Related papers: Sobriety of quantale-valued cotopological spaces
In this talk, we review the basics concepts of fuzzy physics and quantum field theory on the Groenwald-Moyal Plane as examples of noncommutative spaces in physics. We introduce the basic ideas, and discuss some important results in these…
In this work, we provide an analytical proof of the robustness of topological entanglement under a model of random local perturbations. We define a notion of average topological subsystem purity and show that, in the context of quantum…
The notion of soft sets is introduced as a general mathematical tool for dealing with uncertainty. In this paper, we consider the concepts of soft compactness, countably soft compactness and obtain some results. We study some soft…
Quantum uncertainty relations are formulated in terms of relative entropy between distributions of measurement outcomes and suitable reference distributions with maximum entropy. This type of entropic uncertainty relation can be applied…
For a general class of lattice-spin systems, we prove that an abstract Gaussian concentration bound implies positivity of lower relative entropy density. As a consequence we obtain uniqueness of translation-invariant Gibbs measures from the…
A test space is the set of outcome-sets associated with a collection of experiments. This notion provides a simple mathematical framework for the study of probabilistic theories -- notably, quantum mechanics -- in which one is faced with…
We provide a characterization in terms of Fatou closedness for weakly closed monotone convex sets in the space of $\mathcal{P}$-quasisure bounded random variables, where $\mathcal{P}$ is a (possibly non-dominated) class of probability…
The notion of hidden symmetry algebra used in the context of exactly solvable systems is re-examined from the purely algebraic way, analyzing subspaces of commuting polynomials that generate finite-dimensional quadratic algebras. By…
We study entropic uncertainty relations by using stepwise linear functions and quadratic functions. Two kinds of improved uncertainty lower bounds are constructed: the state-independent one based on the lower bound of Shannon entropy and…
Non-Abelian Gauss law is interpreted in terms of area bits described in a local frame which fit together into closed surfaces and the Non-Abelian Stokes law in terms of length bits described in a local frame which fit together into closed…
We investigate compressibility of the dimension of positive semidefinite matrices while approximately preserving their pairwise inner products. This can either be regarded as compression of positive semidefinite factorizations of…
In any static spacetime the quasilocal Tolman mass contained within a volume can be reduced to a Gauss-like surface integral involving the flux of a suitably defined generalized surface gravity. By introducing some basic thermodynamics, and…
The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy…
We consider dynamical systems on the space of functions taking values in a free associative algebra. The system is said to be integrable if it possesses an infinite dimensional Lie algebra of commuting symmetries. In this paper we propose a…
We classify the subvarieties of infinite dimensional affine space that are stable under the infinite symmetric group. We determine the defining equations and point sets of these varieties as well as the containments between them.
Invertibility is an important concept in category theory. In higher category theory, it becomes less obvious what the correct notion of invertibility is, as extra coherence conditions can become necessary for invertible structures to have…
Researchers have long been aiming to understand how the characteristics of Quantum Theory and General Relativity combine to account for regimes in their interface. One reason why this is a hard task is how differently the theories approach…
A quantum fluctuation theorem for a driven quantum subsystem interacting with its environment is derived based solely on the assumption that its reduced density matrix obeys a closed evolution equation i.e. a quantum master equation (QME).…
In these notes we give a brief introduction to decomposition theory and we summarize some classical and well-known results. The main question is that if a partitioning of a topological space (in other words a decomposition) is given, then…
Spaces of quasi-invariant measures supplied with different topologies are studied. Their embeddings, projective decompositions, conditions for their metrizability are investigated. Theorems about convergence of nets of quasi-invariant…