Suppose stfis a collection of subsets of the unit interval and, for A e s/, \iA is a Borel measure on A which vanishes on points and gives A measure 1. The system pA (A e jtf) is called a coherent system if pA(C) = nA(B)pB(C) whenever A dSdC are in .Wand all terms are defined. The existence of a coherent system for the collection of perfect sets is shown to be independent of Zermelo-Fraenkel se...

We studied coherent backscattering (CBS) of light from opal photonic crystals with incomplete band gaps. We observed a dramatic broadening of the CBS cone for incident angles close to the Bragg condition in the crystals. We modify the conventional CBS theory to incorporate Bragg attenuation resulting from the photonic band structure. By fitting the CBS data with the modified theory, we extract ...

Coherent structures are solutions to reaction-diffusion systems that are time-periodic in an appropriate moving frame and spatially asymptotic at x = ±∞ to spatially periodic travelling waves. This paper is concerned with sources which are coherent structures for which the group velocities in the far field point away from the core. Sources actively select wave numbers and therefore often organi...

Although the phenomenon of coherent backscattering (CBS) in nonbiological media has generated substantial research interest, observing CBS in biological tissue has been extremely difficult. Here we show that the combination of low-spatial-coherence, broadband illumination, and low-temporal-coherence, spectrally resolved detection significantly facilitates CBS observation in biological tissue an...

Consider the space L2 C, dμ z , where dμ z e−|z| 2 dz ∧ dz is the Gaussian measure, and its generalized Bargmann subspaces Em which are the null kernels of the operator Δ −∂2/∂z∂z z ∂/∂z − mI; m 0, 1, . . . . In this work, we present an other construction of Em following the Hermite functions which allows us to define a family of generalized Bargmann transform Bm which maps isometrically Em int...

We derive the form of the Belavkin-Kushner-Stratonovich equation describing the filtering of a continuous observed quantum system via non-demolition measurements when the statistics of the input field used for the indirect measurement are in a general coherent state.

We develop an accurate finite-time scaling analysis of the angular width of the coherent backscattering (CBS) peak for waves propagating in 3D random media. Applying this method to ultracold atoms in optical speckle potentials, we show how to determine both the mobility edge and the critical exponent of the Anderson transition from the temporal behavior of the CBS width. Our method could be use...

Coherent backscattering (CBS) of light in random media has been previously investigated by use of coherent light sources. Here we report a novel method of CBS measurement that combines low spatial coherence, broadband illumination, and spectrally resolved detection. We show that low spatial coherence illumination leads to an anomalously broad CBS peak and a dramatic speckle reduction; the latte...

Using both the fermionic-like and the bosonic-like properties of the Pauli spin operators we discuss the Bose description of the Pauli spin operators firstly proposed by Shigefumi Naka, and derive another new bosonic representation of Pauli operators. The eigenvector of σ− in the bosonic representation is a nonlinear coherent state with the eigenvalues being the Grassmann numbers.