Related papers: Quantum stochastic processes in two dimensional sp…
We study a (relativistic) Wiener process on a complexified (pseudo-)Riemannian manifold. Using Nelson's stochastic quantization procedure, we derive three equivalent descriptions for this problem. If the process has a purely real quadratic…
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…
We show that the dynamics of a quantum system can be represented by the dynamics of an underlying classical systems obeying the Hamilton equations of motion. This is achieved by transforming the phase space of dimension $2n$ into a Hilbert…
Algorithms are described for efficiently simulating quantum mechanical systems on quantum computers. A class of algorithms for simulating the Schrodinger equation for interacting many-body systems are presented in some detail. These…
Physical research looks for clues to quantum properties of the gravitational field. On the basis of the common Schr\"odinger theory, a simple model of the quantization of a Friedmann universe comprising dust and radiation is investigated.…
Virtual particles expected to occur in microscopic processes as they are introduced, for instance by Feynman in the Quantum Electro Dynamics, as photons performing in an anonymous way in the interaction between two electrons. This note…
We prove that the well-known Heisenberg uncertainty relations and Landau-Peierls uncertainty relations implicitly contain ``hidden'' angular variables, which belong to new uncertainty relations. Based on the obtained relations, we derive a…
We introduce a numerical method to simulate nonlinear open quantum dynamics of a particle in situations where its state undergoes significant expansion in phase space while generating small quantum features at the phase-space Planck scale.…
Usual quantum mechanics requires a fixed, background, spacetime geometry and its associated causal structure. A generalization of the usual theory may therefore be needed at the Planck scale for quantum theories of gravity in which…
An approach to evaluation of the smooth Feynman path integrals is developed for the study of quantum fluctuations of particles and fields in Euclidean time-space. The paths are described by sum of Gauss functions and are weighted with…
The study of physics at the Planck scale has garnered significant attention due to its implications for understanding the fundamental nature of the universe. At the Planck scale, quantum fluctuations challenge the classical notion of…
The question about the existence of so-called ``hidden'' variables in quantum mechanics and the perception of the completeness of quantum mechanics are two sides of the same coin. Quantum analytical mechanics constitutes a completion of…
The article is devoted to stochastic processes with values in finite- and infinite-dimensional vector spaces over infinite fields $\bf K$ of zero characteristics with non-trivial non-archimedean norms. For different types of stochastic…
A one-dimensional Klein-Gordon problem, which is a physical model for a quantum particle submitted to a potential barrier, is studied numerically : using a variational formulation and a Newmark numerical method, we compute the mean position…
Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
Temporal quantum states generalize the multipartite density operator formalism to the time domain, enabling a unified treatment of quantum systems with both timelike and spacelike correlations. Despite a growing body of temporal state…
Semiclassical Einstein-Langevin equations for arbitrary small metric perturbations conformally coupled to a massless quantum scalar field in a spatially flat cosmological background are derived. Use is made of the fact that for this problem…
The aim of these notes is to elucidate some aspects of quantum field theory in curved spacetime, especially those relating to the notion of particles. A selection of issues relevant to wave-particle duality is given. The case of a generic…
We discuss the quantum dynamics of a particle in static curved spacetimes in a coordinate representation. The scheme is based on the analysis of the squared energy operator E^2, which is quadratic in momenta and contains a scalar curvature…