A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus
We present a simple argument to derive the transformation of the quantum stochastic calculus formalism between inertial observers and derive the quantum open system dynamics for a system moving in a vacuum (or, more generally, a coherent) quantum field under the usual Markov approximation. We argue,...
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MDPI AG
2025-05-01
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| author | John E. Gough |
| author_facet | John E. Gough |
| author_sort | John E. Gough |
| collection | DOAJ |
| description | We present a simple argument to derive the transformation of the quantum stochastic calculus formalism between inertial observers and derive the quantum open system dynamics for a system moving in a vacuum (or, more generally, a coherent) quantum field under the usual Markov approximation. We argue, however, that, for uniformly accelerated open systems, the formalism must break down as we move from a Fock representation over the algebra of field observables over all of Minkowski space to the restriction regarding 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 is ultimately 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 system description of the relaxation to thermal equilibrium at the Unruh temperature. |
| format | Article |
| id | doaj-art-1f7ec44dbbc5418a9a3b8e5412bc6c96 |
| institution | Kabale University |
| issn | 1099-4300 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj-art-1f7ec44dbbc5418a9a3b8e5412bc6c962025-08-20T03:47:49ZengMDPI AGEntropy1099-43002025-05-0127552910.3390/e27050529A Note on the Relativistic Transformation Properties of Quantum Stochastic CalculusJohn E. Gough0Department of Physics, Aberystwyth University, Aberystwyth SY23 3QR, UKWe present a simple argument to derive the transformation of the quantum stochastic calculus formalism between inertial observers and derive the quantum open system dynamics for a system moving in a vacuum (or, more generally, a coherent) quantum field under the usual Markov approximation. We argue, however, that, for uniformly accelerated open systems, the formalism must break down as we move from a Fock representation over the algebra of field observables over all of Minkowski space to the restriction regarding 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 is ultimately 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 system description of the relaxation to thermal equilibrium at the Unruh temperature.https://www.mdpi.com/1099-4300/27/5/529quantum Itō calculusrelativistic fieldsDavies–Unruh effect |
| spellingShingle | John E. Gough A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus Entropy quantum Itō calculus relativistic fields Davies–Unruh effect |
| title | A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus |
| title_full | A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus |
| title_fullStr | A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus |
| title_full_unstemmed | A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus |
| title_short | A Note on the Relativistic Transformation Properties of Quantum Stochastic Calculus |
| title_sort | note on the relativistic transformation properties of quantum stochastic calculus |
| topic | quantum Itō calculus relativistic fields Davies–Unruh effect |
| url | https://www.mdpi.com/1099-4300/27/5/529 |
| work_keys_str_mv | AT johnegough anoteontherelativistictransformationpropertiesofquantumstochasticcalculus AT johnegough noteontherelativistictransformationpropertiesofquantumstochasticcalculus |