From quantum to classical without ħ → 0

In this paper we put forward some simple rules which can be used in order to pass from the quantum Moyal evolution operator to the classical one of Liouville without taking the limit of $?\to 0$. These rules involve the averaging over some auxiliary variables.     

Poincaré's theorem and unitary transformations for classical and quantum systems

Poincaré's celebrated theorem on the nonexistence of analytical invariants of motion is extended to the case of a continuous spectrum to deal with large classical and quantum systems. It is shown that Poincaré's theorem applies to situations where there exist continuous sets of resonances. This condition is equivalent to the nonvanishing of the asymptotic collision operator as defined in modern kinetic theory. Typical examples are systems presenting relaxation processes or exhibiting unstable quantum levels. As the result of Poincaré's theorem, the unitary transformation, leading to a cyclic Hamiltonian in classical mechanics or to the diagonalization of the Hamiltonian operator in quantum mechanics, diverges. We obtain therefore a dynamical classification of large classical or quantum systems. This is of special interest for quantum systems as, historically, quantum mechanics has been formulated following closely the patterns of classical integrable systems. The well known results of Friedrichs concerning the coupling of discrete states with a continuum are recovered. However, the role of the collision operator suggests new ways of eliminating the divergence in the unitary transformation theory.     

Cosmic Masers – From OH to Ho (IAU S287), edited by Roy S. Booth,Wouter H.T. Vlemmings and Elizabeth M.L. Humphreys

‘Flying Triangulation’ (FlyTri) is a recently developed principle which allows for a motion-robust optical 3D measurement of rough surfaces. It combines a simple sensor with sophisticated algorithms: a single-shot sensor acquires 2D camera images. From each camera image, a 3D profile is generated. The series of 3D profiles generated are aligned to one another by algorithms, without relying on any external tracking device. It delivers real-time feedback of the measurement process which enables an all-around measurement of objects. The principle has great potential for small-space acquisition environments, such as the measurement of the interior of a car, and motion-sensitive measurement tasks, such as the intraoral measurement of teeth. This article gives an overview of the basic ideas and applications of FlyTri. The main challenges and their solutions are discussed. Measurement examples are also given to demonstrate the potential of the measurement principle.     

Atom–field interaction under the influence of two external classical and quantum fields

In this paper we introduce a new version of the interaction between a two-level atom and an external electric field in the presence of the classical field. Under a certain condition the system is transformed to the usual Jaynes–Cummings model. The atomic inversion is investigated where the phenomenon of super-structure is reported for a large value of the classical field coupling parameter. Assuming that the field is initially in the displaced thermal state the variance and the entropy squeezing as well as the degree of entanglement are discussed. Our results show that the information of variance and entropy squeezing beside the purity can be controlled by both of the coupling parameter of the classical field and the mean photon number. In this context the variance and the entropy squeezing become more pronounced for large values of the classical field coupling, while the system shows period of disentanglement during the considered time.