Classical Dynamics Based on the Minimal Length Uncertainty Principle

2015 ◽  
Vol 55 (2) ◽  
pp. 825-836 ◽  
Author(s):  
Won Sang Chung
Keyword(s):  
Uncertainty Principle ◽  
Minimal Length ◽  
Classical Dynamics

scholarly journals The uncertainty principle enables non-classical dynamics in an interferometer

2014 ◽  
Vol 5 (1) ◽  
Author(s):  
Oscar C. O. Dahlsten ◽  
Andrew J. P. Garner ◽  
Vlatko Vedral
Keyword(s):  
Uncertainty Principle ◽  
Classical Dynamics

scholarly journals Effect of GUP on the Kepler problem and a variable minimal length

2014 ◽  
Vol 92 (6) ◽  
pp. 484-487 ◽  
Author(s):  
Fatemeh Ahmadi ◽  
Jafar Khodagholizadeh
Keyword(s):  
Cosmological Constant ◽  
Uncertainty Principle ◽  
Kepler Problem ◽  
Rotational Symmetry ◽  
Generalized Uncertainty Principle ◽  
Space Time ◽  
Minimal Length ◽  
De Sitter ◽  
Heisenberg Uncertainty Principle ◽  
Perihelion Shift

Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg uncertainty principle near the Plank scale, known as the generalized uncertainty principle (GUP). Here we study the effects of GUP, which preserves the rotational symmetry of the space–time, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild – de Sitter space–time with the resultant value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the space–time. Now, if the cosmological constant varies with time, we have a variable minimal length in the space–time. Finally, we investigate the effects of GUP on the stability of circular orbits.

scholarly journals Exotic fermionic fields and minimal length

2020 ◽  
Vol 80 (8) ◽  
Author(s):  
J. M. Hoff da Silva ◽  
D. Beghetto ◽  
R. T. Cavalcanti ◽  
R. da Rocha
Keyword(s):  
Dirac Equation ◽  
Quantum Gravity ◽  
Dirac Operator ◽  
Uncertainty Principle ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Dynamical Equations ◽  
Spacetime Manifold ◽  
Fermionic Fields

Abstract We investigate the effective Dirac equation, corrected by merging two scenarios that are expected to emerge towards the quantum gravity scale. Namely, the existence of a minimal length, implemented by the generalized uncertainty principle, and exotic spinors, associated with any non-trivial topology equipping the spacetime manifold. We show that the free fermionic dynamical equations, within the context of a minimal length, just allow for trivial solutions, a feature that is not shared by dynamical equations for exotic spinors. In fact, in this coalescing setup, the exoticity is shown to prevent the Dirac operator to be injective, allowing the existence of non-trivial solutions.

scholarly journals Minimal length uncertainty principle and the trans-Planckian problem of black hole physics

1999 ◽  
Vol 59 (4) ◽  
Author(s):  
R. Brout ◽  
Cl. Gabriel ◽  
M. Lubo ◽  
Ph. Spindel
Keyword(s):  
Black Hole ◽  
Uncertainty Principle ◽  
Black Hole Physics ◽  
Minimal Length

scholarly journals Heisenberg Algebra in the Bargmann-Fock Space with Natural Cutoffs

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Maryam Roushan ◽  
Kourosh Nozari
Keyword(s):  
Uncertainty Principle ◽  
Fock Space ◽  
Generalized Uncertainty Principle ◽  
Heisenberg Algebra ◽  
Minimal Length ◽  
Maximal Momentum

We construct a Heisenberg algebra in Bargmann-Fock space in the presence of natural cutoffs encoded as minimal length, minimal momentum, and maximal momentum through a generalized uncertainty principle.

scholarly journals MICROSCOPIC BLACK HOLE AND UNCERTAINTY PRINCIPLE WITH MINIMAL LENGTH AND MOMENTUM

2013 ◽  
Vol 28 (10) ◽  
pp. 1350029 ◽  
Author(s):  
M. M. STETSKO
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Black Hole ◽  
Uncertainty Principle ◽  
Emission Rate ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Schwarzschild Black Hole ◽  
Evaporation Time ◽  
Thermodynamical Functions

We investigate a microscopic black hole in the case of modified generalized uncertainty principle with a minimal uncertainty in position as well as in momentum. We calculate thermodynamical functions of a Schwarzschild black hole such as temperature, entropy and heat capacity. It is shown that the incorporation of minimal uncertainty in momentum leads to minimal temperature of a black hole. Minimal temperature gives rise to appearance of a phase transition. Emission rate equation and black hole's evaporation time are also obtained.

scholarly journals Maximally Localized States and Quantum Corrections of Black Hole Thermodynamics in the Framework of a New Generalized Uncertainty Principle

2015 ◽  
Vol 2015 ◽  
pp. 1-15 ◽  
Author(s):  
Yan-Gang Miao ◽  
Ying-Jie Zhao ◽  
Shao-Jun Zhang
Keyword(s):  
Black Hole ◽  
Uncertainty Principle ◽  
Decay Time ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Localized States ◽  
Quantum Corrections ◽  
Thermodynamic Quantities ◽  
Mixing Effect ◽  
Significant Difference

As a generalized uncertainty principle (GUP) leads to the effects of the minimal length of the order of the Planck scale and UV/IR mixing, some significant physical concepts and quantities are modified or corrected correspondingly. On the one hand, we derive the maximally localized states—the physical states displaying the minimal length uncertainty associated with a new GUP proposed in our previous work. On the other hand, in the framework of this new GUP we calculate quantum corrections to the thermodynamic quantities of the Schwardzschild black hole, such as the Hawking temperature, the entropy, and the heat capacity, and give a remnant mass of the black hole at the end of the evaporation process. Moreover, we compare our results with that obtained in the frameworks of several other GUPs. In particular, we observe a significant difference between the situations with and without the consideration of the UV/IR mixing effect in the quantum corrections to the evaporation rate and the decay time. That is, the decay time can greatly be prolonged in the former case, which implies that the quantum correction from the UV/IR mixing effect may give rise to a radical rather than a tiny influence to the Hawking radiation.

scholarly journals Quantum cosmology with dynamical vacuum in a minimal-length scenario

2021 ◽  
Vol 81 (4) ◽  
Author(s):  
M. F. Gusson ◽  
A. Oakes O. Gonçalves ◽  
R. G. Furtado ◽  
J. C. Fabris ◽  
J. A. Nogueira
Keyword(s):  
Wave Function ◽  
Commutation Relation ◽  
Uncertainty Principle ◽  
Quantum Cosmology ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Minimum Length ◽  
Position Space ◽  
Infinite Norm ◽  
The Universe

AbstractIn this work, we consider effects of the dynamical vacuum in quantum cosmology in presence of a minimum length introduced by the GUP (generalized uncertainty principle) related to the modified commutation relation $$[{\hat{X}},{\hat{P}}] := \frac{i\hbar }{ 1 - \beta {\hat{P}}^2 }$$ [ X ^ , P ^ ] : = i ħ 1 - β P ^ 2 . We determine the wave function of the Universe $$ \psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) , which is solution of the modified Wheeler–DeWitt equation in the representation of the quasi-position space, in the limit where the scale factor of the Universe is small. Although $$\psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) is a physically acceptable state it is not a realizable state of the Universe because $$ \psi _{qp}(\xi ,t)$$ ψ qp ( ξ , t ) has infinite norm, as in the ordinary case with no minimal length.

scholarly journals Aharonov–Bohm-like scattering in the generalized uncertainty principle-corrected quantum mechanics

2021 ◽  
pp. 2150108
Author(s):  
DaeKil Park
Keyword(s):  
Cross Section ◽  
Uncertainty Principle ◽  
Azimuthal Angle ◽  
Generalized Uncertainty Principle ◽  
Classical Equation ◽  
Minimal Length ◽  
Classical Electrodynamics ◽  
Flux Parameter ◽  
The Cross ◽  
Aharonov Bohm

We discuss classical electrodynamics and the Aharonov–Bohm effect in the presence of the minimal length. In the former, we derive the classical equation of motion and the corresponding Lagrangian. In the latter, we adopt the generalized uncertainty principle (GUP) and compute the scattering cross-section up to the first-order of the GUP parameter [Formula: see text]. Even though the minimal length exists, the cross-section is invariant under the simultaneous change [Formula: see text], [Formula: see text], where [Formula: see text] and [Formula: see text] are azimuthal angle and magnetic flux parameter. However, unlike the usual Aharonv–Bohm scattering, the cross-section exhibits discontinuous behavior at every integer [Formula: see text]. The symmetries, which the cross-section has in the absence of GUP, are shown to be explicitly broken at the level of [Formula: see text].

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