Two-body random ensemble in nuclei

Papenbrock, T.; Weidenmüller, Hans A.

doi:10.1103/physrevc.73.014311

Cited by 30 publications

(21 citation statements)

References 24 publications

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“…A change of the residual interaction causes simultaneous changes in the spectra of all nuclei belonging to the same major shell. Mg. From Papenbrock and Weidenmüller, 2006. In the framework of a statistical description, this fact is tantamount to the existence of spectral correlations. Still, it is remarkable that such correlations have never been addressed in the framework of RMT until quite recently.…”

Section: Correlations Between Spectra Carrying Different Quantum Nmentioning

confidence: 98%

“…͑Color online͒ Roots s ␣ ͑J͒ of the eigenvalues s ␣ 2 ͑J͒ defined in Eq. ͑8͒ vs total spin J for the T = 0 states in 24 Mg. From Papenbrock and Weidenmüller, 2006. highest state since the v͑␣͒ have random signs.͔ The spectral radius is expected to be a random variable. We ask for the probability p j with which, for a given value of J, R J takes maximum value.…”

Section: Preponderance Of Ground States With Spin Zeromentioning

confidence: 99%

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Colloquium: Random matrices and chaos in nuclear spectra

2007

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Chaos occurs in quantum systems if the statistical properties of the eigenvalue spectrum coincide with predictions of random-matrix theory. Chaos is a typical feature of atomic nuclei and other self-bound Fermi systems. How can the existence of chaos be reconciled with the known dynamical features of spherical nuclei? Such nuclei are described by the shell model ͑a mean-field theory͒ plus a residual interaction. The question is answered using a statistical approach ͑the two-body random ensemble͒: The matrix elements of the residual interaction are taken to be random variables. Chaos is shown to be a generic feature of the ensemble and some of its properties are displayed, emphasizing those which differ from standard random-matrix theory. In particular, the existence of correlations among spectra carrying different quantum numbers is demonstrated. These are subject to experimental verification.

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Section: Correlations Between Spectra Carrying Different Quantum Nmentioning

confidence: 98%

Section: Preponderance Of Ground States With Spin Zeromentioning

confidence: 99%

Colloquium: Random matrices and chaos in nuclear spectra

2007

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“…The idea of random walk in the angular momentum space was used long ago by Bethe [191] for estimates of the spin-dependent nuclear level density. This geometric chaoticity plays an important role in statistics of self-bound systems [192,184,185,193] and it can justify the assumption (89) even for the case of intrinsic interactions which are relatively weak to introduce the full dynamical chaos. Irrespectively of dynamic interaction, this leads to chaotic structure of wave functions and, for example, to the predominance of the scalar representation J = 0 in the ground state of an even-even nucleus after averaging over all interactions allowed by the conservation laws [194,195].…”

Section: Statistics Of Resonancesmentioning

confidence: 89%

Super-radiant dynamics, doorways and resonances in nuclei and other open mesoscopic systems

Auerbach¹,

Zelevinsky²

2011

Rep. Prog. Phys.

115

173

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The phenomenon of super-radiance (Dicke effect, coherent spontaneous radiation by a gas of atoms coupled through the common radiation field) is well known in quantum optics. The review discusses similar physics that emerges in open and marginally stable quantum many-body systems. In the presence of open decay channels, the intrinsic states are coupled through the continuum. At sufficiently strong continuum coupling, the spectrum of resonances undergoes the restructuring with segregation of very broad super-radiant states and trapping of remaining long-lived compound states. The appropriate formalism describing this phenomenon is based on the Feshbach projection method and effective non-Hermitian Hamiltonian. A broader generalization is related to the idea of doorway states connecting quantum states of different structure. The method is explained in detail and the examples of applications are given to nuclear, atomic and particle physics. The interrelation of the collective dynamics through continuum and possible intrinsic many-body chaos is studied, including universal mesoscopic conductance fluctuations. The theory serves as a natural framework for general description of a quantum signal transmission through an open mesoscopic system.

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“…(This is not the case in general). Let us consider an arbitrary unitary transformation H → UHU † of the matrices in the ensemble (9). All terms on the right-hand side of Eq.…”

Section: Constrained Gaussian Unitary Random-matrix Ensemblesmentioning

confidence: 99%

Level repulsion in constrained Gaussian random-matrix ensembles

Papenbrock¹,

Pluhař²,

Weidenmüller³

2006

J. Phys. A: Math. Gen.

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Introducing sets of constraints, we define new classes of random-matrix ensembles, the constrained Gaussian unitary (CGUE) and the deformed Gaussian unitary (DGUE) ensembles. The latter interpolate between the GUE and the CGUE. We derive a sufficient condition for GUE-type level repulsion to persist in the presence of constraints. For special classes of constraints, we extend this approach to the orthogonal and to the symplectic ensembles. A generalized Fourier theorem relates the spectral properties of the constraining ensembles with those of the constrained ones. We find that in the DGUEs, level repulsion always prevails at a sufficiently short distance and may be lifted only in the limit of strictly enforced constraints.

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Two-body random ensemble in nuclei

Cited by 30 publications

References 24 publications

Colloquium: Random matrices and chaos in nuclear spectra

Colloquium: Random matrices and chaos in nuclear spectra

Super-radiant dynamics, doorways and resonances in nuclei and other open mesoscopic systems

Level repulsion in constrained Gaussian random-matrix ensembles

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