Related papers: Probing the quantum nature of spacetime by diffusi…
A profound quantum-gravitational effect of space-time dimension running with respect to the size of space-time region has been discovered a few years ago through the numerical simulations of lattice quantum gravity in the framework of…
A new formalism will be presented in order to study real time evolution of quantum systems at finite temperature. Probability distributions for time-correlated observables will be studied non-perturbatively and fully quantized. This works…
This paper is a sequel in which we further analyze the recently derived quantum gravity equations which apply in accelerating cosmological spacetimes and whose solutions should be equivalent to all order re-summations of the perturbative…
Measurable quantities that have positive values in classical dynamical systems need not to be positive in quantum theory. For example, consider a free quantum mechanical particle in one dimension. There are quantum states in which the…
The theory of quantum gravity is aimed to fuse general relativity with quantum theory into a more fundamental framework. The space of quantum gravity provides both the non-fixed causality of general relativity and the quantum uncertainty of…
Fundamental quantum gravity theories are known to be notoriously difficult to extract viable testable predictions out of. In this paper, we aim to incorporate putative quantum corrections coming from loop quantum gravity in deriving…
Using simple kinematical arguments, we derive the Fokker-Planck equation for diffusion processes in curved spacetimes. In the case of Brownian motion, it coincides with Eckart's relativistic heat equation (albeit in a simpler form), and…
We initiate the study of Horava-Lifshitz models of gravity in the framework of spectral geometry. As the first step, we calculate the dimension of space-time. It is shown, that for the natural choice of a Dirac operator (or rather…
The paper examines stochastic diffusion within an expanding space-time framework. It starts with providing a rationale for the considered model and its motivation from cosmology where the expansion of space-time is used in modelling various…
The issue of non-locality in quantum mechanics can potentially be resolved by considering relativistically covariant diffusion in four-dimensional spacetime. Stochastic particles described by the Klein-Gordon equation are shown to undergo a…
The observed large-scale structure in our Universe is seen as a result of quantum fluctuations amplified by spacetime evolution. This, and related problems in cosmology, asks for an understanding of the quantum fields of the standard model…
.Stochastic models based on random diffusivities, such as the diffusing-diffusivity approach, are popular concepts for the description of non-Gaussian diffusion in heterogeneous media. Studies of these models typically focus on the moments…
In this work, we consider a probability representation of quantum dynamics for finite-dimensional quantum systems with the use of pseudostochastic maps acting on true probability distributions. These probability distributions are obtained…
We emphasize that a specific aspect of quantum gravity is the absence of a super-selection rule that prevents a linear superposition of different gravitational charges. As an immediate consequence, we obtain a tiny, but observable,…
Unimodular gravity is an appealing approach to address the cosmological constant problem. In this scenario, the vacuum energy density of quantum fields does not gravitate and the cosmological constant appears merely as an integration…
We develop a novel approach for the construction of quantile processes governing the stochastic dynamics of quantiles in continuous time. Two classes of quantile diffusions are identified: the first, which we largely focus on, features a…
We survey some philosophical aspects of the search for a quantum theory of gravity, emphasising how quantum gravity throws into doubt the treatment of spacetime common to the two `ingredient theories' (quantum theory and general…
For ergodic adiabatic quantum systems, we study the evolution of energy distribution as the system evolves in time. Starting from the von Neumann equation for the density operator, we obtain the quantum analogue of the Smoluchowski equation…
Getting signatures of quantum gravity is one of the topical lines of research in modern theoretical physics and cosmology. This short review faces this challenge under a novel perspective. Instead of separating quantum-gravity effects of a…
Quantum light propagation through turbulent atmosphere has become a subject of intensive research, spanning both theoretical and experimental studies. This interest is driven by its important applications in free-space quantum…