Das, Saurya

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https://opus.uleth.ca/handle/10133/3587

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Browsing Das, Saurya by Author "Ali, Ahmed Farag"

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    Cosmology from quantum potential
    (2016-01-20) Ali, Ahmed Farag; Das, Saurya
    It was shown recently that replacing classical geodesics with quantal (Bohmian) trajectories gives rise to a quantum corrected Raychaudhuri equation (QRE). Here we derive the second order Friedmann equations from the QRE, and show that this also contains a couple of quantum correction terms, the first of which can be interpreted as cosmological constant (and gives a correct estimate of its observed value), or as dark matter, while the second as a radiation term in the early universe, which gets rid of the big-bang singularity and predicts an infinite age of our universe.
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    Discreteness of space from GUP II: relativistic wave equations
    (2015-12-22) Das, Saurya; Vagenas, Elias C.; Ali, Ahmed Farag
    Various theories of Quantum Gravity predict modifications of the Heisenberg Uncertainty Prin- ciple near the Planck scale to a so-called Generalized Uncertainty Principle (GUP). In some recent papers, we showed that the GUP gives rise to corrections to the Schrdinger equation, which in turn affect all quantum mechanical Hamiltonians. In particular, by applying it to a particle in a one- dimensional box, we showed that the box length must be quantized in terms of a fundamental length (which could be the Planck length), which we interpreted as a signal of fundamental discreteness of space itself. In this Letter, we extend the above results to a relativistic particle in a rectangular as well as a spherical box, by solving the GUP-corrected KleinGordon and Dirac equations, and for the latter, to two and three dimensions. We again arrive at quantization of box length, area and volume and an indication of the fundamentally grainy nature of space. We discuss possible implications.
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    Discreteness of space from the generalized uncertainty principle
    (2015-12-15) Ali, Ahmed Farag; Das, Saurya; Vagenas, Elias C.
    Various approaches to Quantum Gravity (such as String Theory and Doubly Special Relativity), as well as black hole physics predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called Generalized Uncertainty Principle (GUP). We propose a GUP consistent with String Theory, Doubly Special Relativity and black hole physics, and show that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it implies that the space which confines it must be quantized. This suggests that space itself is discrete, and that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this signals the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale.
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    Effect of the generalized uncertainty principle on post-inflation preheating
    (2016-01-19) Chemissany, Wissam; Das, Saurya; Ali, Ahmed Farag; Vagenas, Elias C.
    We examine effects of the Generalized Uncertainty Principle, predicted by various theories of quantum gravity to replace the Heisenberg’s uncertainty principle near the Planck scale, on post inflation preheating in cosmology, and show that it can predict either an increase or a decrease in parametric resonance and a corresponding change in particle production. Possible implications are considered.
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    A proposal for testing quantum gravity in the lab
    (2015-12-22) Ali, Ahmed Farag; Das, Saurya; Vagenas, Elias C.
    Attempts to formulate a quantum theory of gravitation are collectively known as quantum gravity. Various approaches to quantum gravity such as string theory and loop quantum gravity, as well as black hole physics and doubly special relativity theories predict a minimum measurable length, or a maximum observable momentum, and related modifications of the Heisenberg Uncertainty Principle to a so-called generalized uncertainty principle (GUP). We have proposed a GUP consistent with string theory, black hole physics and doubly special relativity theories and have showed that this modifies all quantum mechanical Hamiltonians. When applied to an elementary particle, it suggests that the space that confines it must be quantized, and in fact that all measurable lengths are quantized in units of a fundamental length (which can be the Planck length). On the one hand, this may signal the breakdown of the spacetime continuum picture near that scale, and on the other hand, it can predict an upper bound on the quantum gravity parameter in the GUP, from current observations. Furthermore, such fundamental discreteness of space may have observable consequences at length scales much larger than the Planck scale. Because this influences all the quantum Hamiltonians in an universal way, it predicts quantum gravity corrections to various quantum phenomena. Therefore, in the present work we compute these corrections to the Lamb shift, simple harmonic oscillator, Landau levels, and the tunneling current in a scanning tunneling microscope.