Phase singularity diffusion

Rotating Spirals without Phase Singularity in Reaction-Diffusion Systems

Rotating spiral waves without phase singularity are found to arise in a certain class of three-component reaction-diffusion systems of biological relevance. It is argued that this phenomenon is universal when some chemical components involved are diffusion-free. Some more detailed mathematical and numerical analyses are carried out on a complex GinzburgLandau equation with non-local coupling to...

Anisotropic diffusion in oriented environments can lead to singularity formation

Joint estimation of phase and phase diffusion for quantum metrology.

Phase estimation, at the heart of many quantum metrology and communication schemes, can be strongly affected by noise, whose amplitude may not be known, or might be subject to drift. Here we investigate the joint estimation of a phase shift and the amplitude of phase diffusion at the quantum limit. For several relevant instances, this multiparameter estimation problem can be effectively reshape...

Optical phase estimation in the presence of phase diffusion.

The measurement problem for the optical phase has been traditionally attacked for noiseless schemes or in the presence of amplitude or detection noise. Here we address the estimation of phase in the presence of phase diffusion and evaluate the ultimate quantum limits to precision for phase-shifted Gaussian states. We look for the optimal detection scheme and derive approximate scaling laws for ...

Singularity analysis of a reaction-diffusion equation with a solution-dependent Dirac delta source

We analyze the existence and singularity of solution to a reaction-diffusion equation, whose reaction term is represented by a Dirac delta function which depends on the solution itself. We prove that there exists a unique analytic solution with a logarithmic singularity at the origin.