A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866916991159238656 |
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| author | Gough, J. E. |
| author_facet | Gough, J. E. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_07915 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus Gough, J. E. Quantum Physics 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. |
| title | A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2411.07915 |