarization.

Physical Review C•Nov 1, 1982•21 citations
The time-dependent Hartree-Fock solutions of the two-level Lipkin-Meshkov-Glick model are studied by transforming the time-dependent Hartree-Fock equations into Hamilton's canonical form and analyzing the qualitative structure of the Hartree-Fock energy surface in the phase space. It is shown that as the interaction strength increases these time-dependent Hartree-Fock solutions undergo a qualitative change associated with the ground state phase transition previously studied in terms of coherent states. For twobody interactions stronger than the critical value, two types of time-dependent Hartree-Fock solutions (the "librations" and "rotations" in Hamilton's mechanics) exist simultaneously, while for weaker interactions only the rotations persist. It is also shown that the coherent states with the maximum total pseudospin value are determinants, so that time-dependent Hartree-Fock analysis is equivalent to the coherent state method.NUCLEAR STRUCTURE Lipkin-Meshkov-Glick model, TDHF, transformation of TDHF equations to Hamilton's canonical form, coherent states, ground state phase transition.
We examine the complementary types of motion induced by the time-dependent mean field and the related residual interaction in the frame of quasispin systems. The time-dependent Hartree-Fock law of motion is used to generate an instantaneous basis, where the residual interaction induces transitions that deviate the exact motion with respect to the simple Slater determinant evolution. Geometric images of both kinds of dynamics are given and definite time scales are extracted for the validity of the time-dependent Hartree-Fock description, its second order correction, and the building up of a noticeable relative polarization of the exact wave function. It is seen that in addition to the time-dependent Hartree-Fock motion over the Bloch sphere, the exact dynamics contains an "inwards" component as well as additional rotations.NUCLEAR STRUCTURE Time-dependent Hartree-Fock; moving basis; residual interaction; complementary motions; quasispin systems; Slater determinant; time scales; rotations and nonrotations on Bloch sphere; polarization.