Theory of Response to Perturbations in NonHermitian Systems Using FiveHilbertSpace Reformulation of Unitary Quantum Mechanics NonHermitian quantumHamiltoniancandidate combination     H xcexbb     of a nonHermitian unperturbed operator     H   H 0      with an arbitrary xe2x80x9csmallxe2x80x9d nonHermitian perturbation     xcexbb W     is given a mathematically consistent unitaryevolution interpretation. The formalism generalizes the conventional constructive Rayleighxe2x80x93Schrodinger 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.

Adapting Logic to Physics: The QuantumLike Eigenlogic Program Considering links between logic and physics is important because of the fast development of quantum information technologies in our everyday life. This paper discusses a new method in logic inspired from quantum theory using operators, named Eigenlogic. It expresses logical propositions using linear algebra. Logical functions are represented by operators and logical truth tables correspond to the eigenvalue structure. It extends the possibilities of classical logic by changing the semantics from the Boolean binary alphabet 0,1 using projection operators to the binary alphabet 1,1 employing reversible involution operators. Also, manyvalued logical operators are synthesized for whatever alphabet is using operator methods based on Lagrange interpolation and on the Cayleyxe2x80x93Hamilton theorem. Considering a superposition of logical input states one gets a fuzzy logic representation where the fuzzy membership function is the quantum probability given by the Born rule. Historical parallels from Boole, Post, Poincare and Combinatory Logic are presented in relation to probability theory, noncommutative quaternion algebra and Turing machines. An extension to first order logic is proposed inspired by Groverxe2x80x99s algorithm. Eigenlogic is essentially a logic of operators and its truthtable logical semantics is provided by the eigenvalue structure which is shown to be related to the universality of logical quantum gates, a fundamental role being played by noncommutativity and entanglement.