scholarly journals Minimal length uncertainty relation and ultraviolet regularization

1997 ◽  
Vol 55 (12) ◽  
pp. 7909-7920 ◽  
Author(s):  
Achim Kempf ◽  
Gianpiero Mangano
Keyword(s):  
Uncertainty Relation ◽  
Minimal Length ◽  
Ultraviolet Regularization

scholarly journals On the Minimal Length Uncertainty Relation and the Foundations of String Theory

2011 ◽  
Vol 2011 ◽  
pp. 1-30 ◽  
Author(s):  
Lay Nam Chang ◽  
Zachary Lewis ◽  
Djordje Minic ◽  
Tatsu Takeuchi
Keyword(s):  
General Relativity ◽  
Quantum Theory ◽  
String Theory ◽  
Momentum Space ◽  
Vacuum Energy ◽  
Uncertainty Relation ◽  
Minimal Length

We review our work on the minimal length uncertainty relation as suggested by perturbative string theory. We discuss simple phenomenological implications of the minimal length uncertainty relation and then argue that the combination of the principles of quantum theory and general relativity allow for a dynamical energy-momentum space. We discuss the implication of this for the problem of vacuum energy and the foundations of nonperturbative string theory.

scholarly journals Minimal length uncertainty relation and gravitational quantum well

2006 ◽  
Vol 74 (3) ◽  
Author(s):  
Fabian Brau ◽  
Fabien Buisseret
Keyword(s):  
Quantum Well ◽  
Uncertainty Relation ◽  
Minimal Length

scholarly journals The Minimal Length and the Shannon Entropic Uncertainty Relation

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Pouria Pedram
Keyword(s):  
Quantum Mechanics ◽  
Harmonic Oscillator ◽  
Commutation Relation ◽  
Deformation Parameter ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Adjoint Representation ◽  
Minimal Length ◽  
Entropic Uncertainty Relation ◽  
Ordinary Quantum

In the framework of the generalized uncertainty principle, the position and momentum operators obey the modified commutation relationX,P=iħ1+βP2, whereβis the deformation parameter. Since the validity of the uncertainty relation for the Shannon entropies proposed by Beckner, Bialynicki-Birula, and Mycielski (BBM) depends on both the algebra and the used representation, we show that using the formally self-adjoint representation, that is,X=xandP=tan⁡βp/β, where[x,p]=iħ, the BBM inequality is still valid in the formSx+Sp≥1+ln⁡πas well as in ordinary quantum mechanics. We explicitly indicate this result for the harmonic oscillator in the presence of the minimal length.

scholarly journals Thermostatistics with minimal length uncertainty relation

2012 ◽  
Vol 2012 (10) ◽  
pp. P10013 ◽  
Author(s):  
B Vakili ◽  
M A Gorji
Keyword(s):  
Uncertainty Relation ◽  
Minimal Length

scholarly journals Minimal length uncertainty relation and the hydrogen spectrum

2003 ◽  
Vol 572 (1-2) ◽  
pp. 37-42 ◽  
Author(s):  
R Akhoury ◽  
Y.-P Yao
Keyword(s):  
Uncertainty Relation ◽  
Minimal Length

scholarly journals Position and momentum uncertainties of a particle in a V-shaped potential under the minimal length uncertainty relation

2015 ◽  
Vol 30 (35) ◽  
pp. 1550206 ◽  
Author(s):  
Zachary Lewis ◽  
Ahmed Roman ◽  
Tatsu Takeuchi
Keyword(s):  
Harmonic Oscillator ◽  
Commutation Relation ◽  
Classical Limit ◽  
Uncertainty Relation ◽  
Minimal Length ◽  
Positive Energy ◽  
Positive Mass ◽  
Negative Mass ◽  
Energy Eigenstates ◽  
Theory Comparison

We calculate the uncertainties in the position and momentum of a particle in the 1D potential [Formula: see text], [Formula: see text], when the position and momentum operators obey the deformed commutation relation [Formula: see text], [Formula: see text]. As in the harmonic oscillator case, which was investigated in a previous publication, the Hamiltonian [Formula: see text] admits discrete positive energy eigenstates for both positive and negative mass. The uncertainties for the positive mass states behave as [Formula: see text] as in the [Formula: see text] limit. For the negative mass states, however, in contrast to the harmonic oscillator case where we had [Formula: see text], both [Formula: see text] and [Formula: see text] diverge. We argue that the existence of the negative mass states and the divergence of their uncertainties can be understood by taking the classical limit of the theory. Comparison of our results is made with previous work by Benczik.

scholarly journals Effect of the minimal length uncertainty relation on the density of states and the cosmological constant problem

2002 ◽  
Vol 65 (12) ◽  
Author(s):  
Lay Nam Chang ◽  
Djordje Minic ◽  
Naotoshi Okamura ◽  
Tatsu Takeuchi
Keyword(s):  
Cosmological Constant ◽  
Density Of States ◽  
Uncertainty Relation ◽  
Minimal Length ◽  
Cosmological Constant Problem

scholarly journals DSR-GUP, maximally localized state, and black hole thermodynamics

2019 ◽  
Vol 2019 (12) ◽  
Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi
Keyword(s):  
Black Hole ◽  
Special Relativity ◽  
Uncertainty Relation ◽  
Generalized Uncertainty Principle ◽  
Minimal Length ◽  
Black Hole Thermodynamics ◽  
Generalized Uncertainty Relation ◽  
Localized State ◽  
Doubly Special Relativity ◽  
New Type

Abstract We consider a new type of doubly special relativity transformation which gives a new types of generalized uncertainty principle. This model is known to have invariant Planck energy (or Planck momentum) and minimal length. For this model we discuss the generalized uncertainty relation and compute the minimal length and momentum upper bound. We also compute the corresponding maximally localized state explicitly. Finally, we use the generalized uncertainty relation compatible with doubly special relativity to discuss black hole thermodynamics.

scholarly journals Entropic Analysis of the Quantum Oscillator with a Minimal Length

Proceedings ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 57
Author(s):  
David Puertas-Centeno ◽  
Mariela Portesi
Keyword(s):  
Excited State ◽  
Harmonic Oscillator ◽  
Deformation Parameter ◽  
Uncertainty Relation ◽  
Minimal Length ◽  
Quantum Oscillator ◽  
Position Distribution ◽  
Entropic Uncertainty Relation ◽  
First Excited State ◽  
Generalized Entropies

The well-known Heisenberg–Robertson uncertainty relation for a pair of noncommuting observables, is expressed in terms of the product of variances and the commutator among the operators, computed for the quantum state of a system. Different modified commutation relations have been considered in the last years with the purpose of taking into account the effect of quantum gravity. Indeed it can be seen that letting [ X , P ] = i ℏ ( 1 + β P 2 ) implies the existence of a minimal length proportional to β . The Bialynicki-Birula–Mycielski entropic uncertainty relation in terms of Shannon entropies is also seen to be deformed in the presence of a minimal length, corresponding to a strictly positive deformation parameter β . Generalized entropies can be implemented. Indeed, results for the sum of position and (auxiliary) momentum Rényi entropies with conjugated indices have been provided recently for the ground and first excited state. We present numerical findings for conjugated pairs of entropic indices, for the lowest lying levels of the deformed harmonic oscillator system in 1D, taking into account the position distribution for the wavefunction and the actual momentum.

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