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European Journal of Theoretical and Applied Sciences

Fluid Mechanics, and Its Quantum Developments and Applications

Yi-Fang Chang

Published Sep 1, 2024• 1 citation
Publisher

Abstract

Based on the known theories of fluid mechanics, we research the new quantum fluid mechanics by operator method. Further, we discuss its various developments combined the extensive quantum theory and other theories. Finally, we search possible applications in some aspects: in biology many systems are fluids; in astronomy binary stars, the density wave theory and evolutionary direction on spiral galaxies, and sunspot are researched; in geosciences earthquake, formation of basin and hydrocarbon layer are proposed; in social sciences the social hydrodynamics and corresponding waves and tides, the social synergetics, corruption, etc., are discussed.

DOI
10.59324/ejtas.2024.2(5).60

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This book covers the entire span of quantum mechanics whose developments have taken place during the early part of the twentieth century up till the present day. We start with the Rutherford-Bohr model of the atom followed by Schrodinger's wave mechanics with its application to the solution of calculating the energy spectrum of a particle in a box, the harmonic oscillator and finally the hydrogen atom. Heisenberg's matrix mechanics and its duality with Schrodinger's wave mechanics, quantum mechanics in the interaction picture. Dirac's relativistic theory of the electron exhibiting the spin of the electron as a relativistic effect when it interacts with an external electromagnetic field. Feynman's path integral approach to non-relativistic quantum mechanics with is a marvellous intuitive interpretation as a sum over paths and how classical mechanics is obtained from its limit as Planck' constant tends to zero, methods for computing the spectra of the Dirac Hamiltonian in a radial potential, quantum field theory as developed by Feynman, Schwinger, Tomonaga and Dyson for describing the interaction between electrons, positrons, and photons via propagators using both the operator theoretic expansions and Feynman's path integral. We also introduce time independent and time dependent perturbation theory in quantum mechanics with applications to quantum gate design for quantum computers forming a major part of the research conducted by the author's research group, Quantum noise introduced into the Schrodinger and Dirac's equation based on the Hudson-Parthasarathy quantum stochastic calculus in Boson Fock space, scattering theory and wave operators with applications to quantum gate design, some aspects of second quantization like the interpretation of Boson Fock space in terms of harmonic oscillator algebras and the BCS theory of superconductivity, Wigner-Mackey-Frobenius theory of induced representations of a group with applications to Wigner's theory of particle classification, Dirac's equation in a gravitational field and Yang-Mills non-Abelian gauge theories with application to the construction of unified quantum field theories and finally, the more recent theory of super-symmetry which is a Boson-Fermion unification theory. We have discussed the statistics of Boson's, Fermions and Maxwell-Boltzmann based on entropy maximization. The book is written in problem-solution format and it would be of use to physicists and engineers interested respectively in developing unified field theories and in the design of quantum gates. Note: T&F does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka.
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Recent research has developed the Ising model from physics, especially statistical mechanics, and it plays an important role in quantum computing, especially quantum annealing and quantum Monte Carlo methods. The model has also been used in opinion dynamics as a powerful tool for simulating social interactions and opinion formation processes. Individual opinions and preferences correspond to spin states, and social pressure and communication dynamics are modeled through interactions between spins. Quantum computing makes it possible to efficiently simulate these interactions and analyze more complex social networks.Recent research has incorporated concepts from quantum information theory such as Graph State, Stabilizer State, and Surface Code (or Toric Code) into models of opinion dynamics. The incorporation of these concepts allows for a more detailed analysis of the process of opinion formation and the dynamics of social networks. The concepts lie at the intersection of graph theory and quantum theory, and the use of Graph State in opinion dynamics can represent the interdependence of opinions and networks of influence among individuals. It helps to represent the local stability of opinions and the mechanisms for correcting misunderstandings within a social network. It allows us to understand how individual opinions are subject to social pressures and cultural influences and how they change over time.Incorporating these quantum theory concepts into opinion dynamics allows for a deeper understanding of social interactions and opinion formation processes. Moreover, these concepts can provide new insights not only in the social sciences, but also in fields as diverse as political science, economics, marketing, and urban planning.