相关论文: Canonical divergence for flat $\alpha$-connections…

We consider the claim of Hawking and Page that the canonical measure applied to a FRW universe with a massive scalar field can solve the flatness problem regardless of inflation. By considering a general potential we are able to understand…

This paper focuses on local curvature invariants associated with bi-Lagrangian structures. We establish several geometric conditions that determine when the canonical connection is flat, building on our previous findings regarding…

All existing experimental results are currently interpreted using classical geometry. However, there are theoretical reasons to suspect that at a deeper level, geometry emerges as an approximate macroscopic behavior of a quantum system at…

A compact K\"ahler manifold is shown to be simply-connected if its `symmetric cotangent algebra' is trivial. Conjecturally, such a manifold should even be rationally connected. The relative version is also shown: a proper surjective…

It is a classical fact that the cotangent bundle $T^* \M$ of a differentiable manifold $\M$ enjoys a canonical symplectic form $\Omega^*$. If $(\M,\j,g,\omega)$ is a pseudo-K\"ahler or para-K\"ahler $2n$-dimensional manifold, we prove that…

Given a tame differential calculus over a noncommutative algebra $\mathcal{A}$ and an $\mathcal{A}$-bilinear pseudo-Riemannian metric $g_0,$ consider the conformal deformation $ g = k. g_0, $ $k$ being an invertible element of…

A local classification of the Hermitian manifolds with flat associated connection is given. Hermitian manifolds admitting locally a conformal metric with flat associated connection are characterized by a curvature identity. Locally…

Ideas from deformation quantization applied to algebras with one generator lead to methods to treat a nonlinear flat connection. It provides us elements of algebras to be parallel sections. The moduli space of the parallel sections is…

In classical canonical correlation analysis (CCA), the goal is to determine the linear transformations of two random vectors into two new random variables that are most strongly correlated. Canonical variables are pairs of these new random…

A unifying principle explaining the numerical bounds of quantum correlations remains elusive despite the efforts devoted to identifying it. Here we show that these bounds are indeed not exclusive to quantum theory: for any abstract…

We establish a quantitative relationship between mixed de Rham classes and the geometric complexity of metric connections with totally skew torsion on product manifolds where both factors are compact oriented surfaces. For any…

The correspondence principle bridges the quantum and classical worlds by establishing a direct link between their dynamics. This well-accepted tenant of quantum physics has been explored in quantum systems wherein the number of particles is…

In this paper we study relations between various natural structures on F-manifolds. In particular, given an arbitrary Riemannian F-manifold we present a construction of a canonical flat F-manifold associated to it. We also describe a…

We show that the standard Heisenberg algebra of quantum mechanics admits a noncommutative differential calculus $\Omega^1$ depending on the Hamiltonian $p^2/2m + V(x)$, and a flat quantum connection $\nabla$ with torsion such that a…

Similarities between quantum systems and analogous systems for classical waves have been used to great effect in the physics community, be it to gain an intuition for quantum systems or to anticipate novel phenomena in classical waves. This…

This work uncovers variational principles behind symmetrizing the Bregman divergences induced by generic mirror maps over the cone of positive definite matrices. We show that computing the canonical means for this symmetrization can be…

In a recent paper, a "distance" function, \cal D, was defined which measures the distance between pure classical and quantum systems. In this work, we present a new definition of a "distance", D, which measures the distance between either…

There is a received wisdom about where to draw the boundary between classical and nonclassical for various types of quantum processes. For multipartite states, it is the divide between separable and entangled; for channels, the divide…

We discuss the problem of separating consistently the total correlations in a bipartite quantum state into a quantum and a purely classical part. A measure of classical correlations is proposed and its properties are explored.

In [GT], Goldin and the second author extend some ideas from Schubert calculus to the more general setting of Hamiltonian torus actions on compact symplectic manifolds with isolated fixed points. (See also [Kn99] and [Kn08].) The main goal…