Quantum chaos in a schematic shell model

Meredith, Dawn C.; Zirnbauer, Martin R.

doi:10.1103/physreva.37.3499

Cited by 117 publications

(95 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, unlike the usual studies involving the Lipkin model, we have the additional constraint of being in a symmetric S 3 representation. The Lipkin model has been studied in the context of chaos [38] but without explicit reference to its dynamical symmetries.…”

Section: Discussionmentioning

confidence: 99%

Effective group structure in the interacting boson model

Whelan¹

1995

Nuclear Physics A

View full text Add to dashboard Cite

Spectrum generating algebras are used in various fields of physics as models to determine quantum structure, including energy levels and transition strengths. The advantage of such models is that their group structure allows an extensive understanding of the system being studied. In addition they possess a simple classical limit, at least for bosonic systems. In this paper we discuss an algebraic model of nuclear structure, the Interacting Boson Model (IBM), and show that in one limit its group structure is particularly simple. For zero angular momentum there is an effective lower dimensional group structure which describes the system both classically and quantum mechanically.

show abstract

Section: Discussionmentioning

confidence: 99%

Effective group structure in the interacting boson model

Whelan¹

1995

Nuclear Physics A

View full text Add to dashboard Cite

show abstract

“…As discussed in great detail in [20][21][22][23][24][25], the classical Hamiltonian can be obtained in the thermodynamic limit…”

Section: Lmg Modelmentioning

confidence: 99%

“…Another example, taken from nuclear physics, is the three-level Lipkin-MashowGlick (LMG) model [20,21], whose quantum Hamiltonian iŝ…”

Section: Lmg Modelmentioning

confidence: 99%

See 1 more Smart Citation

Energy Level Quasi-Crossings: Accidental Degeneracies or Signature of Quantum Chaos?

Manfredi

Salasnich

2000

Int. J. Mod. Phys. E

View full text Add to dashboard Cite

In the field of quantum chaos, the study of energy levels plays an important role. The aim of this review paper is to critically discuss some of the main contributions regarding the connection between classical dynamics, semi-classical quantization and spectral statistics of energy levels. In particular, we analyze in detail degeneracies and quasi-crossings in the eigenvalues of quantum Hamiltonians which are classically non-integrable.

show abstract

“…Its classical counterpart, obtained in the limit of the number of particles that goes to infinity, is represented by a non-integrable hamiltonian with two degrees of freedom [7,8,9,10]. The semi-classical quantization of this model has been studied in [7] and here we calculate the quantum corrections and then analyze their numerical accuracy.…”

mentioning

confidence: 99%

Quantum Corrections to the Semiclassical Quantization of the Su(3) Shell Model

Manfredi

Salasnich

1995

Int. J. Mod. Phys. B

View full text Add to dashboard Cite

We apply the canonical perturbation theory to the semi-quantal hamiltonian of the SU(3) shell model. Then, we use the Einstein-Brillowin-Keller quantization rule to obtain an analytical semi-quantal formula for the energy levels, which is the usual semi-classical one plus quantum corrections.Finally, a test on the numerical accuracy of the semiclassical approximation and of its quantum corrections is performed.

show abstract

Quantum chaos in a schematic shell model

Cited by 117 publications

References 38 publications

Effective group structure in the interacting boson model

Effective group structure in the interacting boson model

Energy Level Quasi-Crossings: Accidental Degeneracies or Signature of Quantum Chaos?

Quantum Corrections to the Semiclassical Quantization of the Su(3) Shell Model

Contact Info

Product

Resources

About