Dynamic Symmetries and Quantum Nonadiabatic Transitions

TL;DR

This paper generalizes the Kramers degeneracy theorem to time-dependent spin systems, showing that certain symmetries prevent transitions between states, with implications for multistate Landau-Zener theory.

Contribution

It extends the Kramers degeneracy concept to explicitly time-dependent Hamiltonians, establishing conditions under which transition amplitudes vanish.

Findings

Time-reversal symmetry leads to zero scattering amplitude between states in certain spin systems.

The result applies to systems with half-integer total spin and symmetric Hamiltonians.

Implications for multistate Landau-Zener transitions are discussed.

Abstract

Kramers degeneracy theorem is one of the basic results in quantum mechanics. According to it, the time-reversal symmetry makes each energy level of a half-integer spin system at least doubly degenerate, meaning the absence of transitions or scatterings between degenerate states if the Hamiltonian does not depend on time explicitly. We generalize this result to the case of explicitly time-dependent spin Hamiltonians. We prove that for a spin system with the total spin being a half integer, if its Hamiltonian and the evolution time interval are symmetric under a specifically defined time reversal operation, the scattering amplitude between an arbitrary initial state and its time reversed counterpart is exactly zero. We also discuss applications of this result to the multistate Landau-Zener (LZ) theory.