Physical significance of dynamical invariants in non-Hermitian Kondo driving

Determine the physical significance of the time-independent radius and center of the circles traced by the integrability-preserving time-dependent coupling strength in the non-Hermitian Kondo model.

Background

For the time-dependent non-Hermitian Kondo model, integrability permits inverse coupling strengths of the form 1/J(t)=at+b with complex a and b. When the imaginary part of 1/J(t) varies in time, the coupling J(t) traces a circle in the complex-coupling plane whose center and radius remain invariant. These quantities therefore provide dynamical invariants distinct from the RG invariant of the static model.

The paper identifies these invariants but does not determine their physical interpretation or role in the dynamics. Establishing their significance could clarify whether they control observable properties, phase evolution, or other features of the driven non-Hermitian system.

References

Hence we have identified new dynamical invariants in the time-dependent model, although their physical significance is not yet explored.

— Beyond Integrability Preserving Renormalization-Group Protocol in Non-Hermitian Hamiltonians with Time-Dependent Interaction Strengths  (2608.19519 - Pasnoori, 20 Aug 2026) in Paragraph “RG protocol and beyond”