Related papers: Matter in Toy Dynamical Geometries
We study deterministic and quantum dynamics from a constructive "finite" point of view, since the introduction of a continuum, or other actual infinities in physics poses serious conceptual and technical difficulties, without any need for…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…
A purely geometrical relativity theory results from a construction that produces from three-dimensional space a happy unification of Kaluza's five-dimensional theory and Weyl's conformal theory. The theory can provide geometrical…
We consider deformations of quantum mechanical operators by using the novel construction of warped convolutions. The deformation enables us to obtain several quantum mechanical effects where electromagnetic and gravitomagnetic fields play a…
Paths in an appropriate geometry are usually used as trajectories of test particles in geometric theories of gravity. It is shown that non-symmetric geometries possess some interesting quantum features. Without carrying out any quantization…
Scaling properties inherent in quantum dynamics have been studied for various systems in terms of acceleration, deceleration and time reversing. We show a scaling property of quantum dynamics on curved space-time where gravity plays an…
In this Thesis we examine the interplay between the encoding of information in quantum systems and their geometrical and topological properties. We first study photonic qubit probes of space-time curvature, showing how gauge-independent…
The manifold of pure quantum states is a complex projective space endowed with the unitary-invariant geometry of Fubini and Study. According to the principles of geometric quantum mechanics, the detailed physical characteristics of a given…
Recently\cite{BQG}, it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space-time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e.…
The principal goal of this paper is to pass all quantum probability formulas to the projective space associated to the complex Hilbert space of a given quantum system, providing a more complete geometrization of quantum theory. Quantum…
Most of the literature of computational geometry concerns geometric properties of sets of static points. M.J. Atallah introduced dynamic computational geometry, concerned with both momentary and long-term geometric properties of sets of…
In this work the phenomenology of models possessing a non-minimal coupling between matter and geometry is discussed, with a particular focus on the possibility of describing the flattening of the galactic rotation curves as a dynamically…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
This paper aims at presenting a few models of quantum dynamics whose description involves the analysis of random unitary matrices for which dynamical localization has been proven to hold. Some models come from physical approximations…
This thesis is driven by a central question: "What can we learn from random geometries about the structure of quantum spacetime?" In Chapter 2, we provide a partial review of the mathematical foundation of this thesis, random geometry. In…
The phenomenology for the deep spatial geometry of loop quantum gravity is discussed. In the context of a simple model of an atom of space, it is shown how purely combinatorial structures can affect observations. The angle operator is used…
Perceptual geometry refers to the interdisciplinary research whose objectives focuses on study of geometry from the perspective of visual perception, and in turn, applies such geometric findings to the ecological study of vision. Perceptual…
We propose quantum-mechanical systems in which the number of spatial dimensions is promoted to a dynamical quantum variable, making the effective dimension state-dependent. Interestingly, systems of this form can exhibit enhanced symmetries…
Recent results suggest that a crucial crossroad for quantum gravity is the characterization of the effective dimension of spacetime at short distances, where quantum properties of spacetime become significant. This is relevant in particular…