A self-consistent description of systems with many interacting bosons

Dukelsky, J.; Dussel, G.G.; Perazzo, R.P.J.; Reich, S.L.; Sofía, H.M.

doi:10.1016/0375-9474(84)90218-5

Cited by 64 publications

(30 citation statements)

References 23 publications

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“…The intrinsic-state formalism provides a connection between the IBM and the Geometrical Collective Model [22]. The key point for establishing this connection is to consider that the dynamical behavior of the system can be described, to a first approximation, as arising from independent bosons moving in an average field [23]. The ground state of the system is a condensate, |c , of bosons that occupy the lowest-energy phonon state Γ † c ,…”

Section: Transitional Regions and Phase Transitions In The Ibm: Amentioning

confidence: 99%

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

García‐Ramos¹,

Coster²,

Fossión³

et al. 2001

Nuclear Physics A

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Section: Transitional Regions and Phase Transitions In The Ibm: Amentioning

confidence: 99%

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

García‐Ramos¹,

Coster²,

Fossión³

et al. 2001

Nuclear Physics A

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“…(5) exhibits various geometric shapes (as well as the phase transitions inbetween them) which are relevant for the subsequent studies with random interactions. The connection between the vibron model, potential energy surfaces, geometric shapes and phase transitions can be investigated by means of standard Hartree-Bose mean-field methods [24][25][26]. For the vibron model, it is convenient to introduce a coherent, or intrinsic, state expressed as a condensate of deformed bosons with axial symmetry…”

Section: B Geometric Shapesmentioning

confidence: 99%

“…(26). The probability that the equilibrium shape of an ensemble of Hamiltonians is spherical can be obtained by integrating P (a 4 , a 2 ) over the appropriate range I (a 2 > 0,…”

Section: Mean-field Analysismentioning

confidence: 99%

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Regular spectra in the vibron model with random interactions

Bijker

Frank

2002

Phys. Rev. C

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The phenomenom of emerging regular spectral features from random interactions is addressed in the context of the vibron model. A mean-field analysis links different regions of the parameter space with definite geometric shapes. The results that are, to a large extent, obtained in closed analytic form, provide a clear and transparent interpretation of the high degree of order that has been observed in numerical studies.

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“…Thus, we follow a different route that is based on the continuous unitary transformations (CUTs) [19][20][21]. Within this framework, we compute the first correction beyond the standard random phase approximation (RPA) [22], which already contains the key ingredients to analyze the critical point. As already observed in a similar context, [23][24][25], this 1/N expansion becomes, at this order, singular when approaching the critical region so that one gets nontrivial scaling exponents for the physical observables (ground-state energy, gap, occupation number, transition rates).…”

mentioning

confidence: 99%

Finite-size scaling exponents in the interacting boson model

et al. 2005

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We investigate the finite-size scaling exponents for the critical point at the shape-phase transition from U(5) (spherical) to O(6) (deformed γ -unstable) dynamical symmetries of the interacting boson model, making use of the Holstein-Primakoff boson expansion and the continuous unitary transformation technique. We compute exactly the leading-order correction to the ground-state energy, the gap, the expectation value of the d-boson number in the ground state and the E2 transition probability from the ground state to the first excited state and determine the corresponding finite-size scaling exponents. The interest in the study of quantum phase transitions (QPT) has kept growing in the last years in different branches of quantum many-body physics, ranging from macroscopic systems such as quantum magnets, high-T c superconductors [1] or dilute Bose and Fermi gases [2] to mesoscopic systems such as atomic nuclei or molecules [3]. Although, strictly speaking, QPT occurs only in macroscopic systems, there is a renewed interest in studying structural changes in finitesize systems where precursors of the transition are already observed [4]. The understanding of the modifications on the characteristics of the QPT induced by finite-size effects is of crucial importance to extend the concept of phase transitions to finite systems.In the present study, we analyze these finite-size corrections in the interacting boson model (IBM) of nuclei [5], but the same technique can be applied to other boson systems, for instance, to the molecular vibron model [6] or to a multilevel boson model of Bose-Einstein condensates where similar QPT take place [7].The IBM is a two-level boson model that includes an angular momentum L = 0 boson (scalar s boson) and five angular momentum L = 2 bosons (quadrupole d-bosons) separated by an energy gap. The s and d bosons represent s-and d-wave idealized Cooper nucleon pairs. The algebraic structure of this model is governed by the U(6) group and the model has three dynamical symmetries in which the Hamiltonian, written in terms of the invariant (Casimir) operators of a nested chain of subgroups of U(6), is analytically solvable. The dynamical symmetries are named by the first subgroup in the chain: U(5), SU(3), and O(6). The classical or thermodynamic limit of the model was investigated by using an intrinsic state formalism that introduces the shape variables β and γ [8][9][10]. Within this geometric picture the U(5), SU(3), and O(6) dynamical symmetries correspond to spherical, axially deformed, and deformed γ -unstable shapes, respectively. Transition between two of these dynamical symmetry limits are described in terms of a Hamiltonian with a control parameter that mixes the Casimir operators of the two dynamical symmetries. As a function of the control parameter, the system crosses smoothly a region of structural changes in the ground-state wave function for finite number N of bosons. In the large N limit, the smooth crossover turns into a sharp QPT between two well-defined shape phases [9,[11][...

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A self-consistent description of systems with many interacting bosons

Cited by 64 publications

References 23 publications

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

Two-neutron separation energies, binding energies and phase transitions in the interacting boson model

Regular spectra in the vibron model with random interactions

Finite-size scaling exponents in the interacting boson model

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