On Some Quantum Correction to the Coulomb Potential in Generalized Uncertainty Principle Approach

• URL: http://arxiv.org/abs/2401.03463v2
• Date: Thu, 21 Mar 2024 11:27:45 GMT
• Title: On Some Quantum Correction to the Coulomb Potential in Generalized Uncertainty Principle Approach
• Authors: M. Baradaran, L. M. Nieto, S. Zarrinkamar,
• Abstract summary: We consider a modified Schr"odinger equation resulting from a generalized uncertainty principle. As the resulting equation cannot be solved by common exact approaches, we propose a Bethe ansatz approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Taking into account the importance of the unified theory of quantum mechanics and gravity, and the existence of a minimal length of the order of the Planck scale, we consider a modified Schr\"odinger equation resulting from a generalized uncertainty principle, which finds applications from the realm of quantum information to large-scale physics, with a quantum mechanically corrected gravitational interaction proposed very recently. As the resulting equation cannot be solved by common exact approaches, we propose a Bethe ansatz approach, which will be applied and whose results we will discuss, commenting on the analogy of the present study with some other interesting physical problems.

Related papers

• The generalized uncertainty principle within the ordinary framework of quantum mechanics [0.0]
  A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics accounts for the influence of gravity on small scales. Introducing the squared momentum term results in a generalized uncertainty principle, which limits the minimum uncertainty in particle position to the Planck length. It is shown that the deformed algebra of position and momentum operators can be incorporated into the framework of ordinary quantum mechanics.
  arXiv  Detail & Related papers  (2024-07-12T09:37:51Z)
• A Theory of Quantum Jumps [44.99833362998488]
  We study fluorescence and the phenomenon of quantum jumps'' in idealized models of atoms coupled to the quantized electromagnetic field. Our results amount to a derivation of the fundamental randomness in the quantum-mechanical description of microscopic systems.
  arXiv  Detail & Related papers  (2024-04-16T11:00:46Z)
• Causality and a possible interpretation of quantum mechanics [2.7398542529968477]
  Based on quantum field theory, our work provides a framework that harmoniously integrates relativistic causality, quantum non-locality, and quantum measurement. We use reduced density matrices to represent the local information of the quantum state and show that the reduced density matrices cannot evolve superluminally. Unlike recent approaches that focus on causality by introducing new operators to describe detectors, we consider that everything--including detectors, environments, and humans--is composed of the same fundamental fields.
  arXiv  Detail & Related papers  (2024-02-08T07:07:22Z)
• Adherence and violation of the equivalence principle from classical to quantum mechanics [0.0]
  An inhomogeneous gravitational field tidal effects couple the center of mass motion to the quantum fluctuations. The size of this violation is within sensitivities of current Eotvos and clock-based return time experiments.
  arXiv  Detail & Related papers  (2023-10-13T16:12:31Z)
• Quantum data learning for quantum simulations in high-energy physics [55.41644538483948]
  We explore the applicability of quantum-data learning to practical problems in high-energy physics. We make use of ansatz based on quantum convolutional neural networks and numerically show that it is capable of recognizing quantum phases of ground states. The observation of non-trivial learning properties demonstrated in these benchmarks will motivate further exploration of the quantum-data learning architecture in high-energy physics.
  arXiv  Detail & Related papers  (2023-06-29T18:00:01Z)
• Universality of critical dynamics with finite entanglement [68.8204255655161]
  We study how low-energy dynamics of quantum systems near criticality are modified by finite entanglement. Our result establishes the precise role played by entanglement in time-dependent critical phenomena.
  arXiv  Detail & Related papers  (2023-01-23T19:23:54Z)
• On the strangeness of quantum probabilities [0.0]
  We will address in detail the problem of determining how the concept of undecidability leads to substantial changes to classical theory of probability. We will show how such changes produce a theory that coincides with the principles underlying quantum mechanics.
  arXiv  Detail & Related papers  (2022-12-23T13:10:39Z)
• Effective information bounds in modified quantum mechanics [0.03492633112489883]
  We show that quantum systems undergo corrections to the quantum speed limit which, in turn, imply the modification of the Heisenberg limit for parameter estimation. For some nonlocal models inspired by quantum gravity, the bounds are found to oscillate in time, an effect that could be tested in future high-precision quantum experiments.
  arXiv  Detail & Related papers  (2022-11-16T21:37:04Z)
• 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)
• Quantum indistinguishability through exchangeable desirable gambles [69.62715388742298]
  Two particles are identical if all their intrinsic properties, such as spin and charge, are the same. Quantum mechanics is seen as a normative and algorithmic theory guiding an agent to assess her subjective beliefs represented as (coherent) sets of gambles. We show how sets of exchangeable observables (gambles) may be updated after a measurement and discuss the issue of defining entanglement for indistinguishable particle systems.
  arXiv  Detail & Related papers  (2021-05-10T13:11:59Z)
• Quantum Causal Inference in the Presence of Hidden Common Causes: an Entropic Approach [34.77250498401055]
  We put forth a new theoretical framework for merging quantum information science and causal inference by exploiting entropic principles. We apply our proposed framework to an experimentally relevant scenario of identifying message senders on quantum noisy links. This approach can lay the foundations of identifying originators of malicious activity on future multi-node quantum networks.
  arXiv  Detail & Related papers  (2021-04-24T22:45:50Z)

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.