Related papers: Classical Aspects of a Distributional 3+1 Foam Mod…
A mathematical formalism for treating spacetime topology as a quantum observable is provided. We describe spacetime foam entirely in algebraic terms. To implement the correspondence principle we express the classical spacetime manifold of…
Diffusive molecular dynamics is a novel model for materials with atomistic resolution that can reach diffusive time scales. The main ideas of diffusive molecular dynamics are to first minimize an approximate variational Gaussian free energy…
We consider quantization of the positive curvature Friedmann cosmology in the unimodular modification of Einstein's theory, in which the spacetime four-volume appears as an explicit time variable. The Hamiltonian admits self-adjoint…
Diffusion models have garnered significant attention since they can effectively learn complex multivariate Gaussian distributions, resulting in diverse, high-quality outcomes. They introduce Gaussian noise into training data and reconstruct…
A generalized version of Bertrand's theorem on spherically symmetric curved spaces is presented. This result is based on the classification of (3+1)-dimensional (Lorentzian) Bertrand spacetimes, that gives rise to two families of…
A rotating cosmic string spacetime has a singularity along a timelike curve corresponding to a one-dimensional source of angular momentum. Such spacetimes are not globally hyperbolic: they admit closed timelike curves near the string. This…
We present conservative 3+1 general relativistic variable Eddington tensor radiation transport equations, including greater elaboration of the momentum space divergence (that is, the energy derivative term) than in previous work. These…
By using the 3+1 point of view and parametrized Minkowski theories we develop the theory of {\it non-inertial} frames in Minkowski space-time. The transition from a non-inertial frame to another one is a gauge transformation connecting the…
Simple models of a classical spacetime foam are considered, which consist of identical static defects embedded in Minkowski spacetime. Plane-wave solutions of the vacuum Maxwell equations with appropriate boundary conditions at the defect…
A vibrational model of transport properties of dense fluids assumes that solid-like oscillations of atoms around their temporary equilibrium positions dominate the dynamical picture. The temporary equilibrium positions of atoms do not form…
The Wigner function formalism has been applied to the analysis of elastic scattering processes. The new element of known formalism is the choice of the phase space on which the Wigner function is defined. This phase space is 4-dimensional…
We present a classical kinetically constrained model of interacting particles on a triangular ladder, which displays diffusion and jamming and can be treated by means of a classical-quantum mapping. Interpreted as a theory of interacting…
In this paper we show that under general resonance the classical piecewise linear Fermi-Ulam accelerator behaves substantially different from its quantization in the sense that the classical accelerator exhibits typical recurrence and…
By considering a lattice model of extended phase space, and using techniques of noncommutative differential geometry, we are led to: (a) the conception of vector fields as generators of motion and transition probability distributions on the…
The 3+1 Hamiltonian formulation in the gauge $D_tN=-K$ on the lapse function fixes the direction of time associated with the trace $K$ of the extrinsic curvature tensor. The Hamiltonian equations hereby become hyperbolic. We study this new…
Generalized Fourier transformation between the position and the momentum representation of a quantum state is constructed in a coordinate independent way. The only ingredient of this construction is the symplectic (canonical) geometry of…
A time dependent variational approach is used to derive the equations of motion for the \lambda \phi^4 model. The simultaneous evolution of the quantum fluctuations and of the classical part of the field is considered in a lattice of 1+1…
We present a detailed analysis of a recently introduced version of Causal Dynamical Triangulations (CDT) that does not rely on a distinguished time slicing. Focussing on the case of 2+1 spacetime dimensions, we analyze its geometric and…
We develop a new class of chaotic inflation models with spontaneously broken conformal invariance. Observational consequences of a broad class of such models are stable with respect to strong deformations of the scalar potential. This…
A semiclassical description of quantum systems is applied to probe the dynamics of the cosmological model of an inflationary universe with quadratic inflaton potential, described in a quantum framework of geometrodynamics. The systematic…