Analog of Planck's constant for a colloid system

Based on the assumption of the instability of the colloidal state caused by the movement of charged particles, we previously obtained equations characterizing the structure of the colloid: a Schrödinger-type equation that defines the redistribution of thermal and potential energy in the colloid and a material equation – the diffusion equation with the Liesegang operator, which is connected directly with the substance, allowing find breaks in structures caused by vibrations of electrically charged particles. Such effects for colloidal chemical manifestations are called macroscopic quantum effects. That is, macroscopic quantum effects are a combination of phenomena in which the characteristic features of quantum mechanics are directly manifested in the behavior of macroscopic, for example, colloidal objects. As a rule, the behavior of macroscopic objects contains a large number of atoms and is described with high accuracy by the equations of classical physics, which do not include the characteristic quantum value – the constant bar. Based on the equations constructed by the authors, which are the equations of plasma hydrodynamics, a mathematical model is created that reduces the colloidal system to an equation similar to the Schrödinger equation and calculates a certain constant that is an analogue of the Planck constant for macroscopic colloidal systems and computes the constant of this equation , which is equal in magnitude . It differs significantly in magnitude from the Planck constant, because it characterizes the already complex macroscopic quantum oxyhydrate colloidal system.

Directional soliton and breather beams

Solitons and breathers are nonlinear modes that exist in a wide range of physical systems. They are fundamental solutions of a number of nonlinear wave evolution equations, including the unidirectional nonlinear Schrödinger equation (NLSE). We report the observation of slanted solitons and breathers propagating at an angle with respect to the direction of propagation of the wave field. As the coherence is diagonal, the scale in the crest direction becomes finite; consequently, beam dynamics form. Spatiotemporal measurements of the water surface elevation are obtained by stereo-reconstructing the positions of the floating markers placed on a regular lattice and recorded with two synchronized high-speed cameras. Experimental results, based on the predictions obtained from the (2D + 1) hyperbolic NLSE equation, are in excellent agreement with the theory. Our study proves the existence of such unique and coherent wave packets and has serious implications for practical applications in optical sciences and physical oceanography. Moreover, unstable wave fields in this geometry may explain the formation of directional large-amplitude rogue waves with a finite crest length within a wide range of nonlinear dispersive media, such as Bose–Einstein condensates, solids, plasma, hydrodynamics, and optics.