Related papers: On Geometric Quantum Confinement in Grushin-type M…
We study a class of design problems in solid mechanics, leading to a variation on the classical question of equi-dimensional embeddability of Riemannian manifolds. In this general new context, we derive a necessary and sufficient existence…
A number of affine-Weyl-invariant integrable and exactly-solvable quantum models with trigonometric potentials is considered in the space of invariants (the space of orbits). These models are completely-integrable and admit extra particular…
Inspired by the Gromov-Hausdorff distance, we define the intrinsic flat distance between oriented $m$ dimensional Riemannian manifolds with boundary by isometrically embedding the manifolds into a common metric space, measuring the flat…
Optimization with constraints is a typical problem in quantum physics and quantum information science that becomes especially challenging for high-dimensional systems and complex architectures like tensor networks. Here we use ideas of…
The Weyl principle is extended from the Riemannian to the pseudo-Riemannian setting, and subsequently to manifolds equipped with generic symmetric $(0,2)$-tensors. More precisely, we construct a family of generalized curvature measures…
We formulate an inverse problem for an uncoupled space-time fractional Schr\"odinger equation on closed manifolds. Our main goal is to determine the fractional powers and the Riemannian metric (up to an isometry) simultaneously from the…
We discuss the physics of a restricted Weyl symmetry in a curved space-time where a gauge parameter $\Omega(x)$ of Weyl transformation satisfies a constraint $\Box \Omega = 0$. First, we present a model of QED where we have a restricted…
The unification of general relativity with quantum theory will also require a coming together of the two quite different mathematical languages of general relativity and quantum theory, i.e., of differential geometry and functional analysis…
We propose employing the extension of the Lehmann-Maehly-Goerisch method developed by Zimmermann and Mertins, as a highly effective tool for the pollution-free finite element computation of the eigenfrequencies of the resonant cavity…
Explicit formulas for the $G_2$-components of the Riemannian curvature tensor on a manifold with a $G_2$ structure are given in terms of Ricci contractions. We define a conformally invariant Ricci-type tensor that determines the…
We propose an intrinsic geometric framework on the space of operational contexts, specified by channels, stationary states, and self-preservation functionals. Each context C carries a pointer algebra, internal charges, and a self-consistent…
We present an approach to Gromov-Witten invariants that works on arbitrary (closed) symplectic manifolds. We avoid genericity arguments and take into account singular curves in the very formulation. The method is by first endowing mapping…
We give a new proof of the existence of nontrivial quasimeromorphic mappings on a smooth Riemannian manifold, using solely the intrinsic geometry of the manifold.
The boundary-value problem for Laplace-type operators acting on smooth sections of a vector bundle over a compact Riemannian manifold with generalized local boundary conditions including both normal and tangential derivatives is studied.…
To investigate the possibility that intrinsic gravitational decoherence can be theoretically demonstrated within canonical quantum gravity, we develop a model of a self-gravitating interferometer. We search for evidence in the resulting…
We consider the inverse problem of determining the metric-measure structure of collapsing manifolds from local measurements of spectral data. In the part I of the paper, we proved the uniqueness of the inverse problem and a continuity…
We explore two approaches to characterise the quantum geometry of the ground state of correlated fermions in terms of the distance matrix in the spectral parameter space. (a) An intrinsic geometry approach, in which we study the intrinsic…
In the present work, a Klein Gordon particle with singular interactions supported on embedded curves on Riemannian manifolds is discussed from a more direct and physical perspective, via the heat kernel approach. It is shown that the…
The geometry of the symplectic structures and Fubini-Study metric is discussed. Discussion in the paper addresses geometry of Quantum Mechanics in the classical phase space. Also, geometry of Quantum Mechanics in the projective Hilbert…
We report the observation of the controlled expansion of a two-dimensional quantum gas confined onto a curved shell-shaped surface. We start from the ellipsoidal geometry of a dressed quadrupole trap and introduce a novel gravity…