Related papers: Quantum Geometry and Nonlinear Responses in Magnet…
This work reports on the construction of a nonlinear distributional geometry (in the sense of Colombeau's special setting) and its applications to general relativity with a special focus on the distributional description of impulsive…
In this paper we point out some possible links between different approaches to quantum gravity and theories of the Planck scale physics. In particular, connections between Loop Quantum Gravity, Causal Dynamical Triangulations,…
After an introduction to some basic issues in non-commutative geometry (Gel'fand duality, spectral triples), we present a "panoramic view" of the status of our current research program on the use of categorical methods in the setting of…
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We…
We propose a modified Boltzmann nonlinear electric-transport framework which differs from the nonlinear generalization of the linear Boltzmann formalism by a contribution that has no counterpart in linear response. This contribution follows…
We consider a model of Quantum Gravity phenomenology, based on the idea that space-time may have some unknown granular structure that respects the Lorentz symmetry. The proposal involves non-trivial couplings of curvature to matter fields…
Quantum matrix geometry is the underlying geometry of M(atrix) theory. Expanding upon the idea of level projection, we propose a quantum-oriented non-commutative scheme for generating the matrix geometry of the coset space $G/H$. We employ…
This paper proposes a brain-inspired approach to quantum machine learning with the goal of circumventing many of the complications of other approaches. The fact that quantum processes are unitary presents both opportunities and challenges.…
We show that quantum entanglement states are associated with multilinear polynomials that cannot be factored. By using these multilinear polynomials, we propose a geometric representation for entanglement states. In particular, we show that…
In this work we build a theoretical framework for the transport of information in quantum systems. This is a framework aimed at describing how out of equilibrium open quantum systems move information around their state space, using an…
Nonlinear electronic transport has emerged as a powerful probe of the quantum geometry in topological quantum materials, where the band topology and broken symmetries facilitate power law current voltage responses beyond Ohms law. While…
Quantum mechanics in its presently known formulation requires an external classical time for its description. A classical spacetime manifold and a classical spacetime metric are produced by classical matter fields. In the absence of such…
Quantum geometry, which describes the geometry of Bloch wavefunctions in solids, has become a cornerstone of modern quantum condensed matter physics. The quantum geometrical tensor encodes this geometry through two fundamental components:…
The kinematical setting of spherically symmetric quantum geometry, derived from the full theory of loop quantum gravity, is developed. This extends previous studies of homogeneous models to inhomogeneous ones where interesting field theory…
Together with collaborators, we introduced a noncommutative Riemannian geometry over Moyal algebras and systematically developed it for noncommutative spaces embedded in higher dimensions in the last few years. The theory was applied to…
A model of joint random walk of two agents on an infinite plane is considered. The agents possess no means of mutual classical communication, but have access to quantum entanglement resource which is used according to a pre-arranged…
There have been several propositions for a geometric and essentially non-linear formulation of quantum mechanics. From a purely mathematical point of view, the point of view of Jordan algebra theory might give new strength to such…
In this paper and a companion paper, we show how the framework of information geometry, a geometry of discrete probability distributions, can form the basis of a derivation of the quantum formalism. The derivation rests upon a few…
A link between canonical quantum gravity and fermionic quantum field theory is established in this paper. From a spectral triple construction which encodes the kinematics of quantum gravity semi-classical states are constructed which, in a…
A detailed study is made of the noncommutative geometry of $R^3_q$, the quantum space covariant under the quantum group $SO_q(3)$. For each of its two $SO_q(3)$-covariant differential calculi we find its metric, the corresponding frame and…