Towards a Deterministic Interpretation of Quantum Mechanics: Insights from Dynamical Systems

• URL: http://arxiv.org/abs/2405.00707v1
• Date: Tue, 23 Apr 2024 19:00:28 GMT
• Title: Towards a Deterministic Interpretation of Quantum Mechanics: Insights from Dynamical Systems
• Authors: Aminur Rahman,
• Abstract summary: This manuscript develops a deterministic dynamical system with local interactions. The aggregate behavior of the trajectories are reminiscent of a quantum particle evolving under the Schr"odinger equation. Results illustrate a deterministic alternative to probabilistic interpretations and aims to shed light on the transition from quantum to classical mechanics.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Experiments violating Bell's inequality appear to indicate deterministic models do not correspond to a realistic theory of quantum mechanics. The theory of pilot waves seemingly overcomes this hurdle via nonlocality and statistical dependence, however it necessitates the existence of "ghost waves". This manuscript develops a deterministic dynamical system with local interactions. The aggregate behavior of the trajectories are reminiscent of a quantum particle evolving under the Schr\"{o}dinger equation and reminiscent of Feynman's path integral interpretation in three canonical examples: motion in free space, double slit diffraction, and superluminal barrier traversal. Moreover, the system bifurcates into various dynamical regimes including a classical limit. These results illustrate a deterministic alternative to probabilistic interpretations and aims to shed light on the transition from quantum to classical mechanics.

Related papers

• The Quantum Wave Function as a Complex Probability Distribution [0.0]
  We show that the wave function and its complex conjugate can be interpreted as complex probability distributions. It is suggested that embracing the idea of processes in quantum theory may explain the reasons for the appearance of classical behavior in large objects.
  arXiv  Detail & Related papers  (2025-02-14T19:39:06Z)
• Analysis of quantum mechanics with real-valued Schrödinger equation,single-event quantum-path dynamics, Mauprtuis path in parameter space, and branching paths beyond semiclassics [0.0]
  We analyze the Schr"odinger dynamics and the Schr"odinger function (or the so-called wavefunction) The Schr"odinger equation is reconstructed from scratch in the real field only, without referring to Newtonian mechanics nor optics.
  arXiv  Detail & Related papers  (2025-01-15T06:06:42Z)
• 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)
• Unification of Random Dynamical Decoupling and the Quantum Zeno Effect [68.8204255655161]
  We show that the system dynamics under random dynamical decoupling converges to a unitary with a decoupling error that characteristically depends on the convergence speed of the Zeno limit. This reveals a unification of the random dynamical decoupling and the quantum Zeno effect.
  arXiv  Detail & Related papers  (2021-12-08T11:41:38Z)
• Interference of Quantum Trajectories [0.0]
  We prove that general time-local quantum master equations admit an unraveling described by ordinary jump-stochastic differential equations. The influence martingale satisfies a $ 1d $ differential equation enslaved to the ones governing the quantum trajectories. Our result proves the existence of a Markovian quantum trajectory picture in the Hilbert space of the system.
  arXiv  Detail & Related papers  (2021-02-20T14:16:25Z)
• Classical model of delayed-choice quantum eraser [0.0]
  Wheeler's delayed-choice experiment was conceived to illustrate the paradoxical nature of wave-particle duality in quantum mechanics. In the experiment, quantum light can exhibit either wave-like interference patterns or particle-like anti-correlations. A variant known as the quantum eraser uses entangled light to recover the lost interference in a seemingly nonlocal and retrocausal manner.
  arXiv  Detail & Related papers  (2021-01-09T14:47:28Z)
• Quantum dynamics and relaxation in comb turbulent diffusion [91.3755431537592]
  Continuous time quantum walks in the form of quantum counterparts of turbulent diffusion in comb geometry are considered. Operators of the form $hatcal H=hatA+ihatB$ are described. Rigorous analytical analysis is performed for both wave and Green's functions.
  arXiv  Detail & Related papers  (2020-10-13T15:50:49Z)
• Microscopic biasing of discrete-time quantum trajectories [0.0]
  We consider a discrete-time quantum dynamics, where the open system collides sequentially with qubit probes which are then measured. We show that the desired biasing is achieved by suitably modifying the Kraus operators describing the discrete open dynamics. The above extends the theory of biased quantum trajectories from Lindblad-like dynamics to sequences of arbitrary dynamical maps.
  arXiv  Detail & Related papers  (2020-07-30T18:00:02Z)
• 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)
• Quantum Zeno effect appears in stages [64.41511459132334]
  In the quantum Zeno effect, quantum measurements can block the coherent oscillation of a two level system by freezing its state to one of the measurement eigenstates. We show that the onset of the Zeno regime is marked by a $textitcascade of transitions$ in the system dynamics as the measurement strength is increased.
  arXiv  Detail & Related papers  (2020-03-23T18:17:36Z)
• External and internal wave functions: de Broglie's double-solution theory? [77.34726150561087]
  We propose an interpretative framework for quantum mechanics corresponding to the specifications of Louis de Broglie's double-solution theory. The principle is to decompose the evolution of a quantum system into two wave functions. For Schr"odinger, the particles are extended and the square of the module of the (internal) wave function of an electron corresponds to the density of its charge in space.
  arXiv  Detail & Related papers  (2020-01-13T13:41:24Z)

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.