2024/11/12 by John Gough, Gough, J. E. · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Random Matrices and Applications #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.2411.07915
openalex publication_date 2024/11/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a simple argument to derive the transformation of quantum stochastic calculus formalism between inertial observers, and derive the quantum open system dynamics for a system moving in a vacuum (more generally coherent) quantum field under the usual Markov approximation. We argue that for uniformly accelerated open systems, however, the formalism must breakdown as we move from a Fock representation over the algebra of field observables over all Minkowski space to the restriction to the algebra of observables over a Rindler wedge. This leads to quantum noise having a unitarily inequivalent non-Fock representation - in particular, the latter is a thermal representation at the Unruh temperature. The unitary inequivalence ultimately being a consequence of the underlying flat noise spectrum approximation for the fundamental quantum stochastic processes. We derive the quantum stochastic limit for a uniformly accelerated (two-level) detector and establish an open systems description of the relaxation to thermal equilibrium at the Unruh temperature.er is a thermal representation at the Unruh temperature. The unitary inequivalence ultimately being a consequence of the underlying flat noise spectrum approximation for the fundamental quantum stochastic processes.