Chaos in a deformed Dicke model

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.

Killing Tensor and Carter Constant for Painlevé–Gullstrand Form of Lense–Thirring Spacetime

Recently, the authors have formulated and explored a novel Painlevé–Gullstrand variant of the Lense–Thirring spacetime, which has some particularly elegant features, including unit-lapse, intrinsically flat spatial 3-slices, and some particularly simple geodesics—the “rain” geodesics. At the linear level in the rotation parameter, this spacetime is indistinguishable from the usual slow-rotation expansion of Kerr. Herein, we shall show that this spacetime possesses a nontrivial Killing tensor, implying separability of the Hamilton–Jacobi equation. Furthermore, we shall show that the Klein–Gordon equation is also separable on this spacetime. However, while the Killing tensor has a 2-form square root, we shall see that this 2-form square root of the Killing tensor is not a Killing–Yano tensor. Finally, the Killing-tensor-induced Carter constant is easily extracted, and now, with a fourth constant of motion, the geodesics become (in principle) explicitly integrable.

Proper relativistic position operators in 1+1 and 2+1 dimensions

We have revisited the Dirac theory in [Formula: see text] and [Formula: see text] dimensions by using the covariant representation of the parity-extended Poincaré group in their native dimensions. The parity operator plays a crucial role in deriving wave equations in both theories. We studied two position operators, a canonical one and a covariant one that becomes the particle position operator projected onto the particle subspace. In [Formula: see text] dimensions the particle position operator, not the canonical position operator, provides the conserved Lorentz generator. The mass moment defined by the canonical position operator needs an additional unphysical spin-like operator to become the conserved Lorentz generator in [Formula: see text] dimensions. In [Formula: see text] dimensions, the sum of the orbital angular momentum given by the canonical position operator and the spin angular momentum becomes a constant of motion. However, orbital and spin angular momentum do not conserve separately. On the other hand the orbital angular momentum given by the particle position operator and its corresponding spin angular momentum become a constant of motion separately.

A study on the Friedmann-like Universe with torsion using Noether symmetry

This paper deals with the symmetry analysis of the Einstein Cartan Theory [E. Cartan, C. R. Acad. Sci. (Paris) 174, 593 (1922); E. Cartan, Ann. Sci. Ec. Norm. Super 40, 325 (1923)] which is an extension of the general relativity and it accounts for the spacetime torsion [S. Basilakos et al., Phys. Rev. D 88, 103526 (2013)]. We begin by applying Noether theorem [S. Capozziello, La Rivista del Nuovo Cimento (1978–1999) 19(4), 1 (1996)] to the Lagrangian of the FRW type cosmology with torsion and choose a point transformation: [Formula: see text], such that one of the transformed variables is cyclic [S. Capozziello, M. De Laurentis and S. D. Odintsov, Eur. Phys. J. C 72, 2068 (2012)] for the Lagrangian. Then using the conserved charge [S. Capozziello, M. De Laurentis and S. D. Odintsov, Eur. Phys. J. C 72, 2068 (2012)], which is obtained by applying Noether theorem, and the constant of motion, we get the solutions and conclude that due to the presence of torsion, the FRW type cosmology is in the de Sitter phase [D. Kranas, C. G. Tsagas, J. D. Barrow and D. Iosifidis, Eur. Phys. J. C 79, 341 (2019)].