Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics

Non-Hermitian quantum-Hamiltonian-candidate combination <inline-formula> <math display="inline"> <semantics> <msub> <mi>H</mi> <mi>&#955;</mi> </msub> </semantics> </math> </inline-formula> of a non-Hermitian unperturbed operator <inline-formula> <math display="inline"> <semantics> <mrow> <mi>H</mi> <mo>=</mo> <msub> <mi>H</mi> <mn>0</mn> </msub> </mrow> </semantics> </math> </inline-formula> with an arbitrary &#8220;small&#8221; non-Hermitian perturbation <inline-formula> <math display="inline"> <semantics> <mrow> <mi>&#955;</mi> <mi>W</mi> </mrow> </semantics> </math> </inline-formula> is given a mathematically consistent unitary-evolution interpretation. The formalism generalizes the conventional constructive Rayleigh&#8722;Schr&#246;dinger perturbation expansion technique. It is sufficiently general to take into account the well known formal ambiguity of reconstruction of the correct physical Hilbert space of states. The possibility of removal of the ambiguity via a complete, irreducible set of observables is also discussed.