Related papers: A trick for passing degenerate points in Ashtekar …
We perform a phase space analysis of a generalized modified gravity theory with nonminimally coupling between geometry and matter. We apply the dynamical system approach to this generalized model and find that in the cosmological context,…
Timelike and null hypersurfaces in the degenerate space-times in the Ashtekar theory are defined in the light of the degenerate causal structure proposed by Matschull. Using the new definition of null hypersufaces, the conjecture that the…
We develop a new formalism for the treatment of gravitational backreaction in the cosmological setting. The approach is inspired by projective techniques in non-equilibrium statistical mechanics. We employ group-averaging with respect to…
A very small amount of K\"ahler algebra (i.e. Clifford algebra of differential forms) in the real plane makes x + ydxdy emerge as a factor between the differentials of the Cartesian and polar coordinates, largely replacing the concept of…
Identifying an appropriate set of ``observables'' is a nontrivial task for most approaches to quantum gravity. We describe how it may be accomplished in the context of a recently proposed family of stochastic (but classical) dynamical laws…
We investigate the effective dynamics of a spatially flat FLRW universe coupled to a massless scalar field by applying the improved generalized uncertainty principle (GUP)-inspired deformations to the algebra of Ashtekar-Barbero variables.…
In this article we propose a dynamic approach to complex vector reconstruction in the context of quantum tomography. There are two underlying assumptions behind our reasoning. The first one claims that the evolution of a d-level pure…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
We apply the consistent discretization scheme to general relativity particularized to the Gowdy space-times. This is the first time the framework has been applied in detail in a non-linear generally-covariant gravitational situation with…
Here, we introduce the Directional Quantum Evolution Theory (DQET), a covariant reformulation of quantum mechanics where evolution takes place along a four-vector-defined arbitrary timelike direction. This method restores space-time…
We extend the definition of generalized coherent states to include the case of time-dependent dispersion. We introduce a suitable operator providing displacement and dynamical rescaling from an arbitrary ground state. As a consequence,…
On a manifold or a closed subset of a Euclidean vector space, a retraction enables to move in the direction of a tangent vector while staying on the set. Retractions are a versatile tool to perform computational tasks such as optimization,…
Global constraints proved themselves to be an efficient tool for modelling and solving large-scale real-life combinatorial problems. They encapsulate a set of binary constraints and using global reasoning about this set they filter the…
We propose a solution to the problem of time for systems with a single global Hamiltonian constraint. Our solution stems from the observation that, for these theories, conventional gauge theory methods fail to capture the full classical…
In this paper, we study the convergence for solutions to a sequence of (possibly degenerate) stochastic differential equations with jumps, when the coefficients converge in some appropriate sense. Our main tools are the superposition…
A generalized Black-Scholes equation is considered on the semi-axis. It is transformed on the interval (0,1) in order to make the computational domain finite. The new parabolic operator degenerates at the both ends of the interval and we…
We give a proposal to generalize the concept of the differential equations on time scales, such that they can be more appropriate for the analysis of real world problems, and give more opportunities to increase the theoretical depth of…
We derive a generalized deviation equation in Riemann-Cartan spacetime. The equation describes the dynamics of the connecting vector which links events on two general adjacent world lines. Our result is valid for any theory in a…
We use differential equations based approaches to provide some {\it \textbf{physics}} insights into analyzing the dynamics of popular optimization algorithms in machine learning. In particular, we study gradient descent, proximal gradient…
In this paper, we study an ordinary differential equation with a degenerate global attractor at the origin, to which we add a white noise with a small parameter that regulates its intensity. Under general conditions, for any fixed…