One-dimensional point interaction with three complex parameters

For a pair of non-Hermitian Hamiltonian H and its Hermitian adjoint H(dagger), there are situations in which their eigenfunctions form a biorthogonal system. We illustrate such a situation by means of a one-particle system with a one-dimensional point interaction in the form of the Fermi pseudo-potential. The interaction consists of three terms with three strength parameters g(i) (i = 1, 2 and 3), which are all complex. This complex point interaction is neither Hermitian nor PT-invariant in general. The S-matrix for the transmission reflection problem constructed with H (or with H(dagger)) in the usual manner is not unitary, but it conforms to the pseudo-unitarity that we define. The pseudounitarity is closely related to the biorthogonality of the eigenfunctions. The eigenvalue spectrum of H with the complex interaction is generally complex but there are cases where the spectrum is real. In such a case H and H(dagger) form a pseudo-Hermitian pair.

Myofascial trigger point: A possible way of modulating tinnitus

In order to investigate whether myofascial trigger points can modulate tinnitus, as well as the association between tinnitus and myofascial trigger points, 94 individuals with and 94 without tinnitus, matched by age and gender, were analyzed by means of bilateral digital pressure of 9 muscles. Temporary modulation of tinnitus was frequently observed (55.9%) during digital pressure, mainly in the masseter. The rate of tinnitus modulation was significantly higher on the same side of the myofascial trigger point subject to examination in 6 out of 9 muscles. An association between tinnitus and the presence of myofascial trigger points was observed (p < 0.001), as well as a laterality association between the ear with the worst tinnitus and the side of the body with more myofascial trigger points (p < 0.001). Thus, this relationship could be explained not only by somatosensory-auditory system interactions but also by the influence of the sympathetic system. Copyright (c) 2007 S. Karger AG, Basel.