generalized uncertainty relation
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Author(s):  
Rami Ahmad El-Nabulsi

A new generalized uncertainty relation is constructed based on Li-Ostoja-Starzewski fractional gradient operator of order 0 <  α  ≤ 1 introduced recently in literature which is motivated from dimensional regularization method. The new generalized uncertainty relation leads to a new form of Schrödinger equation and emergent position-dependent mass. Special forms of position-dependent mass were studied and the problem of a particle in a box was explored. Dissimilar forms of allowed quantum energies were obtained which lead to different scenarios. We have confronted the theory with observations by evaluating the maximum wavelength obtained in the 1,3-butadiene molecule. Several features were discussed accordingly.


Author(s):  
Won Sang Chung ◽  
Hassan Hassanabadi

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.


Author(s):  
Hung Quang Nguyen ◽  
Tu Quang Bui

We show that the famous Heisenberg uncertainty relation for two incompatible observables can be generalized elegantly to the determinant form for N arbitrary observables. To achieve this purpose, we propose a generalization of the Cauchy-Schwarz inequality for two sets of vectors. Simple consequences of the N-ary uncertainty relation are also discussed. Keywords: Generalized uncertainty relation, Generalized uncertainty principle, Generalized Cauchy-Schwarz inequality.


2016 ◽  
Vol 94 (10) ◽  
pp. 1080-1084 ◽  
Author(s):  
Guqiang Li

By using the brick-wall model, the quantum entropies of static spherical black hole surrounded by quintessence due to the Weyl neutrino, electromagnetic, massless Rarita–Schwinger, and gravitational fields for the source-free case are investigated from a generalized uncertainty relation. It is shown that in addition to the usual quadratically and logarithmically divergent terms, there exist additional quadratic, biquadratic, and logarithmic divergences at ultraviolet σ → 0, which not only depend on the black hole characteristics but also on the spins of the fields and the gravity correction factor. These additional terms describe the contribution of the quantum fields to the entropy and the effect of gravitational interactions on it. After the smallest length scale is taken into account, we find that the contribution of the gravitational interactions to the entropy is larger than the usual dominant term and becomes a part of the whole dominant term, so it is very important and cannot be neglected.


Author(s):  
Liang Cai

Motivated by the direct approach to quantum extensions of Fisher information in Chen and Luo [Front. Math. China 2 (2007) 359], we introduce a further generalized version of Wigner–Yanase–Dyson information, and investigate its fundamental properties including positivity, convexity and super-additivity, etc. As an application, we present a generalized uncertainty relation.


2015 ◽  
Vol 54 (8) ◽  
pp. 2644-2651 ◽  
Author(s):  
Zhengli Chen ◽  
Lili Liang ◽  
Haojing Li ◽  
Wenhua Wang

2009 ◽  
Vol 48 (11) ◽  
pp. 3220-3227
Author(s):  
Ren Zhao ◽  
Lichun Zhang ◽  
Yueqin Wu ◽  
Huaifan Li

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