Phase-space gaussian ensemble quantum camouflage

• URL: http://arxiv.org/abs/2409.16377v1
• Date: Tue, 24 Sep 2024 18:14:07 GMT
• Title: Phase-space gaussian ensemble quantum camouflage
• Authors: Alex E. Bernardini, Orfeu Bertolami,
• Abstract summary: We extend the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum. For gaussian statistical ensembles, the exact phase-space profile of the quantum fluctuations over the classical trajectories are found.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Extending the phase-space description of the Weyl-Wigner quantum mechanics to a subset of non-linear Hamiltonians in position and momentum, gaussian functions are identified as the quantum ground state. Once a Hamiltonian, $H^{W}(q,\,p)$, is constrained by the $\partial ^2 H^{W} / \partial q \partial p = 0$ condition, flow properties for generic $1$-dim systems can be analytically obtained in terms of Wigner functions and Wigner currents. For gaussian statistical ensembles, the exact phase-space profile of the quantum fluctuations over the classical trajectories are found, so to interpret them as a suitable Hilbert space state configuration for confronting quantum and classical regimes. In particular, a sort of {\em quantum camouflage} where the stationarity of classical statistical ensembles can be camouflaged by the stationarity of gaussian quantum ensembles is identified. Besides the broadness of the framework worked out in some previous examples, our results provide an encompassing picture of quantum effects on non-linear dynamical systems which can be interpreted as a first step for finding the complete spectrum of non-standard Hamiltonians.

Related papers

• Scaled quantum theory. The bouncing ball problem [0.0]
  The standard bouncing ball problem is analyzed under the presence of a gravitational field and harmonic potential. The quantum-classical transition of the density matrix is described by the linear scaled von Neumann equation for mixed states.
  arXiv  Detail & Related papers  (2024-10-14T10:09:48Z)
• Efficient Quantum Pseudorandomness from Hamiltonian Phase States [41.94295877935867]
  We introduce a quantum hardness assumption called the Hamiltonian Phase State (HPS) problem. We show that our assumption is plausibly fully quantum; meaning, it cannot be used to construct one-way functions. We show that our assumption and its variants allow us to efficiently construct many pseudorandom quantum primitives.
  arXiv  Detail & Related papers  (2024-10-10T16:10:10Z)
• Quantum Instability [30.674987397533997]
  We show how a time-independent, finite-dimensional quantum system can give rise to a linear instability corresponding to that in the classical system. An unstable quantum system has a richer spectrum and a much longer recurrence time than a stable quantum system.
  arXiv  Detail & Related papers  (2022-08-05T19:53:46Z)
• Non-commutative phase-space Lotka-Volterra dynamics: the quantum analogue [0.0]
  The Lotka-Volterra (LV) dynamics is investigated in the framework of the Weyl-Wigner (WW) quantum mechanics (QM) The WW framework provides the ground for identifying how classical and quantum evolution coexist at different scales. The generality of the framework developed here extends the boundaries of the understanding of quantum-like effects on competitive microscopical bio-systems.
  arXiv  Detail & Related papers  (2022-06-14T11:23:04Z)
• Measurement of a quantum system with a classical apparatus using ensembles on configuration space [0.48733623015338234]
  We use the approach of ensembles on configurations space to give a detailed account of a classical apparatus measuring the position of a quantum particle. We show that the probability of the pointer of the classical apparatus is left in a state that corresponds to the probability of the quantum particle. Since this formalism incorporates uncertainties and finite measurement precision, it is well suited for metrological applications.
  arXiv  Detail & Related papers  (2022-05-19T15:48:12Z)
• Quantum dynamics corresponding to chaotic BKL scenario [62.997667081978825]
  Quantization smears the gravitational singularity avoiding its localization in the configuration space. Results suggest that the generic singularity of general relativity can be avoided at quantum level.
  arXiv  Detail & Related papers  (2022-04-24T13:32:45Z)
• Generalized phase-space description of non-linear Hamiltonian systems and the Harper-like dynamics [0.0]
  Phase-space features of the Wigner flow for generic one-dimensional systems with a Hamiltonian are analytically obtained. A framework can be extended to any quantum system described by Hamiltonians in the form of $HW(q,,p) = K(p) + V(q)$.
  arXiv  Detail & Related papers  (2022-02-24T11:31:54Z)
• Bernstein-Greene-Kruskal approach for the quantum Vlasov equation [91.3755431537592]
  The one-dimensional stationary quantum Vlasov equation is analyzed using the energy as one of the dynamical variables. In the semiclassical case where quantum tunneling effects are small, an infinite series solution is developed.
  arXiv  Detail & Related papers  (2021-02-18T20:55:04Z)
• 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)
• Classical and statistical limits of the quantum singular oscillator [0.0]
  Weyl-Wigner phase-space and Bohmian mechanics frameworks are used. Two inequivalent quantum systems are shown to be statistically equivalent at thermal equilibrium.
  arXiv  Detail & Related papers  (2020-07-10T19:07:33Z)
• Probing the Universality of Topological Defect Formation in a Quantum Annealer: Kibble-Zurek Mechanism and Beyond [46.39654665163597]
  We report on experimental tests of topological defect formation via the one-dimensional transverse-field Ising model. We find that the quantum simulator results can indeed be explained by the KZM for open-system quantum dynamics with phase-flip errors. This implies that the theoretical predictions of the generalized KZM theory, which assumes isolation from the environment, applies beyond its original scope to an open system.
  arXiv  Detail & Related papers  (2020-01-31T02:55:35Z)

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.