Nonlinear quantum mechanics in a q-deformed Hilbert space

Costa, Bruno G. da; Borges, Ernesto P.

doi:10.1016/j.physleta.2019.05.056

Cited by 10 publications

(5 citation statements)

References 31 publications

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“…The smallest change in the space-time structure significantly affects the dynamics of motion since dynamics is coupled to the space-time metric. In our case, there are many sources, such as gravitational waves and the mass distribution in the universe or decoherence and deformation of the Hilbert space at the quantum level 33 , that can cause the space-time deformations at both the local and general cosmological scales. Here, we consider the neutrino oscillation dynamics coupled to the space-time in the stochastic framework, however, the models where the oscillation dynamics explicitly coupled to gravity may also be interesting.…”

Section: Fractional Dynamics Between Mass and Flavour Eigenstatesmentioning

confidence: 99%

Anomalous cyclic in the neutrino oscillations

Aydıner

2023

Sci Rep

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Neutrino physics is one of the most important topics in particle physics and cosmology. As it is known, neutrinos are weakly interacting fundamental particles with chargeless and very small masses. One of the most characteristic features of the neutrino that make a difference from other elementary particles is that it oscillates between the mass and flavour eigenstates. Due to these oscillations, neutrinos change from one flavour to another. So far in theory the possible effects of deformed space-time effects on oscillation have not been considered. In this study, we show for the first time that a deformed space-time metric will lead to fractional dynamics between mass and flavour changes and therefore cause a phase shift in the oscillation period. We also shortly discuss the possible relation between anomalous cyclic and relic neutrinos. The modification in the oscillation probabilities due to the studied effect in this work could be seen using relic neutrinos.

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Section: Fractional Dynamics Between Mass and Flavour Eigenstatesmentioning

confidence: 99%

Anomalous cyclic in the neutrino oscillations

Aydıner

2023

Sci Rep

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“…We will focus on q deformations of SU(2)-like algebras. For a better understanding of q deformations and their various applications, we direct the readers' attention to the references [85][86][87][88][89][90][91][92][93][94][95].…”

Section: Q-deformed Su(2) Algebra and Lanczos Coefficientsmentioning

confidence: 99%

Probing quantum scars and weak ergodicity breaking through quantum complexity

2022

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Scar states are special many-body eigenstates that weakly violate the eigenstate thermalization hypothesis (ETH). Using the explicit formalism of the Lanczos algorithm, usually known as the forward scattering approximation in this context, we compute the Krylov state (spread) complexity of typical states generated by the time evolution of the PXP Hamiltonian, hosting such states. We show that the complexity for the Néel state revives in an approximate sense, while complexity for the generic ETH-obeying state always increases. This can be attributed to the approximate SU(2) structure of the corresponding generators of the Hamiltonian. We quantify such "closeness" by the q-deformed SU(2) algebra and provide an analytic expression of Lanczos coefficients for the Néel state within the approximate Krylov subspace. We intuitively explain the results in terms of a tight-binding model. We further consider a deformation of the PXP Hamiltonian and compute the corresponding Lanczos coefficients and the complexity. We find that complexity for the Néel state shows nearly perfect revival while the same does not hold for a generic ETH-obeying state.

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“…This fact may be ignored when the dynamic is Markovian. However, if space-time is deformed, the physics completely changes and it turns out that the motion is coupled to the space-time where all perturbation and measurement process leads to decoherence and deformation of the Hilbert space [21].…”

Section: Anomalous Cyclic In the Deformed Space-timementioning

confidence: 99%

Anomalous Cyclic in the Neutrino Oscillations

Aydıner¹

2022

Preprint

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Neutrino physics is one of the most important topics in particle physics and cosmology. Despite the many physical properties of neutrinos were understand theoretically and experimentally, it is known that there are many unsolved problems in this area. In this study, we suppose that the deformed space-time caused by the gravitational perturbation can play an important role on the neutrino oscillations. We analytically analyzed these effect on the neutrino oscillation and showed that this effect leads to an anomalous cyclic in the neutrino oscillation. Results clearly indicates that these anomalous cyclic are depending on the degree of deformation of the space-time. The role of this anomaly in neutrino oscillation may be important. There may be a relation between with this cyclic anomaly and other anomalous of neutrinos such as mass limits, energy limits, oscillation lengths, mixing angles, speed of neutrinos. The cyclic anomalies might be detected experimentally. If these anomalies are confirmed, it will appear that we need to think more about neutrino physics.

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Nonlinear quantum mechanics in a q-deformed Hilbert space

Cited by 10 publications

References 31 publications

Anomalous cyclic in the neutrino oscillations

Anomalous cyclic in the neutrino oscillations

Probing quantum scars and weak ergodicity breaking through quantum complexity

Anomalous Cyclic in the Neutrino Oscillations

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