Deformed Heisenberg algebra with minimal length and the equivalence principle

Tkachuk, V. M.

doi:10.1103/physreva.86.062112

Cited by 72 publications

(123 citation statements)

References 40 publications

(54 reference statements)

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“…This assumption has already been used in a previous work and has also led to saving the equivalence principle [31]. Moreover, the natural generalization to Eq.…”

Section: Linear Diatomic Chain (Two-body Problem)mentioning

confidence: 86%

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Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

Bernardo

Esguerra

2015

Few-Body Syst

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We present exact analytical solutions to the classical equations of motion and analyze the dynamical consequences of the existence of a minimal length for the free particle, particle in a linear potential, anti-symmetric constant force oscillator, harmonic oscillator, vertical harmonic oscillator, linear diatomic chain, and linear triatomic chain. It turns out that a minimal length increases the speed of a free particle and the rate of fall of a particle that is subject to the influence of a linear potential. Our results suggest that the characteristic frequency of systems tend to increase when there is a minimal length. This is a common feature that we observed for the oscillator systems that we have considered.

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“…This assumption has already been used in a previous work and has also led to saving the equivalence principle [31]. Moreover, the natural generalization to Eq.…”

Section: Linear Diatomic Chain (Two-body Problem)mentioning

confidence: 86%

“…This ensures that the weak equivalence principle is satisfied [31]. The Hamiltonian equations of motion for the variables x 1 , p 1 , x 2 , and p 2 are given by…”

Section: Linear Diatomic Chain (Two-body Problem)mentioning

confidence: 99%

Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

Bernardo

Esguerra

2015

Few-Body Syst

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“…where m = a m a . Analyzing (32), (33) we can conclude that the kinetic energy has the property of additivity and does not depend on composition due to relation (25).…”

Section: Properties Of Kinetic Energy In a Space With Gup And The Socmentioning

confidence: 99%

Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

Gnatenko

Tkachuk

2020

Mod. Phys. Lett. A

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A space with deformed commutation relations for coordinates and momenta leading to generalized uncertainty principle (GUP) is studied. We show that GUP causes great violation of the weak equivalence principle for macroscopic bodies, violation of additivity property of the kinetic energy, dependence of the kinetic energy on composition, great corrections to the kinetic energy of macroscopic bodies. We find that all these problems can be solved in the case of arbitrary deformation function depending on momentum if parameter of deformation is proportional inversely to squared mass.

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“…Following the ref. [33], we discussed the case the a composite system falls freely in a uniform gravitational field.…”

Section: Resultsmentioning

confidence: 99%

“…Following the Ref. [33], we can consider that a composite system falls freely in a uniform gravitational field. Then, the parameter of deformation for a macroscopic body is…”

Section: (α β)-Deformed Classical Dynamicsmentioning

confidence: 99%

Classical Dynamics Based on the Minimal Length Uncertainty Principle

Chung

2015

Int J Theor Phys

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In this paper we consider the quadratic modification of the Heisenberg algebra and its classical limit version which we call the β-deformed Poisson bracket for corresponding classical variables. We use the β-deformed Poisson bracket to discuss some physical problems in the β-deformed classical dynamics. Finally, we consider the (α, β)-deformed classical dynamics in which minimal length uncertainty principle is given by [x,p] = i (1 + αx 2 + βp 2 ). For two small parameters α, β, we discuss the free fall of particle and a composite system in a uniform gravitational field.

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Deformed Heisenberg algebra with minimal length and the equivalence principle

Cited by 72 publications

References 40 publications

Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

Exactly Solvable Dynamical Models with a Minimal Length Uncertainty

Kinetic energy properties and weak equivalence principle in a space with generalized uncertainty principle

Classical Dynamics Based on the Minimal Length Uncertainty Principle

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