Related papers: Properties of Consistent Histories
In this article, we develop a functional-analytic framework to establish existence, uniqueness, regularity of disintegration, and statistical properties of equilibrium states for a broad class of dynamical systems, potentially discontinuous…
This introductory survey deals with mathematical and physical properties of discrete structures such as point sets and tilings. The emphasis is on proper generalizations of concepts and ideas from classical crystallography. In particular,…
We review the application of the consistent (or decoherent) histories formulation of quantum theory to canonical loop quantum cosmology. Conventional quantum theory relies crucially on "measurements" to convert unrealized quantum…
With the aid of simple analytical computations for the Ehrenfest model, we clarify some basic features of macroscopic irreversibility. The stochastic character of the model allows us to give a non-ambiguous interpretation of the general…
The traditional Standard Quantum Mechanics is unable to solve the Spin-Statistics problem, i.e. to justify the utterly important Pauli Exclusion Principle. We show that this is due to the non completeness of the standard theory due to an…
Random permutations with distribution conditionally uniform given the set of record values can be generated in a unified way, coherently for all values of $n$. Our central example is a two-parameter family of random permutations that are…
We give a novel characterization of the centered model in regularity structures which persists for rough drivers even as a mollification fades away. We present our result for a class of quasilinear equations driven by noise, however we…
After the development of a self-consistent quantum formalism nearly a century ago there began a quest for how to interpret the theoretical constructs of the formalism. In fact, the pursuit of new interpretations of quantum mechanics…
Hartle's generalized quantum mechanics in the sum-over-histories formalism is used to describe a nonabelian gauge theory. Predictions are made for certain alternatives, with particular attention given to coarse-grainings involving the…
We present a general method to derive the classical mechanics of a system of identical particles in a way that retains information about quantum statistics. The resulting statistical mechanics can be interpreted as a classical version of…
Although regular conditional distributions (r.c.d.) are well-defined and widely used measure-theoretic objects, they can violate our intuition from the classical definition of a conditional probability given an event. For that purpose, the…
This paper presents (in its Lagrangian version) a very general "historical" formalism for dynamical systems, including time-dynamics and field theories. It is based on the universal notion of history. Its condensed and universal formulation…
We describe a classical thermodynamic model that reproduces the main features of the solid hydrogen phase diagram. In particular, we show how the general structure types that are found by electronic structure calculations and the quantum…
We study in general algebras Gratzer's notion of congruence preserving function, characterizing functions in terms of stability under inverse image of particular Boolean algebras of subsets generated from any subset of the algebra.…
In a recent short note [Bergeron H, Gazeau J P, Siegl P and Youssef A 2010 EPL 92 60003], we have presented the nice properties of a new family of semi-classical states for P\"oschl-Teller potentials. These states are built from a…
We survey some results that provide different versions of classical results through different summability methods. Specifically, in order to adapt such classical results, we analyze which properties should satisfy the summability methods.…
Spekkens has introduced an epistemically restricted classical theory of discrete systems, based on discrete phase space. The theory manifests a number of quantum-like properties but cannot fully imitate quantum theory because it is…
We study new Legendre transforms in classical mechanics and investigate some of their general properties. The behaviour of the new functions is analyzed under coordinate transformations.When invariance under different kinds of…
Classical nonlinear theories are highly successful in describing far-from-equilibrium dynamics of magnets, encompassing phenomena such as parametric resonance, ultrafast switching, and even chaos. However, at ultrashort length and time…
We introduce a notion of the ``explanation" of one (generalized) probabilistic model by another as particular kind of span in the category $\Prob$ of probabilistic models and morphisms. We show that explanations compose under a standard…