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J. P. Draayer

Publications and source records attributed to J. P. Draayer.

At least 55 records · Page 3Linked to original sources
arXiv2007

Isospin symmetry breaking in an algebraic pairing Sp(4) model

An exactly solvable sp(4) algebraic approach extends beyond the traditional isospin conserving nuclear interaction to bring forward effects of isospin symmetry breaking and isospin mixing resulting from a two-body nuclear interaction that includes proton-neutron (pn) and like-particle isovector pairing correlations plus significant isoscalar pn interactions. The model yields an estimate for the extent to which isobaric analog 0+ states in light and medium mass nuclei may mix with one another and reveals possible, but still extremely weak, non-analog beta-decay transitions.

nucl-th↗
arXiv2007

Underlying symmetries of realistic interactions and the nuclear many-body problem

The present study brings forward important information, within the framework of spectral distribution theory, about the types of forces that dominate three realistic interactions, CD-Bonn, CDBonn+ 3terms and GXPF1, in nuclei and their ability to account for many-particle effects such as the formation of correlated nucleon pairs and enhanced quadrupole collective modes. Like-particle and proton-neutron isovector pairing correlations are described microscopically by a model interaction with Sp(4) dynamical symmetry, which is extended to include an additional quadrupole-quadrupole interaction. The analysis of the results for the 1f7/2 level shows that both CD-Bonn+3terms and GXPF1 exhibit a well-developed pairing character compared to CD-Bonn, while the latter appears to build up more (less) rotational isovector T = 1 (isoscalar T = 0) collective features. Furthermore, the three realistic interactions are in general found to correlate strongly with the pairing+quadrupole model interaction, especially for the highest possible isospin group of states where the model interaction can be used to provide a reasonable description of the corresponding energy spectra.

nucl-th↗
arXiv2007

Dynamical Symmetries Reflected in Realistic Interactions

Realistic nucleon-nucleon (NN) interactions, derived within the framework of meson theory or more recently in terms of chiral effective field theory, yield new possibilities for achieving a unified microscopic description of atomic nuclei. Based on spectral distribution methods, a comparison of these interactions to a most general Sp(4) dynamically symmetric interaction, which previously we found to reproduce well that part of the interaction that is responsible for shaping pairing-governed isobaric analog 0+ states, can determine the extent to which this significantly simpler model Hamiltonian can be used to obtain an approximate, yet very good description of low-lying nuclear structure. And furthermore, one can apply this model in situations that would otherwise be prohibitive because of the size of the model space. In addition, we introduce a Sp(4) symmetry breaking term by including the quadrupole-quadrupole interaction in the analysis and examining the capacity of this extended model interaction to imitate realistic interactions. This provides a further step towards gaining a better understanding of the underlying foundation of realistic interactions and their ability to reproduce striking features of nuclei such as strong pairing correlations or collective rotational motion.

nucl-th↗
arXiv2007

Physical Significance of q Deformation and Many-Body Interactions in Nuclei

The quantum deformation concept is applied to a study of pairing correlations in nuclei with mass 40<A<100. While the nondeformed limit of the theory provides a reasonable overall description of certain nuclear properties and fine structure effects, the results show that the q deformation plays a significant role in understanding higher-order effects in the many-body interaction.

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arXiv2007

Exact boson mapping of the reduced BCS pairing Hamiltonian

An exact boson mapping of the reduced BCS (equal strength) pairing Hamiltonian is considered. In the mapping, fermion pair operators are mapped exactly to the corresponding bosons. The image of the mapping results in a Bose-Hubbard model with level dependent hopping. Though the resultant Bose-Hubbard Hamiltonian is non-Hermitian, all eigenvalues are real when Uk/t< 1, where k is the total number of bosons. When U/t=1, a part of spectrum of the Bose-Hubbard Hamiltonian corresponds exactly to the whole spectrum of the reduced BCS pairing Hamiltonian.

nucl-th↗
arXiv2007

Exact diagonalization for spin-1/2 chains and the first order quantum phase transitions of the XXX chain in a uniform transverse field

A simple Mathematica code based on the differential realization of hard-core boson operators for finding exact solutions of the periodic-N spin-1/2 systems with or beyond nearest neighbor interactions is proposed, which can easily be used to study general spin-1/2 interaction systems. As an example, The code is applied to study XXX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field. It shows that there are [N/2] level-crossing points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitional behavior in the ground state of the system in the thermodynamic limit is also studied.

quant-ph↗
arXiv2007

First order quantum phase transitions in the XX spin chain

Quantum phase transitional behavior of a finite periodic XX spin-1/2 chain with nearest neighbor interaction in a uniform transverse field is studied based on the simple exact solutions. It is found that there are [N/2] level-crossing points in the ground state, where N is the periodic number of the system and [x] stands for the integer part of x, when the interaction strength and magnitude of the magnetic field satisfy certain conditions. The quantum phase transitions are of the first order due to the level-crossing. The ground state in the thermodynamic limit will be divided into three distinguishable quantum phases.

quant-ph↗
arXiv2007

M-body Pure State Entanglement

The simple entanglement of N-body N-particle pure states is extended to the more general M-body or M-body N-particle states where $N\neq M$. Some new features of the M-body N-particle pure states are discussed. An application of the measure to quantify quantum correlations in a Bose-Einstien condensate model is demonstrated.

quant-ph↗
arXiv2006

Classification and Quantification of Entangled Bipartite Qutrit Pure States

A complete analysis of entangled bipartite qutrit pure states is carried out based on a simple entanglement measure. An analysis of all possible extremally entangled pure bipartite qutrit states is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis and the results should be helpful for finding different entanglement types in multipartite pure state systems.

quant-ph↗
arXiv2005

Confined One Dimensional Harmonic Oscillator as a Two-Mode System

The one-dimensional harmonic oscillator in a box problem is possibly the simplest example of a two-mode system. This system has two exactly solvable limits, the harmonic oscillator and a particle in a (one-dimensional) box. Each of the two limits has a characteristic spectral structure describing the two different excitation modes of the system. Near each of these limits, one can use perturbation theory to achieve an accurate description of the eigenstates. Away from the exact limits, however, one has to carry out a matrix diagonalization because the basis-state mixing that occurs is typically too large to be reproduced in any other way. An alternative to casting the problem in terms of one or the other basis set consists of using an "oblique" basis that uses both sets. Through a study of this alternative in this one-dimensional problem, we are able to illustrate practical solutions and infer the applicability of the concept for more complex systems, such as in the study of complex nuclei where oblique-basis calculations have been successful. Keywords: one-dimensional harmonic oscillator, particle in a box, exactly solvable models, two-mode system, oblique basis states, perturbation theory, coherent states, adiabatic mixing.

math-ph↗
arXiv2005

Six-dimensional Davidson potential as a dynamical symmetry of the symplectic Interacting Vector Boson Model

A six-dimensional Davidson potential, introduced within the framework of the Interacting Vector Boson Model (IVBM), is used to describe nuclei that exhibit transitional spectra between the purely rotational and vibrational limits of the theory. The results are shown to relate to a new dynamical symmetry that starts with the $Sp(12,R) \supset SU(1,1) \times SO(6)$ reduction. Exact solutions for the eigenstates of the model Hamiltonian in the basis defined by a convenient subgroup chain of SO(6) are obtained. A comparison of the theoretical results with experimental data for heavy nuclei with transitional spectra illustrates the applicability of the theory.

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arXiv2005

Quantum Phase Transitions in the U(5)-O(6) Large N limit

The U(5)-O(6) transitional behavior of the Interacting Boson Model in the large N limit is revisited. Some low-lying energy levels, overlaps of the ground state wavefunctions, B(E2) transition rate for the decay of the first excited energy level to the ground state, and the order parameters are calculated for different total numbers of bosons. The results show that critical behaviors of these quantities are greatly enhanced with increasing of the total number of bosons N, especially fractional occupation probability for d bosons in the ground state, the difference between the expectation value of n_d in the first excited 0^+ state and the ground state, and another quantity related to the isomer shift behave similarly in both the O(6)-U(5) large N and U(5)-SU(3) phase transitions.

nucl-th↗
arXiv2005

Extremal Entanglement For Triqubit Pure States

A complete analysis of entangled triqubit pure states is carried out based on a new simple entanglement measure. An analysis of all possible extremally entangled pure triqubit states with up to eight terms is shown to reduce, with the help of SLOCC transformations, to three distinct types. The analysis presented are most helpful for finding different entanglement types in multipartite pure state systems.

quant-ph↗
arXiv2004

A simple entanglement measure for multipartite pure states

A simple entanglement measure for multipartite pure states is formulated based on the partial entropy of a series of reduced density matrices. Use of the proposed new measure to distinguish disentangled, partially entangled, and maximally entangled multipartite pure states is illustrated.

quant-ph↗
arXiv2004

Quantum Critical Behavior of Two Coupled Bose-Einstein Condensates

The quantum critical behavior of the Bose-Hubbard model for a description of two coupled Bose-Einstein condensates is studied within the framework of an algebraic theory. Energy levels, wavefunction overlaps with those of the Rabi and Fock regimes, and the entanglement are calculated exactly as functions of the phase parameter and the number of bosons. The results show that the system goes though a phase transition and that the critical behavior is enhanced in the thermodynamic limit.

cond-mat.mes-hall↗
arXiv2004

Staggering behavior of 0^+ state energies in the Sp(4) pairing model

We explore, within the framework of an algebraic sp(4) shell model, discrete approximations to various derivatives of the energies of the lowest isovector-paired 0^+ states of atomic nuclei in the 40 <A < 100 mass range. The results show that the symplectic model can be used to successfully interpret fine structure effects driven by the proton-neutron (pn) and like-particle isovector pairing interactions as well as interactions with higher J multipolarity. A finite energy difference technique is used to investigate two-proton and two-neutron separation energies, observed irregularities found around the N=Z region, and the like-particle and pn isovector pairing gaps. A prominent staggering behavior is observed between groups of even-even and odd-odd nuclides. An oscillation, in addition to that associated with changes in isospin values, that tracks with alternating seniority quantum numbers related to the isovector pairing interaction is also found.

nucl-th↗
arXiv2004

Energy Systematics of Low-lying Collective States within the Framework of the Interacting Vector Boson Model

In a new application of the algebraic Interacting Vector Boson Model (IVBM), we exploit the reduction of its Sp(12,R) dynamical symmetry group to Sp(4,R) x SO(3), which defines basis states with fixed values of the angular momentum L. The relationship of the latter to $U(6) \subset U(3)x U(2), which is the rotational limit of the model, means the energy distribution of collective states with fixed angular momentum can be studied. Results for low-lying spectra of rare-earth nuclei show that the energies of collective positive parity states with L=0,2,4,6... lie on second order curves with respect to the number of collective phonons n or vector bosons N=4n out of which the states are built. The analysis of this behavior leads to insight regarding the common nature of collective states, tracking vibrational as well as rotational features.

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