Modulational instability of a Yukawa fluid excitation under the Quasi-localized charged approximation (QLCA) framework

Collective response of a strongly coupled system departs from that in continuum phase upon transition to the quasi-crystalline phase, or a Wigner lattice. The nonlinearity driven modulational instability, for example, of a quasi-crystalline dusty plasma lattice wave, is predicted to inevitably grow macroscopic envelope structures at the expense of a mesoscopic carrier wave. The modulational instability in the dimensionally extended quasi-crystalline or amorphous phase of a strongly coupled system, uniquely accessed by the quasi-localized charge approximation (QLCA) formulation, is shown to offer conditional stability over the entire range of spectral scales by prescribing a narrower instability regime. In distinction from the excitations of linear one-dimensional chain of strongly coupled dust grains, the longitudinal modes of a quasi-crystalline phase incorporated by means of a pair correlation function in the present QLCA based treatment shows the lattice excitations to be stable for arbitrarily long wavelengths beyond a finite value of screening parameter kappa = a/lambda (D) = 0.182 at low enough temperature, where a is the inter dust separation and lambda (D) is the plasma Debye length. However, this unstable domain of the parameter space does grow with increase in the dust temperature which invokes the weak coupling-like effect. The present results show that in comparison to the one-dimensional chains, the dimensionally extended strongly coupled lattice are potentially stable with respect to the macroscopic amplitude modulations. Results offer a greater handle over the macroscopic structures growing from the mesoscopic fluctuations, a mechanism which underlies a variety of processes, ranging from the barrier formation in strongly coupled turbulence to the highly localized modification, induced by collective excitation, of the ultracold ions trapped in strong electromagnetic fields. The existence of the growth rate of instability as well as the maximum modulational growth rate of instability has been investigated for a wide range of values of the screening parameter.