Related papers: Hyper-atoms applied to the critical pair Theory

We show how classical and quantum dualities, as well as duality relations that appear only in a sector of certain theories ("emergent dualities"), can be unveiled, and systematically established. Our method relies on the use of morphisms of…

We present a detailed proof of the prime number theorem suitable for a typical undergraduate- or graduate-level complex analysis course. Our presentation is particularly useful for any instructor who seeks to use the prime number theorem…

In the theory of conditional sets, many classical theorems from areas such as functional analysis, probability theory or measure theory are lifted to a conditional framework, often to be applied in areas such as mathematical economics or…

The aim of the paper is to derive essential elements of quantum mechanics from a parametric structure extending that of traditional mathematical statistics. The main extensions, which also can be motivated from an applied statistics point…

Modern quantum theory introduces quantum structures (decompositions into subsystems) as a new discourse that is not fully comparable with the classical-physics counterpart. To this end, so-called Entanglement Relativity appears as a…

This paper proposed a framework based on quantum computing for reliability assessment of complex systems. The 'Quantum Twin' concept was also proposed. The framework can be used to accelerate the reliability assessment of large-scale…

Ensembles of atoms interacting via their Rydberg levels, known as "superatoms" for their ability to encode qubits and to emit single photons, attract increasing attention as building blocks for quantum network nodes. Assessing their…

We establish two versions of a central theorem, the Family Colimit Theorem, for the coarse coherence property of metric spaces. This is a coarse geometric property and so is well-defined for finitely generated groups with word metrics. It…

In the paper the well known Riemann Hypothesis is proven. The proof is based on uniform approximation of the zeta function discs of the critical strip placed to the right from the critical line.The basic moment is a use of a new mesure…

We introduce the notion of quasi-log complex analytic spaces and establish various fundamental properties. Moreover, we prove that a semi-log canonical pair naturally has a quasi-log complex analytic space structure. This paper is part of…

We discuss a structural approach to subset-sum problems in additive combinatorics. The core of this approach are Freiman-type structural theorems, many of which will be presented through the paper. These results have applications in various…

Hamiltonian theory of hybrid quantum-classical systems is used to study dynamics of the classical subsystem coupled to different types of quantum systems. It is shown that the qualitative properties of orbits of the classical subsystem…

We present new criteria on the existence of fixed points that combine some monotonicity assumptions with the classical fixed point index theory. As an illustrative application, we use our theoretical results to prove the existence of…

A new concept of the constitution of Nature is proposed. The constructed submicroscopic quantum mechanics is deterministic and is characterised by elementary excitations of the space net that is treated as the tessellation of balls, or…

For a class of quasilinear elliptic equations involving the p-Laplace operator, we develop an abstract critical point theory in the presence of sub-supersolutions. Our approach is based upon the proof of the invariance under the gradient…

Quantum metrology, a cornerstone of quantum technologies, exploits entanglement and superposition to achieve higher precision than classical protocols in parameter estimation tasks. When combined with critical phenomena such as phase…

After a brief historical overview of superfluidity in connection with neutron matter and cold fermionic atoms, we discuss the commonalities between these two systems as well as their relevance to the physics of neutron star crusts. We then…

Topos theory, a branch of category theory, has been proposed as mathematical basis for the formulation of physical theories. In this article, we give a brief introduction to this approach, emphasising the logical aspects. Each topos serves…

A novel approach is proposed to analyze a rather vast counter-rotating Hamiltonian interaction in the context of cavity quantum electrodynamics. The method relies upon the supersymmetric mapping of the corresponding rotating interaction and…

The classical Hermite-Biehler theorem describes possible zero sets of complex linear combinations of two real polynomials whose zeros strictly interlace. We provide the full characterization of zero sets for the case when this interlacing…