Related papers: The commutative Moufang loops with maximum conditi…
We derive the general form of a master equation describing the interaction of an arbitrary multipartite quantum system, consisting of a set of subsystems, with an environment, consisting of a large number of sub-envirobments. Each subsystem…
The stationary solution \rho of a quantum master equation can be represented as an ensemble of pure states in a continuous infinity of ways. An ensemble which is physically realizable through monitoring the system's environment we call an…
We find necessary and sufficient conditions for $P$-equivalence of arbitrary matrices and $P$-congruence of symmetric and alternating matrices, where $P$ is standard parabolic subgroup of $GL_n(F)$ and $F$ is an arbitrary field.
We improve the upper bounds (in terms of $n$) in [9] and [13] on the minimal number of elements required to generate a minimally transitive permutation group of degree $n$.
Andrew Rajah posed at the Loops'11 Conference in Trest, Czech Republic, the following conjecture: Is every variety of loops that satisfies Moufang's theorem contained in the variety of Moufang loops? This paper is motivated by that problem.…
Quantum catalytic transformations play important roles in the transformation of quantum entangled states under local operations and classical communications (LOCC). The key problems in catalytic transformations are the existence and the…
It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and…
Scattering amplitudes in maximally supersymmetric gauge theory are dual to super-Wilson loops on null polygonal contours. The operator product expansion for the latter revealed that their dynamics is governed by the evolution of…
Loop quantum cosmology is shown to provide both the dynamical law and initial conditions for the wave function of a universe by one discrete evolution equation. Accompanied by the condition that semiclassical behavior is obtained at large…
We define a quantum loop group $\mathbf{U}^+_Q$ associated to an arbitrary quiver $Q=(I,E)$ and maximal set of deformation parameters, with generators indexed by $I \times \mathbb{Z}$ and some explicit quadratic and cubic relations. We…
We explore the relationship between limit spaces of contracting self-similar groups and self-similar structures. We give the condition on a contracting group such that its limit space admits a self-similar structure, and also the condition…
We study the fully entangled fraction of quantum states. An upper bound is obtained for arbitrary dimensional bipartite systems. This bound is shown to be exact for the case of two-qubit systems. An inequality related the fully entangled…
When relating the strong coupling $\alpha_s$, measured at the scale of the $Z$ boson mass, to its numerical value at some higher energy, for example the scale of Grand Unification, it is important to include higher order corrections both in…
Code loops are certain Moufang $2$-loops constructed from doubly even binary codes that play an important role in the construction of local subgroups of sporadic groups. More precisely, code loops are central extensions of the group of…
An upper bound on degrees of elements of a minimal generating system for invariants of quivers of dimension (2,...,2) is established over a field of arbitrary characteristic and its precision is estimated. The proof is based on the…
It is shown that the assumptions on macroscopic quantum tunneling and on superposition of two macroscopically distinct quantum states of superconducting loop, considered as flux qubit by many authors, contradict to the fundamental law of…
We use semi-invariant pictures to prove two conjectures about maximal green sequences. First: if $Q$ is any acyclic valued quiver with an arrow $j\to i$ of infinite type then any maximal green sequence for $Q$ must mutate at $i$ before…
Quantum operations are used to describe the observed probability distributions and conditional states of the measured system. In this paper, we address the problem of their joint measurability (coexistence). We derive two equivalent…
Self-interactions and interaction with the environment tend to push quantum systems toward states of maximal entanglement. This is a definition of decoherence. We argue that these maximally entangled states fall into the well-defined…
Let $\mathcal{R}$ be a finite valuation ring of order $q^r$. In this paper we generalize and improve several well-known results, which were studied over finite fields $\mathbb{F}_q$ and finite cyclic rings $\mathbb{Z}/p^r\mathbb{Z}$, in the…