Related papers: A model for the motion of a particle in a quantum …
An otherwise free classical particle moving through an extended spatially homogeneous medium with which it may exchange energy and momentum will undergo a frictional drag force in the direction opposite to its velocity with a magnitude…
We present evidence that a nonperturbative model of quantum gravity defined via Euclidean dynamical triangulations contains a region in parameter space with an extended 4-dimensional geometry when a non-trivial measure term is included in…
This is an introduction to an algebraic construction of a gravity theory on noncommutative spaces which is based on a deformed algebra of (infinitesimal) diffeomorphisms. We start with some fundamental ideas and concepts of noncommutative…
The formalism of classical particle dynamics is reinvestigated according to the basic requirement of causal consistency, and a new equation of particle dynamics, which is more general and more in line with classical mechanics experiments…
We investigate the difference between classical and quantum dynamics of coupled magnetic dipoles. We prove that in general the dynamics of the classical interaction Hamiltonian differs from the corresponding quantum model, regardless of the…
It is often expected that one cannot treat spacetime as a continuous manifold as the Planck scale is approached, because of to possible effects due to a quantum theory of gravity. There have been several proposals to model such a deviation…
We study the role of non-perturbative quantum gravity effects in the Ekpyrotic/Cyclic model using the effective framework of loop quantum cosmology in the presence of anisotropies. We show that quantum geometric modifications to the…
We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…
A formalism is presented in which quantum particle dynamics can be developed on its own rather than `quantization' of an underlying classical theory. It is proposed that the unification of probability and dynamics should be considered as…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function $ d$, or by the world function $\sigma =d^{2}/2$. One suggests a new general method of the…
Lie-Poisson electrodynamics describes the semi-classical limit of non-commutative $U(1)$ gauge theory, characterized by Lie-algebra-type non-commutativity. We focus on the mechanics of a charged point-like particle moving in a given gauge…
A variational phase space is constructed for a compact and piecewise flat Riemannian manifold. An extended action functional is provided such that the variational dynamics generate a symplectic flow on the phase space. This symplectic flow…
Standard particle theory is based on quantized matter embedded in a classical geometry. Here, a complementary model is proposed, based on classical matter -- massive bodies, without quantum properties -- embedded in a quantum geometry. It…
We develop a variational formulation of a particle with spin in a curved space-time background. The model is based on a singular Lagrangian which provides equations of motion, a fixed value of spin and Frenkel condition on spin-tensor.…
In quantum field theory the parameters of the vacuum action are subject to renormalization group running. In particular, the ``cosmological constant'' is not a constant in a quantum field theory context, still less should be zero. In this…
The mechanism of the transition of a dynamical system from quantum to classical mechanics is one of the remaining challenges of quantum theory. Currently, it is considered to occur via decoherence caused by entanglement and/or stochastic…
A proper deformation of the underlying coordinate and momentum commutation relations in quantum mechanics provides a phenomenological approach to account for the influence of gravity on small scales. Introducing the squared momentum term…
Quantum Euclidean spaces, as Moyal deformations of Euclidean spaces, are the model examples of noncompact noncommutative manifold. In this paper, we study the quantum Euclidean space equipped with partial derivatives satisfying canonical…
We study a Newtonian cosmological model in the context of a noncommutative space. It is shown that the trajectories of a test particle undergo modifications such that it no longer satisfies the cosmological principle. For the case of a…
Branching flow -- a phenomenon known for steady wave propagation in two-dimensional weak correlated random potential is also present in the time-dependent Schr\"odinger equation for a single particle in one dimension, moving in a…