Related papers: Nonlinear Schr\"odinger equation from generalized …
We examine quantum gravity effects on entanglement by a straightforward application of the generalized uncertainty principle (GUP) to continuous-variable systems. In particular, we study the following cases: the modified uncertainty…
We explore analytically the implications of a curvature-modified extended uncertainty principle (EUP) derived in a rotating G\"odel spacetime and apply it to the construction of a semiclassical black hole model. Adapting techniques from…
We consider the one-dimensional nonlinear Schr\"odinger equation with a nonlinearity of degree $p>1$. We exhibit measures on the space of initial data for which we describe the non trivial evolution by the linear Schr\"odinger flow and we…
The Generalized Uncertainty Principle (GUP) has emerged in numerous attempts to a theory of quantum gravity and predicts the existence of a minimum length in Nature. In this work, we consider two cosmological models arising from Friedmann…
Various theories of quantum gravity predict the existence of a minimum length scale, which implies the Planck-scale modifications of the Heisenberg uncertainty principle to a so-called generalized uncertainty principle (GUP). Previous…
String theory, quantum geometry, loop quantum gravity and black hole physics all indicate the existence of a minimal observable length on the order of Planck length. This feature leads to a modification of Heisenberg uncertainty principle.…
The dynamics of models described by a one-dimensional discrete nonlinear Schr\"odinger equation is studied. The nonlinearity in these models appears due to the coupling of the electronic motion to optical oscillators which are treated in…
We study numerically the semiclassical limit for the nonlinear Schroedinger equation thanks to a modification of the Madelung transform due to E.Grenier. This approach is naturally asymptotic preserving, and allows for the presence of…
Non-relativistic quantum mechanics is shown to emerge from classical mechanics through the requirement of a relativity principle based on special transformations acting on position and momentum uncertainties. These transformations keep the…
The non-relativistic quantum mechanics with a generalized uncertainty principle (GUP) is examined in $D$-dimensional free particle and harmonic oscillator systems. The Feynman propagators for these systems are exactly derived within the…
Heisenberg showed in the early days of quantum theory that the uncertainty principle follows as a direct consequence of the quantization of electromagnetic radiation in the form of photons. As we show here the gravitational interaction of…
In a previous study, it was shown that the Generalized Uncertainty Principle (GUP) can be derived from non-extensive entropies, particularly those depending only on the probability, denoted as $S_\pm$ in the literature. This finding reveals…
We consider neutrino oscillations in non-uniform matter in a quantum field theoretic (QFT) approach, in which neutrino production, propagation and detection are considered as a single process. We find the conditions under which the…
The existence of a fundamental length scale in Nature is a common prediction of distinct quantum gravity models. Discovery of such would profoundly change current knowledge of quantum phenomena and modifications to the Heisenberg…
Beginning with ordinary quantum mechanics for spinless particles, together with the hypothesis that all experimental measurements consist of positional measurements at different times, we characterize directly a class of nonlinear quantum…
A nonlinear generalisation of Schrodinger's equation is obtained using information-theoretic arguments. The nonlinearities are controlled by an intrinsic length scale and involve derivatives to all orders thus making the equation mildly…
Based on quantum mechanical framework for the minimal length uncertainty, we demonstrate that the generalized uncertainty principle (GUP) parameter could be best constrained by recent gravitational waves observations on one hand. On other…
The non-relativistic quantum mechanics with the generalized uncertainty principle (GUP) is examined when the potential is one-dimensional $\delta-$function. It is shown that unlike usual quantum mechanics, the Schr\"{o}dinger and Feynman's…
Various theories of Quantum Gravity argue that near the Planck scale, the Heisenberg Uncertainty Principle should be replaced by the so called Generalized Uncertainty Principle (GUP). We show that the GUP gives rise to two additional terms…
Various gedanken experiments of quantum gravity phenomenology in search of a complete theory of gravity near the Planck scale indicate a modification of the Heisenberg uncertainty principle to the generalized uncertainty principle (GUP).…