Equivalence of approaches to relational quantum dynamics in relativistic settings

• URL: http://arxiv.org/abs/2007.00580v1
• Date: Wed, 1 Jul 2020 16:12:24 GMT
• Title: Equivalence of approaches to relational quantum dynamics in relativistic settings
• Authors: Philipp A. Hoehn, Alexander R. H. Smith and Maximilian P. E. Lock
• Abstract summary: We show that the trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian.
• Score: 68.8204255655161
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We have previously shown (arXiv:1912.00033) that three approaches to relational quantum dynamics -- relational Dirac observables, the Page-Wootters formalism and quantum deparametrizations -- are equivalent. Here we show that this `trinity' of relational quantum dynamics holds in relativistic settings per frequency superselection sector. We ascribe the time according to the clock subsystem to a POVM which is covariant with respect to its (quadratic) Hamiltonian. This differs from the usual choice of a self-adjoint clock observable conjugate to the clock momentum. It also resolves Kucha\v{r}'s criticism that the Page-Wootters formalism yields incorrect localization probabilities for the relativistic particle when conditioning on a Minkowski time operator. We show that conditioning instead on the covariant clock POVM results in a Newton-Wigner type localization probability commonly used in relativistic quantum mechanics. By establishing the equivalence mentioned above, we also assign a consistent conditional-probability interpretation to relational observables and deparametrizations. Finally, we expand a recent method of changing temporal reference frames, and show how to transform states and observables frequency-sector-wise. We use this method to discuss an indirect clock self-reference effect and explore the state and temporal frame-dependence of the task of comparing and synchronizing different quantum clocks.

Related papers

• Quadratic growth of Out-of-time ordered correlators in quantum kicked rotor model [0.0]
  We study the dynamics of Out-of-Time-Ordered Correlators (OTOCs) in quantum resonance condition for a kicked rotor model. We find that the OTOCs of different types increase in a quadratic function of time, breaking the freezing of quantum scrambling induced by the dynamical localization under non-resonance condition.
  arXiv  Detail & Related papers  (2024-01-19T23:17:31Z)
• Amplification of quantum transfer and quantum ratchet [56.47577824219207]
  We study a model of amplification of quantum transfer and making it directed which we call the quantum ratchet model. The ratchet effect is achieved in the quantum control model with dissipation and sink, where the Hamiltonian depends on vibrations in the energy difference synchronized with transitions between energy levels. Amplitude and frequency of the oscillating vibron together with the dephasing rate are the parameters of the quantum ratchet which determine its efficiency.
  arXiv  Detail & Related papers  (2023-12-31T14:04:43Z)
• General covariance for quantum states over time [0.0]
  We show that a canonical state over time satisfies a notion of general covariance for the theory of quantum states over time. We also show that the dynamical quantum Bayes' rule transforms covariantly with respect to states over time.
  arXiv  Detail & Related papers  (2023-10-31T21:37:54Z)
• A magnetic clock for a harmonic oscillator [89.99666725996975]
  We study how the quantum dynamics transforms into a classical-like behaviour when conditions related with macroscopicity are met by the clock alone. In the description of this emerging behaviour finds its place the classical notion of time, as well as that of phase-space and trajectories on it.
  arXiv  Detail & Related papers  (2023-10-20T09:55:51Z)
• Measurement events relative to temporal quantum reference frames [49.1574468325115]
  We compare two approaches to the Page-Wootters formalism to clarify the operational meaning of evolution and measurements. We show that for non-ideal clocks, the purified measurement approach yields time non-local, non-unitary evolution.
  arXiv  Detail & Related papers  (2023-08-21T18:26:12Z)
• Quantum Effects on the Synchronization Dynamics of the Kuramoto Model [62.997667081978825]
  We show that quantum fluctuations hinder the emergence of synchronization, albeit not entirely suppressing it. We derive an analytical expression for the critical coupling, highlighting its dependence on the model parameters.
  arXiv  Detail & Related papers  (2023-06-16T16:41:16Z)
• Entanglement-asymmetry correspondence for internal quantum reference frames [0.0]
  Internal quantum reference frames R for arbitrary compact symmetry groups are considered. We show that there is an exact quantitative correspondence between the amount of entanglement in the invariant state on RS and the amount of asymmetry in the corresponding conditional state on S. Our results shed light on the role of entanglement for establishing asymmetry in a fully symmetric quantum world.
  arXiv  Detail & Related papers  (2021-11-30T19:07:30Z)
• Effective descriptions of localization in a proper-time parametrized framework [0.0]
  We show the connection between proper-time formalism and usual descriptions parametrized by classical observers. We retrieve the concepts of Newton-Wigner position and Kijowski time of detection.
  arXiv  Detail & Related papers  (2021-07-24T13:04:04Z)
• The Generalized OTOC from Supersymmetric Quantum Mechanics: Study of Random Fluctuations from Eigenstate Representation of Correlation Functions [1.2433211248720717]
  The concept of out-of-time-ordered correlation (OTOC) function is treated as a very strong theoretical probe of quantum randomness. We define a general class of OTOC, which can perfectly capture quantum randomness phenomena in a better way. We demonstrate an equivalent formalism of computation using a general time independent Hamiltonian.
  arXiv  Detail & Related papers  (2020-08-06T07:53:28Z)
• Unraveling the topology of dissipative quantum systems [58.720142291102135]
  We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. We show for a broad family of translation-invariant collapse models that the set of dark state-inducing Hamiltonians imposes a nontrivial topological structure on the space of Hamiltonians.
  arXiv  Detail & Related papers  (2020-07-12T11:26:02Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.