Quantum Phase Transitions in an Accelerated Medium

The usual Minkowski vacuum in an accelerated frame of reference is known to look like a “thermal bath” of particles. This effect is well known and called the Unruh effect, and is an analog of Hawking radiation in space with zero curvature. Thus, the Minkowski vacuum looks like a heated medium from the point of view of an accelerated observer, and the natural goal is to study the properties of such a medium in more detail. We show that if the Minkwoski vacuum is cooled, and we achieve a temperature below the Unruh temperature, then a phase transition occurs associated with the “fall beyond the horizon” of the lower Matsubara modes. This transition has many remarkable features, for example, for massless particles it is “polynomial,” and is also associated with the breaking of conformal symmetry.