We introduce a concept of causality in the framework of generalized pseudo-Riemannian Geometry in the sense of Colombeau. This is motivated by a generalized point value characterization of generalized pseudoRiemannian metrics due to M. Kunzinger et al. We prove an appropriate version of the inverse Cauchy-Schwarz inequality. As an application, we establish a dominant energy condition for some e...

In 2004 Fullér and Majlender introduced the notion of covariance between fuzzy numbers by their joint possibility distribution to measure the degree to which they interact. Based on this approach, in this paper we will present the concept of possibilistic correlation representing an average degree of interaction between marginal distributions of a joint possibility distribution as compared to t...

A scheme for the generation of non-classical pairs of photons in atomic vapours is proposed. The scheme exploits the fact that the cross correlation of the emission of photons from the extreme transitions of a four-level cascade system shows anti-bunching which has not been reported earlier and which is unlike the case of the three level cascade emission which shows bunching. The Cauchy-Schwarz...

The violation of a classical Cauchy-Schwarz (CS) inequality is identified as an unequivocal signature of spontaneous Hawking radiation in sonic black holes. This violation can be particularly large near the peaks in the radiation spectrum emitted from a resonant boson structure forming a sonic horizon. As a function of the frequency-dependent Hawking radiation intensity, we analyze the degree o...

Cylindrical electromagnetic waves have been examined mostly with a radiation condition applied at the radial far field. In modern optical technology, there are however growing number of applications where both radiation and absorption of energy should be taken into account. In order to illustrate the ramifications of such energy balance, we take plasmonic waves propagating around a metallic nan...

If the sequence a = (a„>^ E /2, i.e., ||a||2 = 2~=0 | a„ |2 < oo, define Sa as the sequence of averages 1 " 2 ak n + 1 , It follows easily from the Marcinkiewicz Interpolation Theorem that S is a bounded operator from I2 to I2; this can also be proved directly using the Cauchy-Buniakowski-Schwarz inequality [1]. S is known as the Cesàro operator. S is, of course, not bounded below, but the foll...

We report the continuous and partially nondestructive measurement of optical photons. For a weak light pulse traveling through a slow-light optical medium (signal), the associated atomic-excitation component is detected by another light beam (probe) with the aid of an optical cavity. We observe strong correlations of g_{sp}^{(2)}=4.4(5) between the transmitted signal and probe photons. The obse...

We investigate electromagnetic radiation emitted by a small voltage-biased Josephson junction connected to a superconducting transmission line. At frequencies below the well-known emission peak at the Josephson frequency (2eV/h), extra radiation is triggered by quantum fluctuations in the transmission line. For weak tunneling couplings and typical Ohmic transmission lines, the corresponding pho...

The encoding process of vector quantization (VQ) is very heavy and it constrains VQ’s application to a great deal. In order to speed up VQ encoding, it is most important to avoid unnecessary Euclidean distance computation (k-D) as much as possible by the difference check first that uses simpler features (low dimensional) while winner searching is going on. Sum (1-D) and partial sums (2-D) are u...

Quantum effects in light-matter interaction have always intrigued scientists. Such effects may result in quantum particle-particle correlations, for instance. The first measurement of an intensity-intensity correlation function was performed by Hanbury-Brown and Twiss [1], while the theoretical basis for the full quantum characterization of light was introduced by Glauber [2]. Therefore, resear...