Related papers: Emergence of $\pi$ from Equatorial Quantum Localiz…
Spin networks in loop quantum gravity provide a kinematical picture of quantum geometry but lack a natural mechanism for dynamical Dirac-type evolution, while the Wheeler--DeWitt equation typically enters only as an imposed constraint. We…
We study the quantization of the curved spacetime created by ultrarelativistic particles at Planckian energies. We consider a minisuperspace model based on the classical shock wave metric generated by these particles, and for which the…
A new approach is presented to compute the seismic normal modes of a fully heterogeneous, rotating planet. Special care is taken to separate out the essential spectrum in the presence of a fluid outer core. The relevant…
We show that the covariance matrix of a quantum state can be reconstructed from position measurements using the simple notion of polar duality, familiar from convex geometry. In particular, all multidimensional Gaussian states (pure or…
Quantum Ricci curvature has been introduced recently as a new, geometric observable characterizing the curvature properties of metric spaces, without the need for a smooth structure. Besides coordinate invariance, its key features are…
I consider a quantum system that possesses key features of quantum shape dynamics and show that the evolution of wave-packets will become increasingly classical at late times and tend to evolve more and more like an expanding classical…
In this paper, I propose a realistic interpretation (RI) of quantum mechanics, that is, an interpretation according to which a particle follows a definite path in spacetime. The path is not deterministic but it is rather a random walk.…
Quantum sphere is introduced as a quotient of the so-called Reflection Equation Algebra. This enables us to construct some line bundles on it by means of the Cayley-Hamilton identity whose a quantum version was discovered in \cite{PS},…
Aromaticity is a well-known phenomenon in both physics and chemistry, and is responsible for many unique chemical and physical properties of aromatic molecules. The primary feature contributing to the stability of polycyclic aromatic…
The quantum metric is a fundamental ingredient of band quantum geometry and has recently at tracted intense interest, with most of its transport signatures appearing in the intrinsic second order nonlinear conductivity. In the clean limit,…
In the previous parts of this work, we established the Prequantum Groupoid $\mathbf{T}_\omega$ as the universal geometric container for quantum mechanics. This approach, which we call the "Geometric Quantization by Paths" (GQbP) framework,…
Correspondence between classical periodic orbits and quantum shell structure is investigated for a reflection-asymmetric deformed oscillator model as a function of quadrupole and octupole deformation parameters. Periodic orbit theory…
The possibility that a classical space-time and quantum matter cohabit at the deepest level, i.e. the possibility of having a fundamental and not phenomenological semiclassical gravity, is often disregarded for lack of a good candidate…
Bifurcations of classical orbits introduce divergences into semiclassical spectra which have to be smoothed with the help of uniform approximations. We develop a technique to extract individual energy levels from semiclassical spectra…
We study the general-setting quantum geometric phase acquired by a particle in a vibrating cavity. Solving the two-level theory with the rotating-wave approximation and the SU(2) method, we obtain analytic formulae that give excellent…
In any attempt to build a quantum theory of gravity, a central issue is to unravel the structure of space-time at the smallest scale. Of particular relevance is the possible definition of coordinate functions within the theory and the study…
This paper considers an inverse problem for the classical wave equation in an exterior domain. It is a mathematical interpretation of an inverse obstacle problem which employs the dynamical scattering data of acoustic wave over a finite…
We review and extend the recently proposed model of combinatorial quantum gravity. Contrary to previous discrete approaches, this model is defined on (regular) random graphs and is driven by a purely combinatorial version of Ricci…
A geometric approach to some quantum statistical systems (including the harmonic oscillator) is presented. We regard the (N+1)-dimensional Euclidean {\it coordinate} system (X$^i$,$\tau$) as the quantum statistical system of N quantum…
We recall that in order to obtain the classical limit of quantum mechanics one needs to take the $\hbar\rightarrow 0$ limit. In addition, one also needs an explanation for the absence of macroscopic quantum superposition of position states.…