Coupling of non-crossing wave modes in a two-dimensional plasma crystal

We report an experimental observation of coupling of the transverse vertical and longitudinal in-plane dust-lattice wave modes in a two-dimensional complex plasma crystal in the absence of mode crossing. A new large diameter rf plasma chamber was used to suspend the plasma crystal. The observations are confirmed with molecular-dynamics simulations. The coupling manifests itself in traces of the transverse vertical mode appearing in the measured longitudinal spectra and vice versa. We calculate the expected ratio of the trace to the principal mode with a theoretical analysis of the modes in a crystal with finite temperature and find good agreement with the experiment and simulations.Comment: 4 figures, 5 pages, accepted for publication in PRL Nov 201

On separable Schr\"odinger equations

We classify (1+3)-dimensional Schr\"odinger equations for a particle interacting with the electromagnetic field that are solvable by the method of separation of variables. As a result, we get eleven classes of the electromagnetic vector potentials of the electromagnetic field $A(t, \vec x)=(A_0(t, \vec x)$, $\vec A(t, \vec x))$ providing separability of the corresponding Schr\"odinger equations. It is established, in particular, that the necessary condition for the Schr\"odinger equation to be separable is that the magnetic field must be independent of the spatial variables. Next, we prove that any Schr\"odinger equation admitting variable separation into second-order ordinary differential equations can be reduced to one of the eleven separable Schr\"odinger equations mentioned above and carry out variable separation in the latter. Furthermore, we apply the results obtained for separating variables in the Hamilton-Jacobi equation.Comment: 30 pages, LaTe

Observation of particle pairing in a two-dimensional plasma crystal

The observation is presented of naturally occurring pairing of particles and their cooperative drift in a two-dimensional plasma crystal. A single layer of plastic microspheres was suspended in the plasma sheath of a capacitively coupled rf discharge in argon at a low pressure of 1 Pa. The particle dynamics were studied by combining the top-view and side-view imaging of the suspension. Cross analysis of the particle trajectories allowed us to identify naturally occurring metastable pairs of particles. The lifetime of pairs was long enough for their reliable identification.Comment: 5 pages, 4 figure

Synchronization of particle motion in compressed two-dimensional plasma crystals

The collective motion of dust particles during the mode-coupling induced melting of a two-dimensional plasma crystal is explored in molecular dynamics simulations. The crystal is compressed horizontally by an anisotropic confinement. This compression leads to an asymmetric triggering of the mode-coupling instability which is accompanied by alternating chains of in-phase and anti-phase oscillating particles. A new order parameter is proposed to quantify the synchronization with respect to different directions of the crystal. Depending on the orientation of the confinement anisotropy, mode-coupling instability and synchronized motion are observed in one or two directions. Notably, the synchronization is found to be direction-dependent. The good agreement with experiments suggests that the confinement anisotropy can be used to explain the observed synchronization process.Comment: 6 pages, 4 figure

Channeling of particles and associated anomalous transport in a 2D complex plasma crystal

Implications of recently discovered effect of channeling of upstream extra particles for transport phenomena in a two-dimensional plasma crystal are discussed. Upstream particles levitated above the lattice layer and tended to move between the rows of lattice particles. An example of heat transport is considered, where upstream particles act as moving heat sources, which may lead to anomalous heat transport. The average channeling length observed was 15 - 20 interparticle distances. New features of the channeling process are also reported