Related papers: Matter in Toy Dynamical Geometries

We investigate the geometry of a quantum universe with the topology of the four-torus. The study of non-contractible geodesic loops reveals that a typical quantum geometry consists of a small semi-classical toroidal bulk part, dressed with…

Practical implementations of quantum computing are always done in the presence of decoherence. Geometric phase is useful in the context of quantum computing as a tool to achieve fault tolerance. Recent experimental progresses on coherent…

In this article the geometry of quantum gravity is quantized in the sense of being noncommutative (first quantization) but it is also quantized in the sense of being emergent (second quantization). A new mechanism for quantum geometry is…

Quantum state space is endowed with a metric structure and Riemannian monotone metric is an important geometric entity defined on such a metric space. Riemannian monotone metrics are very useful for information-theoretic and statistical…

States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…

We gather material from many sources about the quantum potential and its geometric nature. The presentation is primarily expository but some new observations relating Q, V, and psi are indicated.

This paper considers a generalization of the notion of quantum observables in ontological models of quantum mechanics. Within this framework it is possible to construct physical models where quantum noncommutativity can arise dynamically.…

We present a simple dynamical systems model for the effect of invisible space dimensions on the visible ones. There are three premises. A: Orbits consist of flows of probabilities [P].which is the case in the setting of quantum mechanics.…

Geometrization of dynamics consists of representing trajectories by geodesics on a configuration space with a suitably defined metric. Previously, efforts were made to show that the analysis of dynamical stability can also be carried out…

We consider a geometrization, i.e., we identify geometrical structures, for the space of density states of a quantum system. We also provide few comments on a possible application of this geometrization for composite systems.

The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…

The paper studies the possible interplay between matter and geometry in scalar tensor theories of gravitation where the energy--momentum tensor is directly coupled with the Einstein tensor. After obtaining the scalar tensor representation…

Some results of author's work in a non-geometrical approach to quantum gravity are reviewed here, among them: a quantum mechanism of classical gravity giving a possibility to compute the Newton constant; asymptotic freedom at short…

The theory of Lie systems has recently been applied to Quantum Mechanics and additionally some integrability conditions for Lie systems of differential equations have also recently been analysed from a geometric perspective. In this paper…

We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by learned Hermitian matrices, and data points are mapped to states in Hilbert space. The quantum…

It is argued that spectral features of quantal systems with random interactions can be given a geometric interpretation. This conjecture is investigated in the context of two simple models: a system of randomly interacting d bosons and one…

A quantum-mechanical system comes naturally equipped with a convex space: each (Hermitian) operator has a (real) expectation value, and the expectation value of the square any Hermitian operator must be non-negative. This space is of…

We introduce the historical development and physical idea behind topological Yang-Mills theory and explain how a physical framework describing subatomic physics can be used as a tool to study differential geometry. Further, we emphasize…

We describe how one may go about performing quantum computation with arbitrary "quantum stuff", as long as it has some basic physical properties. Imagine a long strip of stuff, equipped with regularly spaced wires to provide input settings…

We present a generally covariant approach to quantum mechanics in which generalized positions, momenta and time variables are treated as coordinates on a fundamental "phase-spacetime." We show that this covariant starting point makes…