Complementarity between micro-micro and micro-macro entanglement in a Bose–Einstein condensate with two Rydberg impurities

We theoretically study complementarity between micro-micro and micro-macro entanglement in a Bose–Einstein condensate with two Rydberg impurities. We investigate quantum dynamics of micro-micro and micro-macro entanglement in the micro-macro system. It is found that strong micro-macro entanglement between Rydberg impurities and the BEC can be generated by the use of initial micro-micro entanglement between two Rydberg impurities, which acts as the seed entanglement to create micro-macro entanglement. We demonstrate a curious complementarity relation between micro-micro and micro-macro entanglement, and find that the complementarity property can be sustained to some extent even though in the presence of the BEC decoherence.     

Thermal Equilibrium Between Radiation and Matter

In 1916, Einstein rederived the blackbody radiation law of Planck that originated the idea of quantized energy one hundred years ago. For this purpose, Einstein introduced the concept of transition probability, which had a profound influence on the development of quantum theory. In this article, we adopt Einstein's assumptions with two exceptions and seek the statistical condition for the thermal equilibrium of matter without referring to the inner details of either statistical thermodynamics or quantum theory. It is shown that the conditions of thermodynamic equilibrium of electromagnetic radiation and the energy balance of thermal radiation by the matter, between any of its two energy-states, not only result in Planck's radiation law and the Bohr frequency condition, but they remarkably yield the law of the statistical thermal equilibrium of matter: the Maxwell–Boltzmann distribution. Since the transition probabilities of the modern quantum theory of radiation coincide with their definition in Einstein's theory of blackbody radiation, the presented deduction of the Maxwell–Boltzmann distribution is equally valid within the bounds of modern quantum theory. Consequently, within the framework of the fundamental assumptions, the Maxwell–Boltzmann distribution of energy-states is not only a sufficient, but a necessary condition for thermal equilibrium between the matter and radiation.     

Generalized Einstein conditions on holomorphic Riemannian manifolds

Summary At first, a necessary and sufficient condition for a K?hler-Norden manifold to be holomorphic Einstein is found. Next, it is shown that the so-called (real) generalized Einstein conditions for K?hler-Norden manifolds are not essential since the scalarcurvature of such manifolds is constant. In this context, we study generalized holomorphic Einstein conditions. Using the one-to-one correspondence between K?hler-Norden structures and holomorphic Riemannian metrics, we establish necessary and sufficient conditions for K?hler-Norden manifolds to satisfy the generalized holomorphic Einstein conditions. And a class of new examples of such manifolds is presented. Finally, in virtue of the obtained results, we mention that Theorems 1 and 2 of H. Kim and J. Kim [10] are not true in general.     

Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds

We prove a Hitchin-Thorpe inequality for noncompact Einstein 4-manifolds with specified asymptotic geometry at infinity. The asymptotic geometry at infinity is either a cusp bundle over a compact space (the fibered cusps) or a fiber bundle over a cone with a compact fiber (the fibered boundary). Many noncompact Einstein manifolds come with such a geometry at infinity.     

On quasi-conformally flat weakly Ricci symmetric manifolds

The object of the present paper is to study quasi-conformally flat weakly Ricci symmetric manifolds.      

Motion Control by ZV Shaper Synthesis Extended for Fractional Systems and Its Application to CRONE Control

Shaping command input or preshaping is used for reducing system oscillation in motion control. Desired systems inputs are altered so that the system finishes the requested move without residual oscillation. This technique, developed by N.C. Singer and W.P. Seering, is used for example in the aerospace field, in particular in flexible structure control. This paper presents the study of ZV shaper for explicit fractional derivative systems (generalized derivative systems). A robustness study of ZV shaper is then presented and applied to improve second generation CRONE control response time. Results from simulation and from a DC motor bench are also given.     

Back Reaction in Static Einstein Spaces—Change of Entropy

Using the thermodynamical approach and the method of York, the back-reaction of anti-de Sitter Schwarzschild black hole in thermal equilibrium with conformal spin-2 field is studied. It is found that both approaches give identical results.     

On Some Ricci-Flat Metrics of Cohomogeneity Two on Complex Line Bundles

We construct a family of four-dimensional smooth Ricci-flat Riemann orbifolds of cohomogeneity two which possess the structure of complex line bundles.     

Thermodynamic Limit and Proof of Condensation for Trapped Bosons

We study condensation of trapped bosons in the limit when the number of particles tends to infinity. For the noninteracting gas we prove that there is no phase transition in any dimension, but in any dimension, at any temperature the system is 100% condensated into the one-particle ground state. In the case of an interacting gas we show that for a family of suitably scaled pair interactions, the Gross–Pitaevskii scaling included, a less-than-100% condensation into a single-particle eigenstate, which may depend on the interaction strength, persists at all temperatures.