Theory of Response to Perturbations in Non-Hermitian Systems Using Five-Hilbert-Space Reformulation of Unitary Quantum Mechanics
Miloslav Znojil
Abstract
Non-Hermitian quantum-Hamiltonian-candidate combination H λ of a non-Hermitian unperturbed operator H = H 0 with an arbitrary "small" non-Hermitian perturbation λ W is given a mathematically consistent unitary-evolution interpretation. The formalism generalizes the conventional constructive Rayleigh-Schrödinger 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.
Topics & Concepts
ObservableHilbert spaceUnitary stateFormalism (music)AmbiguityMathematicsPhysicsPerturbation (astronomy)ConstructiveOperator (biology)QuantumMathematical physicsQuantum mechanicsClassical mechanicsPhysical systemTheoretical physicsPerturbation theory (quantum mechanics)Quantum systemQuantum stateHarmonic oscillatorMathematical formulation of quantum mechanicsQuantum processInvariant (physics)ComputationEntropy (arrow of time)Quantum Mechanics and Non-Hermitian PhysicsSpectral Theory in Mathematical PhysicsQuantum and Classical Electrodynamics