We report here the observations that exhibit the existence of matter wave phenomena with wavelength in the macrodomain of a few centimeters, for electrons moving along a magnetic field from an electron gun to a collector plate situated behind a grounded grid. These are in accordance with the predictions of a quantumlike theory for charged particles in the classical macrodomain, given by one of the authors [R. K. Varma, Phys. Rev. A 31, 3951 (1985)] with a recent generalization [R. K. Varma, Phys. Rev. E 64, 036608 (2001)]. The beats correspond to two closely spaced "frequencies" in the system, with the beat frequency given, in accordance with the characteristics of a wave phenomena, by the difference between the two frequencies. The beats ride as a modulation over a discrete energy band structure obtained with only one frequency present. The frequency here corresponds to the distance between the electron gun and the detector plate as it characterizes the variation in the energy band structure as the electron energy is swept. The second "frequency" corresponds to the gun-grid distance. These observations of the beats of matter waves in this experiment, with characteristics in accordance with the wave algorithm, then establish unambiguously the existence of macroscopic matter waves for electrons propagating along a magnetic field.

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It is shown that purely damped convective cell modes acquire a real frequency in the presence of static charged dust grains in a nonuniform magnetized dusty plasma. The frequency of the two-dimensional mode is induced by the plasma density gradient and corresponds to charge density waves arising out of the plasma non-neutrality. The dynamics of weakly interacting finite-frequency convective cell modes is governed by the generalized Navier–Stokes equation. The presence of the new term arising from the dust inhomogeneity in the latter provides the possibility of a two-dimensional dipolar vortex solution in dusty plasmas.

Matter wave interference effects in the macrodomain for charged particles in a magnetic field are reported for different scatterer positions between the electron gun and collector plate. The results obtained serve to validate and establish the important premises of the formalism that it is the scattering, (inter alia off the grid wires in this case) which generates the transition amplitude waves resulting in the novel quantum effects observed on the macro-scale associated with the transition amplitude wave. The variation of the position of origin of the grid-generated transition amplitude wave then leads to the variation of interference characteristics accordingly in the plate and grid currents. A Fourier decomposition of the interference peaks reveal also the presence of harmonics which are a manifestation of the Landau level structure. A rich class of quantum phenomena are thus discovered in the simple dynamical system of charged particles in a magnetic field in the ostensibly classical domain of operation, with the transition amplitude wave generated as a consequence of scattering being the new element of quantum description on the macro-scale.

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