How Chaotic is the Stadium Billiard? A Semiclassical Analysis

The impression gained from the literature published to date is that the spectrum of the stadium billiard can be adequately described, semiclassically, by the Gutzwiller periodic orbit trace formula together with a modified treatment of the marginally stable family of bouncing ball orbits. I show that this belief is erroneous. The Gutzwiller trace formula is not applicable for the phase space dynamics near the bouncing ball orbits. Unstable periodic orbits close to the marginally stable family in phase space cannot be treated as isolated stationary phase points when approximating the trace of the Green function. Semiclassical contributions to the trace show an $\hbar$ - dependent transition from hard chaos to integrable behavior for trajectories approaching the bouncing ball orbits. A whole region in phase space surrounding the marginal stable family acts, semiclassically, like a stable island with boundaries being explicitly $\hbar$-dependent. The localized bouncing ball states found in the billiard derive from this semiclassically stable island. The bouncing ball orbits themselves, however, do not contribute to individual eigenvalues in the spectrum. An EBK-like quantization of the regular bouncing ball eigenstates in the stadium can be derived. The stadium billiard is thus an ideal model for studying the influence of almost regular dynamics near marginally stable boundaries on quantum mechanics.Comment: 27 pages, 6 figures, submitted to J. Phys.

A survey of equine abortion and perinatal foal losses in Hungary during a three-year period (1998-2000)

Cases of equine abortion and perinatal foal losses were investigated in Hungary during a three-year period (1998-2000). Samples from aborted equine fetuses and newborn foals (total n = 96) were examined using bacteriological, virological, pathological, immunohistochemical (IHC), molecular biological and serological methods. The cause of abortion and perinatal foal loss was identified in 67/96 cases (70%); viral infection was found in 22 (23%), viral and bacterial coinfection in 1 (1%), bacterial infection in 23 (24%), protozoan infection in 1 (1%) and fungal infection in 2 cases (2%). Morphological lesions suggestive of infection were recorded in 2 (2%) and non-infectious causes in 16 cases (17%)

Study of the role of chlamydia, mycoplasma, ureaplasma and other microaerophilic and aerobic bacteria in uterine infections of mares with reproductive disorders

In six healthy mares and 24 mares showing reproductive disorders swab samples were taken from the fossa clitoridis to isolate Taylorella equigenitalis, and from the uterus to isolate mycoplasmas, ureaplasmas and other aerobic bacteria. Swab samples were also taken from the uterus for Chlamydiaantigen ELISA and ChlamydiaPCR studies. The uterus of 27 mares was examined cytologically, and biopsy samples were taken from the endometrium for histological examinations and for immunohistochemical examinations aimed at the detection of chlamydiae. T. equigenitalis, mycoplasmas, ureaplasmas and chlamydiae could not be detected from any of the mares examined. Aerobic facultative pathogenic bacteria were isolated from mares with endometritis in four cases. In 18 out of 22 mares with endometritis (82%) no infective agents could be demonstrated. Further studies are needed to elucidate the relative importance of non-infectious causes of endometritis and of anaerobic bacteria often detectable in the uterus in the aetiology of the reproductive disorders observed