On the sensitivity of gravitational wave resonant bar detectors

Different theoretical estimates of the sensitivity of gravitational wave resonant bar-detectors, which have been published in the last decades, are reviewed and discussed. The "classical" cross-section estimate is obtained considering the bar as a classical or quantum oscillator, whose initial thermal state is that of a single oscillator driven by a single external stochastic force. Other theoretical studies computed a much larger cross-section, using a variety of quantum-mechanical arguments. The review of the existing literature shows that there is no well established model for the response of a resonant detector to gravitational waves. The resonant, yet random, nature of the Brownian thermal motion may justify considering the bar response at the fundamental longitudinal eigenfrequency as that of a large number of effective quantum mechanical oscillators. Assuming this hypothesis, quantum coherence effects, as first suggested by Weber, lead to a much larger cross-section than that "classically" predicted. The reduction of this amplification due to thermal noise itself is also computed.