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| Format: | Preprint |
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2024
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| Online Access: | https://arxiv.org/abs/2402.14794 |
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| _version_ | 1866912034476523520 |
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| author | Passegger, Albert Georg Verch, Rainer |
| author_facet | Passegger, Albert Georg Verch, Rainer |
| contents | For any local, translation-covariant quantum field theory on Minkowski spacetime, we prove that two distinct states that are invariant under the inertial time evolutions in different inertial reference frames are disjoint, i.e. neither state is a perturbation of the other, if the states are primary, have separating Gelfand-Naimark-Segal (GNS) vectors, and satisfy a timelike cluster property called the mixing property. These conditions are fulfilled by the inertial Kubo-Martin-Schwinger (KMS) states of the free scalar field, thus showing that a state satisfying the KMS condition relative to one inertial frame is far from thermal equilibrium relative to other inertial frames. We review the property of return to equilibrium (RTE) in open quantum systems theory and discuss the implications of disjointness on the asymptotic behavior of detector systems coupled to states of a free massless scalar field. We argue that the coupled system of an Unruh-DeWitt detector moving with constant velocity relative to the field in a KMS state, or an excitation thereof, cannot thermalize under generic conditions. This leads to an illustration of the physical differences between heat baths in inertial systems and the alleged "heat bath" of the Unruh effect. This paper also sketches the construction and RTE property of the quantum dynamical system of an Unruh-DeWitt detector coupled to a massless scalar field in a KMS state relative to the inertial rest frame of the detector. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2402_14794 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization Passegger, Albert Georg Verch, Rainer Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics 46L60, 81T05, 82B10, 82C10 For any local, translation-covariant quantum field theory on Minkowski spacetime, we prove that two distinct states that are invariant under the inertial time evolutions in different inertial reference frames are disjoint, i.e. neither state is a perturbation of the other, if the states are primary, have separating Gelfand-Naimark-Segal (GNS) vectors, and satisfy a timelike cluster property called the mixing property. These conditions are fulfilled by the inertial Kubo-Martin-Schwinger (KMS) states of the free scalar field, thus showing that a state satisfying the KMS condition relative to one inertial frame is far from thermal equilibrium relative to other inertial frames. We review the property of return to equilibrium (RTE) in open quantum systems theory and discuss the implications of disjointness on the asymptotic behavior of detector systems coupled to states of a free massless scalar field. We argue that the coupled system of an Unruh-DeWitt detector moving with constant velocity relative to the field in a KMS state, or an excitation thereof, cannot thermalize under generic conditions. This leads to an illustration of the physical differences between heat baths in inertial systems and the alleged "heat bath" of the Unruh effect. This paper also sketches the construction and RTE property of the quantum dynamical system of an Unruh-DeWitt detector coupled to a massless scalar field in a KMS state relative to the inertial rest frame of the detector. |
| title | Disjointness of inertial KMS states and the role of Lorentz symmetry in thermalization |
| topic | Mathematical Physics General Relativity and Quantum Cosmology High Energy Physics - Theory Quantum Physics 46L60, 81T05, 82B10, 82C10 |
| url | https://arxiv.org/abs/2402.14794 |