Related papers: Canonical measures and the dynamical systems of Be…

The traditional approach to quantum parameter estimation focuses on the quantum state, deriving fundamental bounds on precision through the quantum Fisher information. In most experimental settings, however, performing arbitrary quantum…

We present a diagrammatic approach to quantum dynamics based on the categorical algebraic structure of strongly complementary observables. We provide physical semantics to our approach in terms of quantum clocks and quantisation of time. We…

An invariant kernel for the pluricanonical system of a projective manifold of general type is introduced. Using this kernel we prove that the Yau volume form on a smooth projective variety has seminegative Ricci curvature. As a biproduct we…

We set up the Sugawara-Sommerfield (SS) construction and generalize it by the inclusion of canonical spin current. Using the techniques of current algebra, we infer that the canonical spin current are linear in the vector-axial vector…

We investigate the classical limit of non-Hermitian quantum dynamics arising from a coherent state approximation, and show that the resulting classical phase space dynamics can be described by generalised "canonical" equations of motion,…

This is a review of the aspirations and disappointments of the canonical quantization of geometry. I compare the two chief ways of looking at canonical gravity, geometrodynamics and connection dynamics. I capture as much of the classical…

This is the first of a series of papers in which a new formulation of quantum theory is developed for totally constrained systems, that is, canonical systems in which the hamiltonian is written as a linear combination of constraints…

Analysis of images of sets of fibers such as myelin sheaths or skeletal muscles must account for both the spatial distribution of fibers and differences in fiber shape. This necessitates a combination of point process and shape analysis…

The main result of the present article is a (practically optimal) criterium for the pseudoeffectivity of the twisted relative canonical bundles of surjective projective maps. Our theorem has several applications in algebraic geometry; to…

The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating…

We define a quantisation of the J-flow over a projective complex manifold. As corollaries, we obtain new proofs of uniqueness of critical points of the J-flow and that these critical points achieve the absolute minimum of an associated…

The Cartan-Hartogs domains are defined as a class of Hartogs type domains over irreducible bounded symmetric domains. The purpose of this paper is twofold. Firstly, for a Cartan-Hartogs domain $\Omega^{B^{d_0}}(\mu)$ endowed with the…

In the spirit of Marcus canonical stochastic differential equations, we study a similar notion of rough differential equations (RDEs), notably dropping the assumption of continuity prevalent in the rough path literature. A new metric is…

In the iconic measurements of atomic spin-1/2 or photon polarization, one employs two spatially separated and noninteracting detectors. Each detector is binary, registering the presence or absence of the atom or the photon. For measurements…

Let X be a smooth projective Berkovich space over a complete discrete valuation field K of residue characteristic zero, endowed with an ample line bundle L. We introduce a general notion of (possibly singular) semipositive (or…

The present work is devoted to the study of dynamical features of Bohmian measures, recently introduced by the authors. We rigorously prove that for sufficiently smooth wave functions the corresponding Bohmian measure furnishes a…

Relying on the recent work of Liu-Sz\'ekelyhidi we give a weak asymptotic estimate for the Bergman kernels of polarized K\"ahler manifolds with Ricci lower bound and Sobolev constant upper bound. We will also give a simple proof for the…

We present a new formulation for the emergence of classical dynamics in a quantum world by considering a path integral approach that also incorporates continuous measurements. Our program is conceptually different from the decoherence…

We present a new reformulation of the canonical quantum geometrodynamics, which allows to overcome the fundamental problem of the frozen formalism and, therefore, to construct an appropriate Hilbert space associate to the solution of the…

Call and Silverman introduced the canonical height associated to a polarized dynamical system, that is, an endomorphism of a projective variety and an ample line bundle which pulls back to a tensor power of itself. They also presented an…