Connecting the circular and drifted Rindler Unruh effects

In Minkowski spacetime quantum field theory, each stationary motion is associated with an effective, energy-dependent notion of temperature, which generalizes the familiar Unruh temperature of uniform linear acceleration. Motivated by current experimental interest in circular motion, we analyze the effective temperature for drifted Rindler motion, generated by a boost and a spacelike translation (drift), and the way in which drifted Rindler motion can be smoothly (and in fact real analytically) deformed to circular motion through a third type of motion known as parator. For an Unruh-DeWitt detector coupled linearly to a massless scalar field in <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mn>2</a:mn><a:mo>+</a:mo><a:mn>1</a:mn></a:math> and <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mn>3</c:mn><c:mo>+</c:mo><c:mn>1</c:mn></c:math> spacetime dimensions, we establish analytic results in the limits of large gap, small gap and large drift speed. For fixed proper acceleration, the drifted Rindler temperature remains bounded in the large gap limit, in contrast to the circular motion temperature, which can be arbitrarily large in this limit. Finally, in <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mn>2</e:mn><e:mo>+</e:mo><e:mn>1</e:mn></e:math> dimensions, we trace the vanishing of the circular motion temperature in the small gap limit to the weak decay of the Wightman function, and we show that, among all types of stationary motion in all dimensions, this phenomenon is unique to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mn>2</g:mn><g:mo>+</g:mo><g:mn>1</g:mn></g:math> dimensions and therein to circular and parator motion.