Statistical approach of modulational instability beyond Gaussian approximation

General approach to spatiotemporal modulational instability processes

Variational approach to the modulational instability.

We study the modulational stability of the nonlinear Schrödinger equation using a time-dependent variational approach. Within this framework, we derive ordinary differential equations (ODE's) for the time evolution of the amplitude and phase of modulational perturbations. Analyzing the ensuing ODE's, we rederive the classical modulational instability criterion. The case (relevant to application...

Modulational instability of spinor condensates

We demonstrate, analytically and numerically, that the ferromagnetic phase of the spinor Bose-Einstein condenstate may experience modulational instability of the ground state leading to a fragmentation of the spin domains. Together with other nonlinear effects in the atomic optics of ultra-cold gases (such as coherent photoassociation and four-wave mixing) this effect provides one more analogy ...

Rough Interfaces Beyond the Gaussian Approximation

We compare predictions of the Capillary Wave Model beyond its Gaussian approximation with Monte Carlo results for the energy gap and the surface energy of the 3D Ising model in the scaling region. Our study reveals that the finite size effects of these quantities are well described by the Capillary Wave Model, expanded to two–loop order (one order beyond the Gaussian approximation).

Quantum dynamics beyond the Gaussian approximation.

The time dependent quantum variational principle is emerging as an important means of studying quantum dynamics, particularly in early universe scenarios. To date all investigations have worked within a Gaussian framework. Here we present an improved method which is demonstrated to be superior to the Gaussian approach and may be naturally extended to the eld{theoretic case.