Quantum fluctuations and unusual critical exponents in a quantum Rabi Triangle

Quantum fluctuations of a quantum Rabi triangle are studied using an analytical approach beyond the mean-field theory. By applying an artificial magnetic field among three cavities, time-reversal symmetry breaking is manifested through a directional transfer dynamics of photons. In contrast to previous studies, we focus on the scaling exponents of the fluctuations of the local photon number and the position variance near the critical point. By accurate calculation using Bogoliubov transformation we show that two scaling laws emerge respectively for the frustrated cavity and the remaining cavities, which are associated with the geometric frustrations. Especially, for the frustrated cavity, the scaling exponent in the chiral superradiant phase is different from that in the frustrated antiferromagnetic superradiant phase without an artificial magnetic field. The unusual scaling exponents predict distinct universality classes from the single-cavity Rabi universality. We suggest that the accurate critical exponents in few-body system is useful for identifying exotic quantum phase transition in light-matter coupling system.Comment: 8 pages,4 figure

New Confidence Intervals for the Difference between Two Sensitivities at a Fixed Level of Specificity

For two continuous-scale diagnostic tests, it is of interest to compare their sensitivities at a predetermined level of specificity. In this paper we propose three new intervals for the difference between two sensitivities at a fixed level of specificity. These intervals are easy to compute. We also conduct simulation studies to compare the relative performance of the new intervals with the existing normal approximation based interval proposed by Wieand et al (1989). Our simulation results show that the newly proposed intervals perform better than the existing normal approximation based interval in terms of coverage accuracy and interval length

Gravito-Electromagnetic coupled perturbations and quasinormal modes of a charged black hole with scalar hair

From the quantum point of view, singularity should not exist. Recently, Bah and Heidmann constructed a five-dimensional singularity free topology star/black hole [Phys. Rev. Lett. 126, 151101 (2021)]. By integrating the extra dimension, a four-dimensional static spherical black hole with a magnetic charge and scalar hair can be obtained. In this paper, we study the quasinormal modes (QNMs) of the magnetic field and gravitational field on the background of this four-dimensional charged black hole with scalar hair. The odd parity of the gravitational perturbations couples with the even parity of the magnetic field perturbations. Two coupled second-order derivative equations are obtained. Using the matrix-valued direct integration method, we obtain the fundamental QNM frequencies numerically. The effect of the magnetic charge on the QNMs is studied. The differences of the frequencies of the fundamental QNMs between the charged black hole with scalar hair and the Reissner-Norstr\"{o}m black hole are very small for the angular number $l=2$. However, some new interesting results are found for higher angular number.Comment: 10 pages, 3 figures, 2 tables, some mistakes have been correcte

(E)-N′-[(2-Hydroxynaphthalen-1-yl)methylidene]nicotinohydrazide

In the mol­ecule of the title compound, C17H13N3O2, the naphthyl ring system and the pyridine ring form a dihedral angle of 12.2 (3)°. An intra­molecular O—H⋯N hydrogen bond generates a six-membered ring with an S(6) ring motif. This also contributes to the relative overall near planarity of the mol­ecule [r.m.s. deviation of all 22 non-H atoms = 0.107 (5) Å]. In the crystal, mol­ecules are linked through inter­molecular N—H⋯N hydrogen bonds, forming chains along the a axis

Gravitational resonances on f(T)f(T)-branes

In this work, we investigate the gravitational resonances in various $f(T)$-brane models with the warp factor $\text{e}^{A(y)}=\tanh\big(k(y+b)\big)-\tanh\big(k(y-b)\big)$. For three kinds of $f(T)$, we give the solutions to the system. Besides, we consider the tensor perturbation of vielbein and obtain the effective potentials by the Kaluza-Klein (KK) decomposition. Then, we analyze what kind of effective potential can produce the gravitational resonances. Effects of different parameters on the gravitational resonances are analysed. The lifetimes of the resonances could be long enough as the age of our universe in some ranges of the parameters. This indicates that the gravitational resonances might be considered as one of the candidates of dark matter. Combining the current experimental observations, we constrain the parameters for these brane models.Comment: 12 pages, 14 figure

Characteristic modes of thick brane model: resonances and quasinormal modes

In this work, we investigate the gravitational quasinormal modes (QNMs) and the gravitational resonances of a thick brane model. We use the asymptotic iteration and shooting methods to obtain the quasinormal frequencies (QNFs) of the brane. On the other hand, we investigate the resonances and their evolution numerically. The results show that the oscillations of the resonances equal (up to numerical error) to the real parts of the QNFs, while the damping rates of the resonances equal to the imaginary parts of the QNFs. The QNMs and resonances, both of them can be regarded as the characteristic modes of the thick brane, are closely related with each other. In addition, the lifetimes of the QNMs might reach the age of our universe. Such a long-lived Kaluza-Klein modes could be a candidate for dark matter.Comment: 10 pages, 6 figure

Evolution of Fermion Resonance in Thick Brane

In this work, we investigate numerical evolution of massive Kaluza-Klein (KK) modes of a Dirac field on a thick brane. We deduce the Dirac equation in five-dimensional spacetime, and obtain the time-dependent evolution equation and Schr\"odinger-like equation of the extra-dimensional component. We use the Dirac KK resonances as the initial data and study the corresponding dynamics. By monitoring the decay law of the left- and right-chiral KK resonances, we compute the corresponding lifetimes and find that there could exist long-lived KK modes on the brane. Especially, for the lightest KK resonance with a large coupling parameter and a large three momentum, it will have an extremely long lifetime.Comment: 26 pages, 12 figure