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Response of Unruh-DeWitt detector with time-dependent acceleration · Around

2009

Response of Unruh-DeWitt detector with time-dependent acceleration

Kothawala, Dawood, Padmanabhan, T.

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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 $\eta = \dot g / g^2$.
In this case, we have three length scales in the problem: $g^{-1}, (\dot g/g)^{-1}$ and $\omega^{-1}$ where $\omega$ is the energy difference between the two levels of the detector at which the spectrum is probed.

Built on

W. G. Unruh, Phys. Rev
1976
Earlier work this paper cites.
J. R. Letaw, J. D. Pfautsch, Phys. Rev
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Bryce DeWitt, The Global Approach to Quantum Field Theory
1982
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T. Padmanabhan , Astrophys. Sp. Sc
1982
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W. G. Unruh and R. M. Wald, Phys. Rev
1985
Earlier work this paper cites.

Similar

T. Padmanabhan, T. P. Singh, Class. Quan. Grav
1987
Cited alongside, same era.
L. Sriramkumar, T. Padmanabhan, Class. Quant. Grav
1996
Cited alongside, same era.
L. Sriramkumar, T. Padmanabhan, Int. Jour. Mod. Phys
2002
Cited alongside, same era.
T. Padmanabhan, [arXiv:0910.0839]; [arXiv:0903.1254]; Gen.Rel.Grav
Original
2002
Cited alongside, same era.
Incidentally, this can also be seen directly in the Euclidean sector, in which the hyperbolic trajectory of the uniformly accelerated detector maps to a circle of constant radius g 0 − 1 g_{0}^{-1} . Now, G + G^{+} for any two points on the circle depends on the chordal distance between the points, and it follows from trivial geometry that this chordal distance can be completely expressed in terms of sin ⁡ ( Δ θ ) \sin(\Delta\theta) where Δ θ \Delta\theta is the angular separation between the points. Analytically continuing back, we see that G + G^{+} depends only on u = i Δ θ u=i\Delta\theta
Cited in the paper.
J. Russo, P. Townsend, [arXiv:0904.4628]
Original
Cited in the paper.

Then

T. Padmanabhan, Phys. Reports
2005
Later among the works it cites.
N. Obadia, M. Milgrom, Phys. Rev. D
Original
2007
Later among the works it cites.
L. C. B. Crispino, A. Higuchi, G. E. A. Matsas, Rev. Mod. Phys
2008
Later among the works it cites.
J. Louko, A. Satz, Class. Quant. Grav
Original
2008
Later among the works it cites.

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