Response of Unruh-DeWitt detector with time-dependent acceleration

It is well known that a detector, coupled linearly to a quantum field and accelerating through the inertial vacuum with a constant acceleration g, will behave as though it is immersed in a radiation field with temperature T = (g/2 pi). We study a generalization of this result for detectors moving with a time-dependent acceleration g(tau) along a given direction. After defining the rate of excitation of the detector appropriately, we evaluate this rate for time-dependent acceleration, g(tau), to linear order in the parameter eta = (g) over dot/g(2). In this case, we have three length scales in the problem: g(-1), ((g) over dot/g)(-1) and omega(-1) where omega is the energy difference between the two levels of the detector at which the spectrum is probed. We show that: (a) When omega(-1) << g(-1) ((g) over dot/g)(-1), the rate of transition of the detector corresponds to a slowly varying temperature T(tau) = g(tau)/2 pi, as one would have expected. (b) However, when g(-1) << omega(-1) << ((g) over dot/g)(-1), we find that the spectrum is modified even at the order O(eta). This is counter-intuitive because, in this case, the relevant frequency does not probe the rate of change of the acceleration since ((g) over dot/g) << omega and we certainly do not have deviation from the thermal spectrum when (g) over dot = 0. This result shows that there is a subtle discontinuity in the behavior of detectors with (g) over dot = 0 and (g) over dot/g(2) being arbitrarily small. We corroborate this result by evaluating the detector response for a particular trajectory which admits an analytic expression for the poles of the Wightman function. (C) 2010 Elsevier B.V. All rights reserved.