Related papers: Quantitative shrinking target properties for rotat…
We study the ergodicity and mixing of quantum kicked rotor (QKR) with two distinct approaches. In one approach, we use the definitions of quantum ergodicity and mixing recently proposed in [Phys. Rev. E 94, 022150 (2016)], which involve…
An effective model is introduced to illustrate finite volume effects beyond the usual momentum space constraints. The fluctuations of the chiral order parameter and the net baryon number, as well as their scaling properties, are…
Interval exchange transformations are typically uniquely ergodic maps and therefore have uniformly distributed orbits. Their degree of uniformity can be measured in terms of the star-discrepancy. Few examples of interval exchange…
This paper provides unified calculations regarding certain measures and transformations in interacting particle systems. More specifically, we provide certain general conditions under which an interacting particle system will have a…
We prove that any over-twist pattern is conjugate to an interval exchange transformation with bounded number of segments of isometry, restricted on one of its cycles. The bound is independent of the period and over-rotation number of the…
We present an approach to quantum dynamical lower bounds for discrete one-dimensional Schr\"odinger operators which is based on power-law bounds on transfer matrices. It suffices to have such bounds for a nonempty set of energies. We apply…
We discuss the shrinking target property of irrational rotations. We obtain the condition of an irrational $\theta$ and monotone increasing $\varphi(n)$ such that $$ \liminf_{n \to \infty} n \varphi (n) \| n\theta - s \| = 0 \text{ for…
We show that there exists an interval exchange and a point so that the orbit of the point equidistributes for a measure that is not ergodic.
The state-of-the-art methods for estimating high-dimensional covariance matrices all shrink the eigenvalues of the sample covariance matrix towards a data-insensitive shrinkage target. The underlying shrinkage transformation is either…
We show the equivalence of two possible definitions of a rotational interval exchange transformation: by the first one, it is a first return map for a circle rotation onto a union of finite number of circle arcs, and by the second one, it…
Irreducible interval exchange transformations are studied with regard to whirly property, a condition for non-trivial spatial factor. Uniformly whirly transformation is defined and to be further studied. An equivalent condition is…
The goal of this article is to draw new applications of small scale quantum ergodicity in nodal sets of eigenfunctions. We show that if quantum ergodicity holds on balls of shrinking radius $r(\lambda) \to 0$, then one can achieve…
We consider the restriction of interval exchange transformations to algebraic number fields, which leads to maps on lattices. We characterize renormalizability arithmetically, and study its relationships with a geometrical quantity that we…
We analyze an exchange algorithm for the numerical solution total-variation regularized inverse problems over the space M($\Omega$) of Radon measures on a subset $\Omega$ of R d. Our main result states that under some regularity conditions,…
On account of its application to the present and future analysis of the virtual photon correction to the hadronic properties by means of lattice QCD simulation, we initiate the study of the finite size scaling effect on the QED correction…
Two-body interactions of elementary particles are useful in particle and nuclear physics to describe qualitatively and quantitatively few- and many-body systems. We are extending for this purpose the quantum inversion approach for systems…
We establish stable quantum ergodicity for spin Hamiltonians, also known as Pauli-Schr\"odinger operators. Our approach combines new analytic techniques of mixed quantization, inspired by local index theory, with stable ergodicity results…
We introduce a definition of admissibility for subintervals in interval exchange transformations. Using this notion, we prove a property of the natural codings of interval exchange transformations, namely that any derived set of a regular…
Stein showed that the multivariate sample mean is outperformed by "shrinking" to a constant target vector. Ledoit and Wolf extended this approach to the sample covariance matrix and proposed a multiple of the identity as shrinkage target.…
In this paper, the purpose is to introduce and study a new modified shrinking projection algorithm with inertial effects, which solves split common fixed point problems in Banach spaces. The corresponding strong convergence theorems are…