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Lattice Boltzmann equation for relativistic quantum mechanics
1Instituto Applicazioni Calcolo, IAC-CNR, Rome, Italy.
Summary
This study introduces relativistic quantum lattice Boltzmann equations, replacing the standard collision operator with dynamic fields for nonlinear interactions. This approach enables a multicomponent complex lattice Boltzmann equation for relativistic wave functions.
Area of Science:
- Quantum physics
- Computational fluid dynamics
- Relativistic mechanics
Background:
- The quantum lattice Boltzmann equation (QLBE) is a powerful tool for simulating quantum systems.
- Standard QLBE formulations often struggle to incorporate nonlinear interactions and relativistic effects accurately.
Purpose of the Study:
- To develop a relativistic version of the QLBE capable of handling nonlinear interactions.
- To explore the theoretical framework for describing relativistic quantum phenomena using lattice Boltzmann methods.
Main Methods:
- Discussion of relativistic formulations of the QLBE.
- Theoretical analysis of nonlinear interaction inclusion.
- Development of a multicomponent complex lattice Boltzmann equation.
Main Results:
- Demonstration that nonlinear interactions necessitate replacing the standard collision operator.
- Introduction of a pair of dynamic fields that couple to the relativistic wave function.
- The proposed framework is described by a multicomponent complex lattice Boltzmann equation.
Conclusions:
- The developed multicomponent complex lattice Boltzmann equation provides a novel approach for relativistic quantum simulations.
- This work extends the applicability of lattice Boltzmann methods to complex relativistic quantum systems with nonlinear dynamics.
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