19. “Repulsion” of nuclear levels

Gurevich, I.I.; Pevzner, M.I.

doi:10.1016/s0031-8914(56)90086-6

Cited by 6 publications

(1 citation statement)

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“…One first needs to desymmetrize the spectrum, i.e., separate the eigenvalues in symmetry subspaces. This is because the eigenlevels belonging to different symmetry sectors are uncorrelated, and thus in mixing them all one can easily miss [22,23] the paradigmatic feature of quantum chaotic spectra: level correlations. The result would appear to be a significantly less chaotic system.…”

Section: Introductionmentioning

confidence: 99%

Chaos in a deformed Dicke model

Corps¹,

Molina²,

Relaño³

2022

J. Phys. A: Math. Theor.

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The critical behavior in an important class of excited state quantum phase transitions is signaled by the presence of a new constant of motion onlyat one side of the critical energy. We study the impact of this phenomenon in the development of chaos in a modified version of the paradigmatic Dicke model of quantum optics, in which a perturbation is added that breaks the parity symmetry. Two asymmetric energy wells appear in the semiclassical limit of the model, whose consequences are studied both in the classical and in the quantum cases. Classically, Poincar ́e sections reveal that the degree of chaos not only depends on the energy of the initial condition chosen, but also on the particular energy well structure of the model. In the quantum case, Peres lattices of physical observables show that the appearance of chaos critically depends on the quantum conserved number provided by this constant of motion. The conservation law defined by this constant is shown to allow for the coexistence between chaos and regularity at the same energy. We further analyze the onset of chaos in relationwith an additional conserved quantity that the model can exhibit.

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Section: Introductionmentioning

confidence: 99%

Chaos in a deformed Dicke model

Corps¹,

Molina²,

Relaño³

2022

J. Phys. A: Math. Theor.

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From Quantum Systems to L-Functions: Pair Correlation Statistics and Beyond

Barrett

Firk

Miller

et al. 2016

Open Problems in Mathematics

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The discovery of connections between the distribution of energy levels of heavy nuclei and spacings between prime numbers has been one of the most surprising and fruitful observations in the twentieth century. The connection between the two areas was first observed through Montgomery's work on the pair correlation of zeros of the Riemann zeta function. As its generalizations and consequences have motivated much of the following work, and to this day remains one of the most important outstanding conjectures in the field, it occupies a central role in our discussion below. We describe some of the many techniques and results from the past sixty years, especially the important roles played by numerical and experimental investigations, that led to the discovery of the connections and progress towards understanding the behaviors. In our survey of these two areas, we describe the common mathematics that explains the remarkable universality. We conclude with some thoughts on what might lie ahead in the pair correlation of zeros of the zeta function, and other similar quantities.

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