Related papers: Quantum Limits on product manifolds
Quantum ergodicity theorem states that for quantum systems with ergodic classical flows, eigenstates are, in average, uniformly distributed on energy surfaces. We show that if N is a hypersurface in the position space satisfying a simple…
In this paper, we construct and classify minimal surfaces foliated by horizontal constant curvature curves in product manifolds $M \times \R$, where $M$ is the hyperbolic plane, the Euclidean plane or the two dimensional sphere. The main…
On a $2m$-dimensional closed manifold we investigate the existence of prescribed $Q$-curvature metrics with conical singularities. We present here a general existence and multiplicity result in the supercritical regime. To this end, we…
We prove that a broad array of capacities of a quantum channel are continuous. That is, two channels that are close with respect to the diamond norm have correspondingly similar communication capabilities. We first show that the classical…
We study the limit geometry of complete projective special real manifolds. By limit geometry we mean the limit of the evolution of the defining polynomial and the centro-affine fundamental form along certain curves that leave every compact…
We prove that if a positive closed current is bounded by another one with bounded, continuous or Hoelder continuous super-potentials, then it inherits the same property. There are two different methods to define wedge-products of positive…
This paper investigates asymptotic properties of multifractal products of random fields. The obtained limit theorems provide sufficient conditions for the convergence of cumulative fields in the spaces $L_q.$ New results on the rate of…
In this paper, we classify the characteristic matrices associated to quasitoric manifolds over a vertex cut of a finite product of simplices. We discuss the integral cohomology rings of these quasitoric manifolds with possibly minimal…
In the present contribution we discuss the role of experimental limitations in the classical limit problem. We studied some simple models and found that Quantum Mechanics does not re-produce classical mechanical predictions, unless we…
Given a fixed closed manifold M, we exhibit an explicit formula for the distance function of the canonical L^2 Riemannian metric on the manifold of all smooth Riemannian metrics on M. Additionally, we examine the (metric) completion of the…
We show that in finite dimension a quantum measurement with continuous set of outcomes is always equivalent to a continuous random choice of measurements with only finite outcomes.
We establish a boundary maximum principle for free boundary minimal submanifolds in a Riemannian manifold with boundary, in any dimension and codimension. Our result holds more generally in the context of varifolds.
We describe the local structure of Riemannian manifolds with harmonic curvature which admit a maximum number, in a well-defined sense, of local warped-product decompositions, and at the same time their Ricci tensor has, at some point, only…
We investigate a two-component, cylindrical, quasi-one-dimensional quantum plasma subjected to a {\em radial} confining harmonic potential and an applied magnetic field in the symmetric gauge. It is demonstrated that such a system as can be…
Quantum physics on manifolds with boundary brings novel aspects due to boundary conditions. One important feature is the appearance of localised negative eigenmodes for the Laplacian on the boundary. These can potentially lead to…
This paper provides necessary and sufficient conditions for constructing a universal quantum computer over continuous variables. As an example, it is shown how a universal quantum computer for the amplitudes of the electromagnetic field…
In this paper, we try to generalize to the case of compact Riemannian orbifolds $Q$ some classical results about the existence of closed geodesics of positive length on compact Riemannian manifolds $M$. We shall also consider the problem of…
The space of quantum states can be endowed with a metric structure using the second order derivatives of the relative entropy, giving rise to the so-called Kubo-Mori-Bogoliubov inner product. We explore its geometric properties on the…
We prove that, given any smooth action of a compact quantum group (in the sense of \cite{rigidity}) on a compact smooth manifold satisfying some more natural conditions, one can get a Riemannian structure on the manifold for which the…
We introduce the first minimal and complete equational theory for quantum circuits. Hence, we show that any true equation on quantum circuits can be derived from simple rules, all of them being standard except a novel but intuitive one…