Método Crank-Nicolson (2 + 1) Para Busca de Soluções Para a Equação de Wheeler-DeWitt
Resumo
Neste trabalho fazemos o uso do método de diferenças finitas no esquema Crank-nicolson (2+1) para a quantização dos modelos de Friedmann–Robertson–Walker (FRW) com curvatura positiva (k = 1), campo escalar conformalmente acoplado à gravitação e um fluido de radiação. Tais modelos ainda não possuem soluções numéricas. Na abordagem criamos uma biblioteca modelo genérica para solução de problemas semelhantes.Referências
Alvarenga, F. G. and Fabris, J. C. (1995). Primordial cosmology with a contraction phase. Classical and Quantum Gravity, 12(8):L69.
Alvarenga, F. G. and Fabris, J. C. (1996). A primordial cosmological scenario and the horizon problem. General Relativity and Gravitation, 28(6):645–662.
DeWitt, B. S. (1967). Quantum Theory of Gravity. I. The Canonical Theory. Physical Review, 160(5):1113–1148. Publisher: American Physical Society.
Dodelson, S. and Schmidt, F. (2020). Modern Cosmology. Academic Press, London, United Kingdom ; San Diego, CA, 2nd ed. edição edition.
Halliwell, J. J. (2009). Introductory Lectures on Quantum Cosmology (1990). arXiv:0909.2566 [gr-qc].
Hestenes, M. R. and Stiefel, E. (1952). Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards, 49(6):2379.
Lemos, N. A. and Alvarenga, F. G. (1999). Wormholes, Classical Limit and Dynamical Vacuum in Quantum Cosmology. General Relativity and Gravitation, (31):1743.
Lemos, N. A., Monerat, G. A., Oliveira, H. P. d., Soares, I. D., and Tonini, E. V. (2003). Role of quantum cosmology in the chaotic dynamics of inflation. Phys. Rev. D, (68):083516.
Schutz, B. F. (1971). Hamiltonian Theory of a Relativistic Perfect Fluid. Phys. Rev. D, (4):3559.
van Dijk, W., Vanderwoerd, T., and Prins, S.-J. (2017). Numerical solutions of the timedependent Schrodinger equation in two dimensions. Physical Review E, 95(2):023310. arXiv:1701.08137 [physics].
Alvarenga, F. G. and Fabris, J. C. (1996). A primordial cosmological scenario and the horizon problem. General Relativity and Gravitation, 28(6):645–662.
DeWitt, B. S. (1967). Quantum Theory of Gravity. I. The Canonical Theory. Physical Review, 160(5):1113–1148. Publisher: American Physical Society.
Dodelson, S. and Schmidt, F. (2020). Modern Cosmology. Academic Press, London, United Kingdom ; San Diego, CA, 2nd ed. edição edition.
Halliwell, J. J. (2009). Introductory Lectures on Quantum Cosmology (1990). arXiv:0909.2566 [gr-qc].
Hestenes, M. R. and Stiefel, E. (1952). Methods of Conjugate Gradients for Solving Linear Systems. Journal of Research of the National Bureau of Standards, 49(6):2379.
Lemos, N. A. and Alvarenga, F. G. (1999). Wormholes, Classical Limit and Dynamical Vacuum in Quantum Cosmology. General Relativity and Gravitation, (31):1743.
Lemos, N. A., Monerat, G. A., Oliveira, H. P. d., Soares, I. D., and Tonini, E. V. (2003). Role of quantum cosmology in the chaotic dynamics of inflation. Phys. Rev. D, (68):083516.
Schutz, B. F. (1971). Hamiltonian Theory of a Relativistic Perfect Fluid. Phys. Rev. D, (4):3559.
van Dijk, W., Vanderwoerd, T., and Prins, S.-J. (2017). Numerical solutions of the timedependent Schrodinger equation in two dimensions. Physical Review E, 95(2):023310. arXiv:1701.08137 [physics].
Publicado
18/09/2023
Como Citar
BRUMATTO, Hamilton J.; MONERAT, Germano A..
Método Crank-Nicolson (2 + 1) Para Busca de Soluções Para a Equação de Wheeler-DeWitt. In: ESCOLA REGIONAL DE COMPUTAÇÃO BAHIA, ALAGOAS E SERGIPE (ERBASE), 23. , 2023, Ilhéus/BA.
Anais [...].
Porto Alegre: Sociedade Brasileira de Computação,
2023
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p. 108-113.
DOI: https://doi.org/10.5753/erbase.2023.236202.
