Related papers: Nonabelian lattice theories: Consistent measures a…
We study the scalar modes of linear perturbations in loop quantum cosmology. This is done on a lattice where each cell is taken to be homogeneous and isotropic and can be quantized via standard homogeneous loop quantum cosmology techniques.…
A geometric analysis of the Shake and Rattle methods for constrained Hamiltonian problems is carried out. The study reveals the underlying differential geometric foundation of the two methods, and the exact relation between them. In…
The t-statistic is a widely-used scale-invariant statistic for testing the null hypothesis that the mean is zero. Martingale methods enable sequential testing with the t-statistic at every sample size, while controlling the probability of…
Assuming $\mathfrak b = \mathfrak c$ (or some weaker statement), we construct a compactification $\gamma\omega$ of $\omega$ such that its remainder $\gamma\omega\setminus\omega$ is nonseparable and carries a strictly positive measure.
This paper is concerned with the study of the stability of dynamical systems evolving on time scales. We first {formalize the notion of matrix measures on time scales, prove some of their key properties and make use of this notion to study…
In this paper, we study the competition of linear and nonlinear lattices and its effects on the stability and dynamics of bright solitary waves. We consider both lattices in a perturbative framework, whereby the technique of Hamiltonian…
Detailed study of spectral properties and of linear stability is presented for a class of lattice Boltzmann models with a non-ideal equation of state. Examples include the van der Waals and the shallow water models. Both analytical and…
This note presents two ideas. The first one is that quantum theory has a fundamentally perturbative basis but leads to nonperturbative states which it would seem natural to take into account in the foundation of a theory of quantum…
As new experimental data arrive from the LHC the prospect of indirectly detecting new physics through precision tests of the Standard Model grows more exciting. Precise experimental and theoretical inputs are required to test the unitarity…
Classical conditions for ensuring the robust stability of a linear system in feedback with a sector-bounded nonlinearity include small gain, circle, passivity, and conicity theorems. In this work, we present a similar stability condition,…
In this paper, the development of a mathematical method is presented to explore spatially non-uniform phases with no long-range order in mathematical models of first order phase transitions. We use essential results regarding the…
The stability requirements for a noncommutative scalar field coupled to gravity is investigated through the positive energy theorem. It is shown that for a noncommutative scalar with a polynomial potential, the stability conditions are…
This paper is devoted to improvements of functional inequalities based on scalings and written in terms of relative entropies. When scales are taken into account and second moments fixed accordingly, deficit functionals provide explicit…
A general class of loop quantizations for anisotropic models is introduced and discussed, which enhances loop quantum cosmology by relevant features seen in inhomogeneous situations. The main new effect is an underlying lattice which is…
Formulating gauge theories on a lattice offers a genuinely non-perturbative way of studying quantum field theories, and has led to impressive achievements. In particular, it significantly deepened our understanding of quantum…
A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be interpreted as typicality measures. However, a…
Measures of discordance between datasets have become an essential part of cosmological analyses. It is important to accurately evaluate the significance of such discordances when present. We propose here a Bayesian interpretation of…
In order to claim that one has experimentally tested whether a noncontextual ontological model could underlie certain measurement statistics in quantum theory, it is necessary to have a notion of noncontextuality that applies to unsharp…
The process of measuring a two-level quantum system was examined by applying Hamiltonian formalism. For the measurement of an observable that does not commute with the system Hamiltonian, a non-trivial relationship among the strength of…
In this article we study the expanding properties of random perturbations of contracting Lorenz maps satisfying the summability condition of exponent 1. Under general conditions on the maps and perturbation types, we prove stochastic…