The Lee model was introduced in the 1950s as an elementary quantum field theory in which mass, wave function, and charge renormalization could be carried out exactly. In early studies of this model it was found that there is a critical value of g 2 , the square of the renormalized coupling constant, above which g 2 0 , the square of the unrenormalized coupling constant, is negative. Thus, for g 2 larger than this critical value, the Hamiltonian of the Lee model becomes non-Hermitian. It was also discovered that in this non-Hermitian regime a new state appears whose norm is negative. This state is called a ghost state. It has always been assumed that in this ghost regime the Lee model is an unacceptable quantum theory because unitarity appears to be violated. However, in this regime while the Hamiltonian is not Hermitian, it does possess PT symmetry. It has recently been discovered that a non-Hermitian Hamiltonian having PT symmetry may define a quantum theory that is unitary. The proof of unitarity requires the construction of a new time-independent operator called C. In terms of C one can define a new inner product with respect to which the norms of the states in the Hilbert space are positive. Furthermore, it has been shown that time evolution in such a theory is unitary. In this paper the C operator for the Lee model in the ghost regime is constructed in the V /N θ sector. It is then shown that the ghost state has a positive norm and that the Lee model is an acceptable unitary quantum field theory for all values of g 2 .

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It has been found that complex non-Hermitian quantum-mechanical Hamiltonians may have entirely real spectra and generate unitary time evolution if they possess an unbroken PT symmetry. A well-studied class of such Hamiltonians is H = p 2 + x 2 (ix) ǫ (ǫ ≥ 0). This paper examines the underlying classical theory. Specifically, it explores the possible trajectories of a classical particle that is governed by this class of Hamiltonians. These trajectories exhibit an extraordinarily rich and elaborate structure that depends sensitively on the value of the parameter ǫ and on the initial conditions. A system for classifying complex orbits is presented.

Titrations were carried out between solutions of a strong poly-acid (polyvinylsulfate, potassium salt) and a strong poly-base (polydiallyldimethylammonium chloride) over a range of salt concentrations. Streaming current analysis of the titration endpoints appeared to show increasing deviations from 1:1 stoichiometry of complexation with increased salt. The results depended on the direction of the titration, such that a stoichiometric excess of the titrant (second additive) was required to achieve a streaming current reading of zero. These symmetrical results, depending on the order of addition, were obtained despite the fact that the plastic surfaces of the streaming current device had a slight negative charge and differing adsorption tendencies for the two kinds of polymer. A qualitative model of molecular events, based on non-equilibrium entrapment of non-complexed polymer segments was found to be inconsistent with results of tests carried out over a range of initial polymer concentration. Results were better described by a qualitative model involving formation of polyelectrolyte complexes (PECs) in solution, in which nearstoichiometric core complexes are stabilized by an excess of the second additive on their surface. Implications of the latter model were compared with the results of turbidimetric tests, aqueous contact angles on polymer-treated plastic surfaces, and microelectrophoresis of PECs. Results of this study have consequences for interpretation of polyelectrolyte titrations, as well as for industrial operations that involve the mixing of oppositely charged polyelectrolytes.