Comparison of quantum and classical relaxation in spin dynamics

Area of Science:

• Quantum Mechanics
• Classical Mechanics
• Spin Dynamics

Background:

• The Landau-Lifshitz equation models classical spin dynamics.
• Quantum mechanics describes spin using operators and wave functions.
• Investigating the connection between classical and quantum descriptions of spin is crucial.

Purpose of the Study:

• To derive the classical Landau-Lifshitz equation from quantum mechanics.
• To compare classical spin trajectories with quantum mechanical expectation values.
• To identify conditions under which classical and quantum spin descriptions agree or disagree.

Main Methods:

• Derivation of the Landau-Lifshitz equation from a non-Hermitian Hamilton operator.
• Time evolution of a quantum mechanical wave function.
• Comparison of classical spin (S) trajectories with the expectation value of the spin operator (Ŝ).

Main Results:

• The classical Landau-Lifshitz equation with damping can be derived from quantum mechanics.
• Good agreement is observed between classical and quantum spin trajectories for linear Hamiltonians.
• Disagreement arises for quadratic or higher-order terms in the Hamiltonian.

Conclusions:

• The classical Landau-Lifshitz equation is a valid approximation for certain quantum spin systems.
• Hamiltonian complexity influences the accuracy of the classical description.
• Quantum effects become significant for non-linear spin interactions.