Moving away from equilibrium

Abstract: The seminar takes up on several aspects related to the Unruh effect. In a nutshell, a mathematically rigorous treatment of the Unruh effect by de Biévre and Merkli has shown that a quantum mechanical, finite-energy level "detector" system which moves with constant acceleration with respect to an inertial system, and is locally coupled to a quantum field in the inertial vacuum state, will asymptotically for large times approximate a Gibbs (thermal equilibrium) state. In a new work with A.G. Passegger, we show that the behaviour of such a detector system is quite different if it moves with constant velocity with respect to an inertial system in which a quantum field is in a KMS state, and to which the detector is locally coupled. Concretely, combining previous results known in the literature, we show that for any quantum field theory in Minkowski spacetime, two primary states KMS states with respect to different inertial frames are disjoint (belong to inequivalent folia of states) if they fulfill a suitable clustering condition. The quantized free scalar field is an example where the conditions are fulfilled. Put differently, Lorentz symmetry is broken (not unitarily implementable) in quantum field theory in inertial thermal (KMS) representations. (This seems to belong to "general wisdom", but appears to have never been fully proved in the literature.) We argue, along the lines of G. Sewell, that the detector moving with constant velocity against the thermal background of a quantum field in an inertial KMS state, will not asymptotically thermalize - at least the return to equilibrium arguments are not applicable in this context because of the broken Lorentz symmetry in inertial KMS states. We also argue that this corroborates the view expressed by D. Buchholz and R. Verch, and others, that the Unruh effect is not due to thermal contact of the detector with a "heat bath" supplied by the quantum field, but is rather due to conversion of work to heat through the coupling of the detector to the quantum field and the externally driven motion of the detector.

mathematical physics

Audience: researchers in the discipline

One world IAMP mathematical physics seminar

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