Auxiliary matrix formalism for interaction representation transformations, optimal control, and spin relaxation...

Area of Science:

• Quantum mechanics
• Theoretical chemistry
• Computational physics

Background:

• Traditional methods for average Hamiltonian theory, relaxation, and quantum optimal control are computationally intensive.
• Calculating spin dynamics often involves complex theoretical frameworks that are difficult to implement numerically.
• Existing matrix factorization techniques can be inefficient for large Hamiltonian matrices.

Purpose of the Study:

• To derive simple and numerically efficient general expressions for key theoretical methods.
• To introduce the auxiliary matrix exponential method as a superior alternative for spin dynamics.
• To enhance the computational feasibility of complex quantum mechanical theories.

Main Methods:

• Application of the auxiliary matrix exponential method.
• Derivation of general expressions for average Hamiltonian theory, Bloch-Redfield-Wangsness theory, and quantum optimal control.
• Comparison with matrix factorization methods for spin dynamics.

Main Results:

• Simple and efficient general expressions were derived for historically cumbersome theoretical methods.
• The auxiliary matrix exponential method demonstrates superior efficiency compared to matrix factorization.
• Favorable complexity scaling with Hamiltonian matrix dimension was observed.

Conclusions:

• The auxiliary matrix exponential method provides a significant advancement in computational efficiency for spin dynamics.
• This method simplifies the application of advanced quantum mechanical theories.
• It offers a more scalable and robust approach for theoretical calculations in quantum systems.