相关论文: Scott Continuity in Generalized Probabilistic Theo…
The separately continuity topology is considered and some its properties are investigated. With help of these properties a generalization of Sierpinski theorem on determination of real separately continuous function by its values on an…
We find the symmetry generators for the Friedman equations emanating from a perfect fluid source, in the presence of a cosmological constant term. The relevant dynamics is seen to be governed by two coupled, first order ordinary…
A two-dimensional Gauss-Kuzmin theorem for $N$-continued fraction expansions is shown. More exactly, we obtain a Gauss-Kuzmin theorem related to the natural extension of the measure-dynamical system corresponding to these expansions. Then,…
We study the category Cstabm of measurable cones and measurable stable functions, which is a denotational model of an higher-order language with continuous probabilities and full recursion. We look at Cstabm as a model for discrete…
In this work, we show how states with conserved numbers of dynamical defects (strings, domain walls, etc.) can be understood as possessing generalised global symmetries even when the microscopic origins of these symmetries are unknown.…
The quantum mechanical transition probability is symmetric. A probabilistically motivated and more general quantum logical definition of the transition probability was introduced in two preceding papers without postulating its symmetry, but…
The spectrum profile that emerges in molecular spectroscopy and atmospheric radiative transfer as the combined effect of Doppler and pressure broadenings is known as the Voigt profile function. Because of its convolution integral…
We demonstrate how large classes of discrete and continuous statistical distributions can be incorporated into coherent states, using the concept of a reproducing kernel Hilbert space. Each family of coherent states is shown to contain, in…
By considering the quantum-mechanically minimum allowable energy interval, we exactly count number of states (NOS) and introduce discrete density of states (DOS) concept for a particle in a box for various dimensions. Expressions for…
Probability theory can be studied synthetically as the computational effect embodied by a commutative monad. In the recently proposed Markov categories, one works with an abstraction of the Kleisli category and then defines deterministic…
Building on the theory of quantum posets, we introduce a non-commutative version of suplattices, i.e., complete lattices whose morphisms are supremum-preserving maps, which form a step towards a new notion of quantum topological spaces. We…
We study the back stable $K$-theory Schubert calculus of the infinite flag variety. We define back stable (double) Grothendieck polynomials and double $K$-Stanley functions and establish coproduct expansion formulae. Applying work of…
We introduce new coherent states and use them to prove semi-classical estimates for Schr\"odinger operators with regular potentials. This can be further applied to the Thomas-Fermi potential yielding a new proof of the Scott correction for…
We provide a generalized treatment of uncertainties, von Neumann entropy, and squeezing in entangled bipartite pure state of two-level atoms. We observe that when the bipartite state is entangled, though the von Neumann entropy of the…
The notion of equality between two observables will play many important roles in foundations of quantum theory. However, the standard probabilistic interpretation based on the conventional Born formula does not give the probability of…
Inspired by its fundamental importance in quantum mechanics, we define and study the notion of entanglement for abstract physical theories, investigating its profound connection with the concept of superposition. We adopt the formalism of…
The purpose of this paper is to build a new bridge between category theory and a generalized probability theory known as noncommutative probability or quantum probability, which was originated as a mathematical framework for quantum theory,…
In recent years a great deal of attention has been paid to discretizations of the incompressible Stokes equations that exactly preserve the incompressibility constraint. These are of substantial interest because these discretizations are…
Web spaces, wide web spaces and worldwide web spaces (alias C-spaces) provide useful generalizations of continuous domains. We present new characterizations of such spaces and their patch spaces, obtained by joining the original topology…
We extend the key notion of Martin-L\"of randomness for infinite bit sequences to the quantum setting, where the sequences become states of an infinite dimensional system. We work towards showing an analogy with the Levin-Schnorr theorem to…