Twenty years have passed since the author first questioned the importance of nonclassical structures for carbonium ions at the 1962 Symposium on "The Transition State" at Sheffield. At that time nonclassical structures were being advanced for essentially all carbocations known to man. There appeared to be general agreement that the 2-norbornyl cation was the most favorable example of a nonclass...

The interaction of mesoscopic interference devices with nonclassical electromagnetic fields is studied. The external quantum fields induce a phase factor on the electric charges. This phase factor, which is a generalization of the standard Aharonov-Bohm phase factor, is in the case of nonclassical electromagnetic fields a quantum mechanical operator. Its expectation value depends on the density...

With reference to two well known scenarios, we discuss, for nonclassical light, the competition between quantum and thermal effects. It is seen that for nonclassical light to be produced some amount of temperature-induced disorder is needed plus quantum fluctuations of order ħ squared.

A simple model allows us to study the nonclassical behavior of slowly moving atoms interacting with a quantized field. Atom and field become entangled and their joint state can be identified as a mesoscopic " Schrödinger–cat ". By introducing appropriate observables for atom and field and by analyzing correlations between them based on a Bell–type inequality we can show the corresponding noncla...

Breaking the time-reversal symmetry of light is great importance for fundamental physics and has attracted increasing interest in study non-reciprocal photonic devices. Here, a chiral cavity quantum electrodynamics system with multiple atoms strongly coupled to Fabry–Pérot experimentally demonstrated. By polarizing internal state atoms, atom-cavity interaction broken. The can be described by qu...

In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry method for third-order differential equations.In this paper, we will obtain first integral, integrating factor and λ-symmetry of third-order ODEs u ⃛=F(x,u,u ̇,u ̈). Also we compare Prelle -Singer (PS) method and λ-symmetry m...

Abstract In this paper, by using the Lie symmetry analysis, all of geometric vector fields $(3+1)$ (3+1) -Burgers system are obtained. We find 1, 2, and 3-dimensional optimal Burger then applying reduce order system. Also nonclassical symmetrie...

A suppressive surround modulates the responsiveness of cells in the lateral geniculate nucleus (LGN), but we know nothing of its spatial structure or the way in which it combines signals arising from different locations. It is generally assumed that suppressive signals are either uniformly distributed or balanced in opposing regions outside the receptive field. Here, we examine the spatial dist...

Nonclassical states of the electromagnetic field have for many years provided an excellent playground for testing fundamental concepts of quantum mechanics [1]. Recently, nonclassical light has also become an important asset to the rapidly developing applied fields of quantum optics, such as quantum communication and quantum information technology. Its applications, to name only a few, include ...