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A dissipation-preserving finite-difference scheme for a generalized Higgs boson equation in the de Sitter space–time

2020; Elsevier BV; Volume: 107; Linguagem: Inglês

10.1016/j.aml.2020.106425

1873-5452

Luis F. Muñoz-Pérez, Jorge E. Macías‐Díaz, J A Guerrero,

Quantum many-body systems

For the first time in the literature, a dissipation-preserving computational technique to approximate the solutions of a dissipative generalization of the Higgs boson equation in the de Sitter space–time is proposed. The model is a multidimensional system which considers a generalized potential and a general time-dependent diffusion coefficient. The system has an associated energy functional which is dissipated in time. Motivated by this fact, we propose a finite-difference methodology to approximate the solutions of the mathematical model. In addition to the numerical approximation for the solutions of the system, we propose also a discrete energy functional which is dissipated with respect to the discrete time. Using a computer implementation in two spatial dimensions, we provide some simulations that confirm the presence of bubble-like solutions, in agreement with the theory available in the literature.