Quantum Tunneling in Deformed Quantum Mechanics with Minimal Length

Guo, Xiansheng; Lv, Bochen; Tao, Jun; Wang, Peng

doi:10.1155/2016/4502312

Cited by 4 publications

(7 citation statements)

References 30 publications

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“…This means that these probabilities are actually correlated. One may compare the above mentioned correlation function with the similar expressions obtained in [4] and [19,21] with using of other phenomenological approaches to quantum gravity. In each case the correlation is appeared due to incorporation of the characteristic parameter (λ in our case) of the relevant theory.…”

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 83%

“…Now, we obtain a detailed quantum tunneling calculation from the S-BH event horizon. According to [13,19], to describe the process of quantum tunneling where a particle moves in dynamical geometry and crosses through the horizon without singularity on its path, there should be a coordinates system in terms of which the metric is not singular at the horizon. In this sense, the above metric may be written as…”

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 99%

“…So, assume the trajectory of a massless particle and consider the response of the background geometry to the radiated quantum of energy E with polymer space correction, i.e. E. Since the WKB approximation is valid near the horizon [19], for the classically prohibited region at the stationary phase, the tunneling probability as a function of the particle action takes the form…”

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 99%

“…where ∆S is related to the change of Bekenstein Hawking entropy before and after emission [19,21,22,23,24]. In the string theory, it is expected that the the emission rates from excited D-branes on the Planck scales is related to differences between the counting of microstates in the canonical and microcanonical ensembles.…”

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 99%

“…Thus, we obtain the polymer corrected temperature as Now, by using of the saturated form of the uncertainty principle E∆x = 1 2 and ∆x = 2M [26,19] (which comes from the saturated form of the Heisenberg uncertainty principle ∆p∆x = h 2 ) in the above equation, its Taylor expansion takes the form…”

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 99%

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Polymer deformation and particle tunneling from Schwarzschild black hole

Amirfakhrian

Vakili

2019

Int. J. Geom. Methods Mod. Phys.

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In this paper, we investigate a tunneling mechanism of massless particles from the Schwarzschild black hole in the framework of polymer quantum mechanics. According to the corresponding invariant Liouville volume, we determine the tunneling rate from Schwarzschild black hole by the polymeric quantization procedure. In this regard, we show that the temperature and tunneling radiation of the black hole receive new corrections in such a way that the exact radiant spectrum is no longer precisely thermal.

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Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 83%

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 99%

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 99%

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 99%

Section: S-bh and The Polymeric Tunneling Mechanismmentioning

confidence: 99%

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Polymer deformation and particle tunneling from Schwarzschild black hole

Amirfakhrian

Vakili

2019

Int. J. Geom. Methods Mod. Phys.

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Minimal length effects on motion of a particle in Rindler space *

Guo¹,

Liang²,

Mu³

et al. 2021

Chinese Phys. C

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Various quantum theories of gravity predict the existence of a minimal measurable length. In this paper, we study effects of the minimal length on the motion of a particle in the Rindler space under a harmonic potential. This toy model captures key features of particle dynamics near a black hole horizon and allows us to make three observations. First, we find that chaotic behavior becomes stronger with increases in minimal length effects, leading predominantly to growth in the maximum Lyapunov characteristic exponents, while the KAM curves on Poincaré surfaces of a section tend to disintegrate into chaotic layers. Second, in the presence of the minimal length effects, it can take a finite amount of Rindler time for a particle to cross the Rindler horizon, which implies a shorter scrambling time of black holes. Finally, the model shows that some Lyapunov characteristic exponents can be greater than the surface gravity of the horizon, violating the recently conjectured universal upper bound. In short, our results reveal that quantum gravity effects may make black holes prone to more chaos and faster scrambling.

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WKB Approximation for a Deformed Schrodinger-like Equation and its Applications to Quasinormal Modes of Black Holes and Quantum Cosmology

Lv¹,

Wang²,

Yang³

2017

Preprint

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In this paper, we use the WKB approximation method to approximately solve a deformed Schrodinger-like differential equation:, which are frequently dealt with in various effective models of quantum gravity, where the parameter α characterizes effects of quantum gravity. For an arbitrary function g (x) satisfying several properties proposed in the paper, we find the WKB solutions, the WKB connection formulas through a turning point, the deformed Bohr-Sommerfeld quantization rule, and the deformed tunneling rate formula through a potential barrier. Several examples of applying the WKB approximation to the deformed quantum mechanics are investigated. In particular, we calculate the bound states of the Pöschl-Teller potential and estimate the effects of quantum gravity on the quasinormal modes of a Schwarzschild black hole. Moreover, the area quantum of the black hole is considered via Bohr's correspondence principle. Finally, the WKB solutions of the deformed Wheeler-DeWitt equation for a closed Friedmann universe with a scalar field are obtained, and the effects of quantum gravity on the probability of sufficient inflation is discussed in the context of the tunneling proposal.

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Quantum Tunneling in Deformed Quantum Mechanics with Minimal Length

Cited by 4 publications

References 30 publications

Polymer deformation and particle tunneling from Schwarzschild black hole

Polymer deformation and particle tunneling from Schwarzschild black hole

Minimal length effects on motion of a particle in Rindler space *

WKB Approximation for a Deformed Schrodinger-like Equation and its Applications to Quasinormal Modes of Black Holes and Quantum Cosmology

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