Choice of the constraining operator in the constrained hartree-fock method

Holzwarth, G.; Yukawa, Tetsuyuki

doi:10.1016/0375-9474(74)90087-6

Cited by 79 publications

(46 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In turn, given this basis, the local harmonic equation determines f ph . If we neglect the affine connection we obtain a set of equations that is very close to the set derived in the Holzwarth-Yukawa formalism [71] by Pelet and Letourneux, [69,70], the only difference being that we use RPA where they use a further approximation, the TDA (Tamm-Dancoff approximation) [6].…”

Section: Equations Of the Local Harmonic Formulationsupporting

confidence: 54%

“…(By comparison, the kinetic energy is of relative order (1/N), where N is the number of degrees of freedom that participate in the motion.) Among previous attempts to found a theory of large amplitude collective motion on a quantum basis such as the method of generator coordinates [71,76], the Born-Oppenheimer method [77], a generalized coherent state method [78], and the equations of motion method [64,10], none provided a systematic expansion in (1/N). (The work mentioned here for the first time will be reviewed in Sec.…”

Section: Quantum Correctionsmentioning

confidence: 99%

“…Unfortunately this appears to rule out simple separable interactions (such as the quadrupole-quadrupole interaction), at least for 28 Si. Furthermore, for this nucleus we can compare our calculation with the only existing application to a bound system [69,70] of a "competing" self-consistent theory of large amplitude collective motion [71].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

View full text Add to dashboard Cite

The goal of the present account is to review our efforts to obtain and apply a "collective" Hamiltonian for a few, approximately decoupled, adiabatic degrees of freedom, starting from a Hamiltonian system with more or many more degrees of freedom. The approach is based on an analysis of the classical limit of quantum-mechanical problems. Initially, we study the classical problem within the framework of Hamiltonian dynamics and derive a fully self-consistent theory of large amplitude collective motion with small velocities. We derive a measure for the quality of decoupling of the collective degree of freedom. We show for several simple examples, where the classical limit is obvious, that when decoupling is good, a quantization of the collective Hamiltonian leads to accurate descriptions of the low energy properties of the systems studied. In nuclear physics problems we construct the classical Hamiltonian by means of time-dependent mean-field theory, and we transcribe our formalism to this case. We report studies of a model for monopole vibrations, of 28 Si with a realistic interaction, several qualitative models of heavier nuclei, and preliminary results for a more realistic approach to heavy nuclei. Other * Email: Giu.Dodang@th.u-psud.fr † Email: aklein@walet.physics.upenn.edu ‡ Email: Niels.Walet@umist.ac.uk 1 topics included are a nuclear Born-Oppenheimer approximation for an ab initio quantum theory and a theory of the transfer of energy between collective and non-collective degrees of freedom when the decoupling is not exact. The explicit account is based on the work of the authors, but a thorough survey of other work is included. PACS number(s): 21.60.-n, 21.60.Jz, 21.60.Ev

show abstract

Section: Equations Of the Local Harmonic Formulationsupporting

confidence: 54%

Section: Quantum Correctionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

2000

View full text Add to dashboard Cite

show abstract

“…With the variational principle, Holzwarth and Yukawa [98] proved that the meanfield states parametrized by a single optimal generator coordinate run along a valley of the collective potential energy surface. This line of investigation was further developed [99] and greatly stimulated the challenge toward constructing a microscopic theory of LACM.…”

Section: Generator Coordinate Methodsmentioning

confidence: 99%

Microscopic derivation of the quadrupole collective Hamiltonian for shape coexistence/mixing dynamics

Matsuyanagi

Nakatsukasa

Yoshida

et al. 2016

J. Phys. G: Nucl. Part. Phys.

View full text Add to dashboard Cite

Assuming that the time-evolution of the self-consistent mean field is determined by five pairs of collective coordinate and collective momentum, we microscopically derive the collective Hamiltonian for low-frequency quadrupole modes of excitation. We show that the five-dimensional collective Schrödinger equation is capable of describing large-amplitude quadrupole shape dynamics seen as shape coexistence/mixing phenomena. We focus on basic ideas and recent advances of the approaches based on the time-dependent mean-field theory, but relations to other time-independent approaches are also briefly discussed.

show abstract

“…Recently, the energy functional (in terms of occupation numbers) was constructed for the pairing Hamiltonian [24]. In this paper we consider the three-level Lipkin model [25,26,27,28]. This is another solvable model that is relevant for nuclei.…”

Section: Introductionmentioning

confidence: 99%

Energy functional for the three-level Lipkin model

Bertolli

Papenbrock

2008

Phys. Rev. C

View full text Add to dashboard Cite

We compute the energy functional of a three-level Lipkin model via a Legrendre transform and compare exact numerical results with analytical solutions obtained from the random phase approximation (RPA). Except for the region of the phase transition, the RPA solutions perform very well. We also study the case of three non-degenerate levels and again find that the RPA solution agrees well with the exact numerical result. For this case, the analytical results give us insight into the form of the energy functional in the presence of symmetry-breaking one-body potentials.

show abstract

Choice of the constraining operator in the constrained hartree-fock method

Cited by 79 publications

References 9 publications

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Self-consistent theory of large-amplitude collective motion: applications to approximate quantization of nonseparable systems and to nuclear physics

Microscopic derivation of the quadrupole collective Hamiltonian for shape coexistence/mixing dynamics

Energy functional for the three-level Lipkin model

Contact Info

Product

Resources

About