Related papers: Quantum ergodic sequences and equilibrium measures

A comprehensive review of the equations of general relativity in the quasi-Maxwellian (QM) formalism introduced by Jordan, Ehlers and Kundt is made. Our main interest concerns its applications to the analysis of the perturbation of standard…

We construct explicit examples of quaternion-K\"ahler and hypercomplex structures on bundles over hyperK\"ahler manifolds. We study the infinitesimal symmetries of these examples and the associated Galicki-Lawson quaternion-K\"ahler moment…

It is shown how to resolve the apparent contradiction between the macroscopic approach of phase space and the validity of the uncertainty relations. The main notions of statistical mechanics are re-interpreted in a quantum-mechanical way,…

This paper primarily concerns the variance estimate of zeros of systems of random holomorphic sections associated with a sequence of smooth Hermitian holomorphic line bundles on a compact Kahler manifold X. The probability measures taken…

Let $( X ,d ,p ) $ be the pointed Gromov-Hausdorff limit of a sequence of pointed complete polarized K\"ahler manifolds $( M_l ,\omega_l ,\mathcal{L}_l ,h_l ,p_l ) $ with $Ric ( h_l ) =2\pi \omega_l $, $Ric ( \omega_l ) \geq -\Lambda…

In this paper we study Spectral Decomposition Theorem [1] and translate it to quantum language by means of the Wigner transform. We obtain a quantum version of Spectral Decomposition Theorem (QSDT) which enables us to achieve three distinct…

Let $X$ be a compact normal complex space of dimension $n$, and $L$ be a holomorphic line bundle on $X$. Suppose $\Sigma=(\Sigma_1,\ldots,\Sigma_\ell)$ is an $\ell$-tuple of distinct irreducible proper analytic subsets of $X$,…

The purpose of this article is to show a geometric version of Zabrodin-Wiegmann conjecture for an integer Quantum Hall state. Given an effective reduced divisor on a compact connected Riemann surface, using the canonical holomorphic section…

Let $M$ be a semifinite von Neumann algebra and $T$ a positive contraction on both $L^1(M)$ and $L^\infty(M)$. We consider ergodic averages along a random sparse subsequence determined by independent Bernoulli variables $(X_n)_{n\geq 1}$…

We consider dynamics of scalar semilinear parabolic equations on bounded intervals with periodic boundary conditions, and on the entire real line, with a general nonlinearity $g(t,x,u,u_x)$ either not depending on $t$, or periodic in $t$.…

In this paper we consider random block matrices, which generalize the general beta ensembles, which were recently investigated by Dumitriu and Edelmann (2002, 2005). We demonstrate that the eigenvalues of these random matrices can be…

We study the ergodic properties of eigenfunctions of Schr\"odinger operators on a closed connected Riemannian manifold $M$ in case that the underlying Hamiltonian system possesses certain symmetries. More precisely, let $M$ carry an…

Let X be a smooth complex projective variety of dimension d. It is classical that ample line bundles on X satisfy many beautiful geometric, cohomological, and numerical properties that render their behavior particularly tractable. By…

We show that certain linear elliptic equations (and systems) in divergence form with almost periodic coefficients have bounded, almost periodic correctors. This is proved under a new condition we introduce which quantifies the almost…

We study the asymptotics of almost holomorphic sections $s \in H^0_J(M, \omega)$ of an ample line bundle $L \to M$ over an almost complex symplectic manifold in the sense of Boutet de Monvel-Guillemin. Such sections are defined as the…

We attempt a clarification of geometric aspects of quantum field theory by using the notion of smoothness introduced by Fr\"olicher and exploited by several authors in the study of functional bundles. A discussion of momentum and position…

A new symmetry of $(1,0)$ supersymmetric non-linear $\sigma$-models in two dimensions with Fermi and mass sectors is introduced. It is a generalisation of the so-called special holonomy $W$-symmetry of Howe and Papadopoulos associated with…

We consider random polynomials of the form $H_n(z)=\sum_{j=0}^n\xi_jq_j(z)$ where the $\{\xi_j\}$ are i.i.d non-degenerate complex random variables, and the $\{q_j(z)\}$ are orthonormal polynomials with respect to a compactly supported…

A distributional symmetry is invariance of a distribution under a group of transformations. Exchangeability and stationarity are examples. We explain that a result of ergodic theory provides a law of large numbers: If the group satisfies…

Local mean and individual (with respect to almost uniform convergence in Egorov's sense) ergodic theorems are established for actions of the semigroup $\mathbb R_+^d$ in symmetric spaces of measurable operators associated with a semifinite…