Dynamic Symmetries and Quantum Nonadiabatic Transitions

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.

9 pages, 2 figures; Special V. Chernyak Festschrift Issue, Chemical Physics

References in corpus (8)

• Solvable 4-state Landau-Zener model of two interacting qubits with path interference
• Landau-Zener sweeps and sudden quenches in coupled Bose-Hubbard chains
• Quantum integrability in the multistate Landau-Zener problem
• Exact transition probabilities in a six-state Landau-Zener system with path interference
• Dynamics of the (spin-) Hall effect in topological insulators and graphene
• Incoherent Landau-Zener-Stuckelberg Transitions in Single-Molecule Magnets
• Time-dependent two-level models and zero-area pulses
• Quantum quench dynamics and population inversion in bilayer graphene

Cited by in corpus (6)

• Constraints on scattering amplitudes in multistate Landau-Zener theory
• Multistate Landau-Zener models with all levels crossing at one point
• Nonadiabatic transitions in Landau-Zener grids: integrability and semiclassical theory
• Dynamic spin localization and gamma-magnets
• Integrable multistate Landau-Zener models with parallel energy levels
• SU(3) Landau-Zener interferometry with a transverse periodic drive