Perumusan Hamiltonian Hidrodinamika Kuantum Nonrelativistik

Andika Kusuma Wijaya, Sumarli Sumarli

Abstract


Penelitian ini bertujuan untuk merumuskan Hamiltonian hidrodinamika kuantum nonrelativistik yang tidak terkopling medan elektromagnetik dalam ruang fase kovarian dan kerangka geometri simplektik yang dibatasi dalam permukaan Cauchy . Metode dalam penelitian ini merupakan kajian teoritik matematik untuk mencari struktur pre-simplektik dan Hamiltonian Persamaan Madelung nonrelativistic. Hasil yang diperoleh yaitu simplektik forma-satu, simplektik forma-2 dan Hamiltonian hidrodinamika kuantum nonrelativistik yang identik  dengan yang diungkapkan oleh Spera (2016).

Kata Kunci:

Teori Medan Geometrik; Hamiltonian; Persamaan Madelung; Struktur Pre-Simplektik


The Hamiltonian Formulation of Nonrelativistic Quantum Hydrodynamics

ABSTRACT

This study aimed to formulate the Hamiltonian of nonrelativistic quantum hydrodynamics that is not coupled to electromagnetic fields in the covariant phase space and in the framework of symplectic geometry bounded in the Cauchy surface  The method in this research was a mathematical theoretical study to find the pre-symplectic structure and Hamiltonian of the nonrelativistic Madelung Equation. The results obtained were forma-one symplectic, forma-2 symplectic, and Hamiltonian of nonrelativistic quantum hydrodynamics which are identical to those revealed by Spera (2016).

Keywords


Geometric Field Theory; Hamiltonian; Madelung Equation; Pre-Simplectic Structure

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References


Crnkovic, C. (1988). Symplectic geometry of the convariant phase space. Classical and Quantum Gravity, 5(12), 1557.

Crnkovic, C., & Witten, E. (1987). Covariant description of canonical formalism in geometrical theories. Three hundred years of gravitation, 676-684.

Delphenich, D. H. (2013). A strain tensor that couples to the Madelung stress tensor. arXiv preprint arXiv:1303.3582.

Forger, M., & Romero, S. V. (2005). Covariant Poisson brackets in geometric field theory. Communications in Mathematical Physics, 256, 375-410.

Greiner, W. (2000). Relativistic quantum mechanics (Vol. 2). springer, Berlin.

Kalinowski, M. W., & Piechocki, W. (1996). Symplectic structure for field theory. ACTA PHYSICA POLONICA SERIES B, 27, 2735-2740.

Kalinowski, M. W., & Piechocki, W. (1999). Geometric Quantization Of Field Theory On Curved Space–Time. International Journal of Modern Physics A, 14(07), 1087-1110.

Nonnenmacher, T. F. (2005, July). Hamiltonian models for the Madelung fluid and generalized Langevin equations. In Stochastic Processes in Classical and Quantum Systems: Proceedings of the 1st Ascona-Como International Conference, Held in Ascona, Ticino (Switzerland), June 24–29, 1985 (pp. 470-480). Berlin, Heidelberg: Springer Berlin Heidelberg.

Sonego, S. (1991). Interpretation of the hydrodynamical formalism of quantum mechanics. Foundations of physics, 21(10), 1135-1181.

Spera, M. (2016). Moment map and gauge geometric aspects of the Schrödinger and Pauli equations. International Journal of Geometric Methods in Modern Physics, 13(04), 1630004.

Takabayasi, T. (1953). Remarks on the formulation of quantum mechanics with classical pictures and on relations between linear scalar fields and hydrodynamical fields. Progress of Theoretical Physics, 9(3), 187-222.

Von Renesse, M. K. (2012). An optimal transport view of Schrödinger's equation. Canadian mathematical bulletin, 55(4), 858-869.

Wijaya, A. K., Hermanto, A., & Rosyid, M. F. (2022). The symplectic geometrical formulation of quantum hydrodynamics. International Journal of Geometric Methods in Modern Physics, 19(12), 2250194-2285.

Woodhouse, N. M. J. (1992). Geometric quantization. Oxford university press.

Wyatt, R. E. (2005). Quantum dynamics with trajectories: introduction to quantum hydrodynamics (Vol. 28). Springer Science & Business Media.




DOI: http://dx.doi.org/10.26737/var.v6i2.4792

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