| This thesis deals with three topics, all of which are related to the generation or detection of gravitational waves:; I. The standard quantum limit (SQL) for LIGO and quantum non-demolition (QND) measurements, which allow one to overcome the SQL. Two particular QND measurement schemes are considered: (i) a Speed Meter; and (ii) the Braginsky-Khalili nonlinear meter (BK-meter). Our analysis shows that (a) Using the Speed Meter one can perform naturally a broad-band QND measurement of a force acting on the test mass. (b) The BK-meter can provide a natural way to perform a narrow-band QND measurement of a force acting on the mirrors of the optical cavity.; While neither of these QND measurement schemes can be immediately implemented for LIGO, they might provide conceptual steps towards the design of a practical QND interferometer.; II. Mechanical thermal noise in LIGO. We develop a new method of calculating thermal noise in mechanical systems, which is based on a direct application of the Fluctuation-Dissipation theorem. This method is capable of handling mechanical systems with inhomogeneous dissipation.; We apply our direct method to an internal thermal noise in LIGO test masses. We find that: (a) The test-mass surface defects will make a larger contribution to thermal noise than was previously inferred. (b) Our direct method is more precise and computationally less expensive for small beam sizes than the previous mode-sum method.; We also apply our direct method of analysis to suspension thermal noise in LIGO. We find that by positioning the laser beam spot on the mirror face and by monitoring the motion of the suspension wires, it may be possible to reduce the suspension thermal noise by a factor 100.; III. R-modes in neutron stars (NS) in low-mass x-ray binaries (LMXBs). We study the suggestion that the accretion of gas onto a neutron star in an LMXB triggers an instability in which the star's r-modes are amplified by gravitational-wave emission. We find that if this is the case, then the subsequent neutron-star evolution depends critically on whether the neutron-star viscosity decreases with temperature, or is temperature-independent.; In the former case, the Neutron Star goes through runaway cycles of rapid (1 month) heating—rapid (1 month) spindown—slow (105 years) cooling—slow (106 years) spin-up.; In the latter (temperature-independent) case, the Neutron Star probably settles down into an equilibrium state with constant spin rate and temperature, and becomes a steady emitter of gravitational waves.; All of the chapters in this thesis, except the introductory chapter I, have been published or are in press. (Abstract shortened by UMI.)... |
