Related papers: Fractional quantum mechanics meets quantum gravity…
We study the fractional gravity for spacetimes with non-integer dimensions. Our constructions are based on a geometric formalism with the fractional Caputo derivative and integral calculus adapted to nonolonomic distributions. This allows…
The dynamics of a two-dimensional Bose-Einstein condensate in a presence of quantum fluctuations is studied. The properties of localized density distributions, quantum droplets (QDs), are analyzed by means of the variational approach. It is…
The coupling between internal degrees of freedom of quantum systems and their overall motion in an external gravitational field plays a central role in multiple extensions of Einstein's equivalence principle to quantum physics. While…
It is well known that in quantum gravity, the very geometry of space and time is subject to continual fluctuation. The mathematical formulation for this old theory is still lacking. This article formulates this more than forty-year-old…
We discuss a large class of phenomenological models incorporating quantum gravity motivated corrections to electrodynamics. The framework is that of electrodynamics in a birefringent and dispersive medium with non-local constitutive…
Quantum gravity effects are traditionally tied to short distances and high energies. In this essay we argue that, perhaps surprisingly, quantum gravity may have important consequences for the phenomenology of the infrared. We center our…
We present an analogue spacetime model that reproduces the salient features of the most common ansatz for quantum gravity phenomenology. We do this by investigating a system of two coupled Bose-Einstein condensates. This system can be tuned…
Several approaches to quantum gravity lead to nonlocal modifications of fields' dynamics. This, in turn, can give rise to nonlocal modifications of quantum mechanics at non-relativistic energies. Here, we analyze the nonlocal…
Covariant generalizations of well-known wave equations predict the existence of inertial-gravitational effects for a variety of quantum systems that range from Bose-Einstein condensates to particles in accelerators. Additional effects arise…
We propose that large quantum fluctuations of the conformal factor drastically modify classical general relativity at cosmological distance scales, resulting in a scale invariant phase of quantum gravity in the far infrared. We derive…
Using the analogy between acoustic perturbations in an ideal fluid and the description of a Klein-Gordon scalar field in a curved spacetime, we study the quasinormal modes of a quantum system: the rotating Bose-Einstein condensate. To…
Inspired by the similarity between the fractal Weierstrass function and quantum systems with discrete scaling symmetry, we establish general conditions under which the dynamics of a quantum system will exhibit fractal structure in the time…
We show that the uncertainty in distance and time measurements found by the heuristic combination of quantum mechanics and general relativity is reproduced in a purely classical and flat multi-fractal spacetime whose geometry changes with…
Phenomenological models aiming to join gravity and quantum mechanics often predict effects that are potentially measurable in refined low-energy experiments. For instance, modified commutation relations between position and momentum, that…
We here conjecture that two much-studied aspects of quantum gravity, dimensional flow and spacetime fuzziness, might be deeply connected. We illustrate the mechanism, providing first evidence in support of our conjecture, by working within…
In this thesis we investigate quantum mechanical effects to various aspects of gravitational collapse. These quantum mechanical effects are implemented in the context of the Functional Schr\"odinger formalism. The Functional Schr\"odinger…
Several quantum gravity scenarios lead to physics below the Planck scale characterised by nonlocal, Lorentz invariant equations of motion. We show that such non-local effective field theories lead to a modified Schr\"odinger evolution in…
A review of fundamentals and physical applications of fractional quantum mechanics has been presented. Fundamentals cover fractional Schr\"odinger equation, quantum Riesz fractional derivative, path integral approach to fractional quantum…
Nonlinear modifications of quantum mechanics generically lead to nonlocal effects which violate relativistic causality. We study these effects using the functional Schrodinger equation for quantum fields and identify a type of nonlocality…
The properties of quasi-one-dimensional quantum droplets of Bose-Einstein condensates are investigated analytically and numerically, taking into account the contribution of quantum fluctuations. Through the development of a variational…