Related papers: Metrics and geodesics on fuzzy spaces
We study geodesics on the parameter manifold, for systems exhibiting second order classical and quantum phase transitions. The coupled non-linear geodesic equations are solved numerically for a variety of models which show such phase…
Understanding out-of-equilibrium quantum dynamics is a critical outstanding problem, with key questions regarding characterizing adiabaticity for applications in quantum technologies. We show how the metric-space approach to quantum…
Quantum coherence is a central ingredient in quantum physics with several theoretical and technological ramifications. In this work we consider a figure of merit encoding the information on how the coherence generated on average by a…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
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…
Exactly soluble models can serve as excellent tools to explore conceptual issues in non-perturbative quantum gravity. In perturbative approaches, it is only the two radiative modes of the linearized gravitational field that are quantized.…
We use the quantum metric to understand the properties of quasicrystals, represented by the one-dimensional (1D) Fibonacci chain. We show that the quantum metric can relate the localization properties of the eigenstates to the…
A special class of soft quantum measurements as a physical model of the fuzzy measurements widely used in physics is introduced and its information properties are studied in detail.
The geometro-stochastic method of quantization provides a framework for quantum general relativity, in which the principal frame bundles of local Lorentz frames that underlie the fibre-theoretical approach to classical general relativity…
Continuous quantum metrology holds promise for realizing high-precision sensing by harnessing information progressively carried away by the radiation quanta emitted into the environment. Despite recent progress, a comprehensive…
The quantum geometric tensor (QGT) characterizes the Hilbert space geometry of the eigenstates of a parameter-dependent Hamiltonian. In recent years, the QGT and related quantities have found extensive theoretical and experimental utility,…
We construct a model of quantum gravity in which dimension, topology and geometry of spacetime are dynamical. The microscopic degree of freedom is a real rectangular matrix whose rows label internal flavours, and columns label spatial…
The Einstein action for the gravitational field has some properties which make of it, after quantization, a rare prototype of systems with quantum configurations that do not have a classical analogue. Assuming spherical symmetry in order to…
We consider functional-integral quantisation of the moduli of all quantum metrics defined as square-lengths $a$ on the edges of a Lorentzian square graph. We determine correlation functions and find a fixed relative uncertainty $\Delta…
It has been found that the quantum-to-classical transition can be observed independent of macroscopicity of the quantum state for a fixed degree of fuzziness in the coarsened references of measurements. Here, a general situation, that is…
Fuzzy measures, also referred to as nonadditive measures, emerge from the foundational concept of additive measures by transforming additivity into monotonicity. In comparison to the expansive $2^n$ coefficients of fuzzy measures, additive…
Spacetime geometry is supposed to be measured by identifying the trajectories of free test particles with geodesics. In practice, this cannot be done because, being described by Quantum Mechanics, particles do not follow trajectories. As a…
We develop a geometric formulation of stochastic dynamics in which noise, diffusion, path probabilities, fluctuation theorems, and entropy production arise from the intrinsic geometry of an evolving manifold rather than from externally…
We establish a direct connection between the power of a unitary map in $d$-dimensions ($d<\infty$) to generate quantum coherence and the geometry of the set ${\cal M}_d$ of maximally abelian subalgebras (of the quantum system full operator…
We study phase structures of quantum field theories in fuzzy geometries. Several examples of fuzzy geometries as well as QFT's on such geometries are considered. They are fuzzy spheres and beyond as well as noncommutative deformations of…