scholarly journals Broadening quantum cosmology with a fractional whirl

2021 ◽  
pp. 2140005
Author(s):  
S. M. M. Rasouli ◽  
S. Jalalzadeh ◽  
P. V. Moniz
Keyword(s):  
Quantum Mechanics ◽  
Fractional Calculus ◽  
Quantum Cosmology ◽  
Cosmological Solution ◽  
Isotropic Universe ◽  
Fractional Quantum ◽  
Stiff Matter ◽  
Standard Quantum

We start by presenting a brief summary of fractional quantum mechanics, as means to convey a motivation towards fractional quantum cosmology. Subsequently, such application is made concrete with the assistance of a case study. Specifically, we investigate and then discuss a model of stiff matter in a spatially flat homogeneous and isotropic universe. A new quantum cosmological solution, where fractional calculus implications are explicit, is presented and then contrasted with the corresponding standard quantum cosmology setting.

scholarly journals From Fractional Quantum Mechanics to Quantum Cosmology: An Overture

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 313
Author(s):  
Paulo Vargas Moniz ◽  
Shahram Jalalzadeh
Keyword(s):  
Quantum Mechanics ◽  
Fractional Calculus ◽  
Quantum Cosmology ◽  
Quantum Physics ◽  
Fractional Derivatives ◽  
Fractional Quantum ◽  
Standard Cosmology ◽  
Previous Decade ◽  
The Subject ◽  
Flatness Problem

Fractional calculus is a couple of centuries old, but its development has been less embraced and it was only within the last century that a program of applications for physics started. Regarding quantum physics, it has been only in the previous decade or so that the corresponding literature resulted in a set of defying papers. In such a context, this manuscript constitutes a cordial invitation, whose purpose is simply to suggest, mostly through a heuristic and unpretentious presentation, the extension of fractional quantum mechanics to cosmological settings. Being more specific, we start by outlining a historical summary of fractional calculus. Then, following this motivation, a (very) brief appraisal of fractional quantum mechanics is presented, but where details (namely those of a mathematical nature) are left for literature perusing. Subsequently, the application of fractional calculus in quantum cosmology is introduced, advocating it as worthy to consider: if the progress of fractional calculus serves as argument, indeed useful consequences will also be drawn (to cite from Leibnitz). In particular, we discuss different difficulties that may affect the operational framework to employ, namely the issues of minisuperspace covariance and fractional derivatives, for instance. An example of investigation is provided by means of a very simple model. Concretely, we restrict ourselves to speculate that with minimal fractional calculus elements, we may have a peculiar tool to inspect the flatness problem of standard cosmology. In summary, the subject of fractional quantum cosmology is herewith proposed, merely realised in terms of an open program constituted by several challenges.

scholarly journals Kajian Integral Lintasan Levy dalam Mekanika Kuantum Fraksional untuk Membentuk Persamaan Schrodinger Fraksional

2020 ◽  
Vol 5 (1) ◽  
pp. 80-86
Author(s):  
Chandra Halim ◽  
M. Farchani Rosyid
Keyword(s):  
Stochastic Process ◽  
Quantum Mechanics ◽  
Fractal Dimension ◽  
Schrödinger Equation ◽  
Path Integral ◽  
Schrodinger Equation ◽  
Fractional Quantum ◽  
Standard Quantum ◽  
Fractional Schrödinger Equation ◽  
Fractional Schrodinger Equation

The implementation of Lévy path integral generated by Lévy stochastic process on fractional Schrödinger equation has been investigated in the framework of fractional quantum mechanics. As the comparison, the implementation of Feynmann path integral generated by Wiener stochastic process on Schrödinger equation also has been investigated in the framework of standard quantum mechanics. There are two stochastic processes. There are Lévy stochastic and Wiener stochastic process. Both of them are able to produce fractal. In fractal’s concept, there is a value known as fractal dimension. The implementation of fractal dimension is the diffusion equation obtained by using Fokker Planck equation. In this paper, Lévy and Wiener fractal dimension have been obtained. There are  for Lévy and 2 for Wiener/Brown fractal dimension. Fractional quantum mechanics is generalization of standard quantum mechanics. A fractional quantum mechanics state is represented by wave function from fractional Schrödinger equation. Fractional Schrödinger equation is obtained by using kernel of Lévy path integral generated by Lévy stochastic process. Otherwise, standard quantum mechanics state is represented by wave function from standard Schrödinger equation. Standard Schrödinger equation is obtained by using kernel of Feynmann path integral generated by Wiener/Brown stochastic process.  Both Lévy and Feynmann Kernel have been investigated and the outputs are the Fourier Integral momentum phase of those kernels. We find that the forms of those kernels have similiraty. Therefore, we obtain Schrödinger equation from Lévy and Feynmann Kernel and also the comparison of Lévy energy in fractional quantum mechanics and particle energy in standard quantum mechanics.

scholarly journals Standard quantum mechanics without observers

2021 ◽  
Vol 103 (3) ◽  
Author(s):  
Ovidiu Cristinel Stoica
Keyword(s):  
Quantum Mechanics ◽  
Standard Quantum

scholarly journals p-ADIC AND ADELIC MINISUPERSPACE QUANTUM COSMOLOGY

2002 ◽  
Vol 17 (10) ◽  
pp. 1413-1433 ◽  
Author(s):  
GORAN S. DJORDJEVIĆ ◽  
BRANKO DRAGOVICH ◽  
LJUBIŠA D. NEŠIĆ ◽  
IGOR V. VOLOVICH
Keyword(s):  
Quantum Mechanics ◽  
Cosmological Constant ◽  
Quantum Cosmology ◽  
Quantum Effects ◽  
De Sitter Space ◽  
Cosmological Models ◽  
De Sitter ◽  
Adelic Quantum Mechanics ◽  
Matter Fields

We consider the formulation and some elaboration of p-adic and adelic quantum cosmology. The adelic generalization of the Hartle–Hawking proposal does not work in models with matter fields. p-adic and adelic minisuperspace quantum cosmology is well defined as an ordinary application of p-adic and adelic quantum mechanics. It is illustrated by a few cosmological models in one, two and three minisuperspace dimensions. As a result of p-adic quantum effects and the adelic approach, these models exhibit some discreteness of the minisuperspace and cosmological constant. In particular, discreteness of the de Sitter space and its cosmological constant is emphasized.

scholarly journals Prospecting black hole thermodynamics with fractional quantum mechanics

2021 ◽  
Vol 81 (7) ◽  
Author(s):  
S. Jalalzadeh ◽  
F. Rodrigues da Silva ◽  
P. V. Moniz
Keyword(s):  
Black Hole ◽  
Quantum Mechanics ◽  
Main Tool ◽  
Acta Math ◽  
Black Hole Thermodynamics ◽  
Point Of View ◽  
Black Hole Mass ◽  
Fractional Quantum ◽  
C 73 ◽  
Fractional Parameter

AbstractThis paper investigates whether the framework of fractional quantum mechanics can broaden our perspective of black hole thermodynamics. Concretely, we employ a space-fractional derivative (Riesz in Acta Math 81:1, 1949) as our main tool. Moreover, we restrict our analysis to the case of a Schwarzschild configuration. From a subsequently modified Wheeler–DeWitt equation, we retrieve the corresponding expressions for specific observables. Namely, the black hole mass spectrum, M, its temperature T, and entropy, S. We find that these bear consequential alterations conveyed through a fractional parameter, $$\alpha $$ α . In particular, the standard results are recovered in the specific limit $$\alpha =2$$ α = 2 . Furthermore, we elaborate how generalizations of the entropy-area relation suggested by Tsallis and Cirto (Eur Phys J C 73:2487, 2013) and Barrow (Phys Lett B 808:135643, 2020) acquire a complementary interpretation in terms of a fractional point of view. A thorough discussion of our results is presented.

OBSERVABLE TIME IN QUANTUM COSMOLOGY

1995 ◽  
Vol 04 (01) ◽  
pp. 105-113 ◽  
Author(s):  
V. PERVUSHIN ◽  
T. TOWMASJAN
Keyword(s):  
Quantum Mechanics ◽  
First Principles ◽  
Quantum Cosmology ◽  
Correspondence Principle ◽  
Proper Time ◽  
Relativistic Quantum ◽  
Relativistic Quantum Mechanics ◽  
Conformal Time ◽  
Energy Factor ◽  
Definition Of

We show that the first principles of quantization and the experience of relativistic quantum mechanics can lead to the definition of observable time in quantum cosmology as a global quantity which coincides with the constrained action of the reduced theory up to the energy factor. The latter is fixed by the correspondence principle once one considers the limit of the “dust filled” Universe. The “global time” interpolates between the proper time for dust dominance and the conformal time for radiation dominance.

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