Extended Weyl-Wigner phase-space framework for nonlinear systems: Typical and modified prey-predator-like dynamics.

The extension of the phase-space Weyl-Wigner quantum mechanics to the subset of Hamiltonians in the form of H(q,p)=K(p)+V(q) [with K(p) replacing single p^{2} contributions] is revisited. Deviations from classical and stationary profiles are identified in terms of Wigner functions and Wigner currents for Gaussian and gamma/Laplacian distribution ensembles. The procedure is successful in accounting for the exact pattern of quantum fluctuations when compared with the classical phase-space pattern.

Distorted stability pattern and chaotic features for quantized prey-predator-like dynamics.

Nonequilibrium and instability features of prey-predator-like systems associated to topological quantum domains emerging from a quantum phase-space description are investigated in the framework of the Weyl-Wigner quantum mechanics. Reporting about the generalized Wigner flow for one-dimensional Hamiltonian systems, H(x,k), constrained by ∂^{2}H/∂x∂k=0, the prey-predator dynamics driven by Lotka-Volterra (LV) equations is mapped onto the Heisenberg-Weyl noncommutative algebra, [x,k]=i, where the canonical variables x and k are related to the two-dimensional LV parameters, y=e^{-x} and z=e^{-k}. From the non-Liouvillian pattern driven by the associated Wigner currents, hyperbolic equilibrium and stability parameters for the prey-predator-like dynamics are then shown to be affected by quantum distortions over the classical background, in correspondence with nonstationarity and non-Liouvillianity properties quantified in terms of Wigner currents and Gaussian ensemble parameters.

Noncommutative phase-space Lotka-Volterra dynamics: The quantum analog.

The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics extended to one-dimensional Hamiltonian systems, H(x,k) constrained by the ∂^{2}H/∂x∂k=0 condition. Supported by the Heisenberg-Weyl noncommutative algebra, where [x,k]=i, the canonical variables x and k are interpreted in terms of the LV variables, y=e^{-x} and z=e^{-k}, eventually associated with the number of individuals in a closed competitive dynamics: the so-called prey-predator system. The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales and for quantifying quantum analog effects.

Using numerical methods from nonlocal optics to simulate the dynamics of N-body systems in alternative theories of gravity.

The generalized Schrödinger-Newton system of equations with both local and nonlocal nonlinearities is widely used to describe light propagating in nonlinear media under the paraxial approximation. However, its use is not limited to optical systems and can be found to describe a plethora of different physical phenomena, for example, dark matter or alternative theories for gravity. Thus, the numerical solvers developed for studying light propagating under this model can be adapted to address these other phenomena.