C T symmetry in nonlinear time-dependent electronic structure theories

Area of Science:

• Quantum Mechanics
• Computational Chemistry
• Theoretical Physics

Background:

• Nonlinear time-dependent (NLTD) electronic structure theories often yield unstable "complex excitation energy" solutions.
• These instabilities limit the applicability of methods like time-dependent Hartree-Fock and density functional theory.
• The underlying cause of these instabilities in NLTD response theories was not fully understood.

Purpose of the Study:

• To identify the fundamental cause of instabilities in NLTD electronic structure theories.
• To develop a theoretical framework for stable and physically meaningful NLTD response calculations.
• To demonstrate how to recover stable, oscillatory solutions in NLTD theories.

Main Methods:

• Analysis of CT (charge-conjugation/time-reversal) symmetry in NLTD response theories.
• Formulation of a non-Hermitian quantum mechanics framework extended to a Krein space.
• Investigation of analytic continuation from Hilbert to Krein space for effective Hamiltonians.

Main Results:

• CT symmetry breaking is identified as the source of exponential instabilities in NLTD theories.
• Extending the Hilbert space to a Krein space allows for a well-defined, stable response theory.
• Stable solutions exhibit double "generalized Kramers" degeneracy, interpretable as particle-antiparticle pairs.
• CT symmetry guarantees real observables and oscillatory time-evolution in the stable theory.

Conclusions:

• CT symmetry is crucial for the stability and physical interpretability of NLTD electronic structure calculations.
• The Krein space formulation provides a robust theoretical foundation for NLTD response theories.
• This work resolves long-standing issues with instabilities in computational electronic structure methods.