Related papers: On quantum quadratic operators of $\bm_2(\mathbb{C…
In the present paper we study description of Kadison-Schwarz type quantum quadratic operators acting from $\bm_2(\mathbb{C})$ into $\bm_2(\mathbb{C})\o\bm_2(\mathbb{C})$. Note that such kind of operator is a generalization of quantum…
A quadratic stochastic operator (in short QSO) is usually used to present the time evolution of differing species in biology. Some quadratic stochastic operators have been studied by Lotka and Volterra. The general problem in the nonlinear…
This article presents a full operator analytical method for studying the quadratic nonlinear interactions in quantum optomechanics. The method is based on the application of higher-order operators, using a six-dimensional basis of second…
The spectral analysis of a non-Hermitian unbounded operator appearing in quantum physics is our main concern. The properties of such an operator are essentially different from those of Hermitian Hamiltonians, namely due to spectral…
Many systems are presented using theory of nonlinear operators. A quadratic stochastic operator (QSO) is perceived as a nonlinear operator. It has a wide range of applications in various disciplines, such as mathematics, biology, and other…
In this paper we describe bistochastic Kadison-Schawrz operators acting on $M_2(\mathbb{C})$. Such a description allows us to find positive, but not Kadison-Schwarz operators. Moreover, by means of that characterization we construct…
It is proposed the scheme of quantum mechanics, in which a Hilbert space and the linear operators are not primary elements of the theory. Instead of it certain variant of the algebraic approach is considered. The elements of noncommutative…
The choice of mathematical representation when describing physical systems is of great consequence, and this choice is usually determined by the properties of the problem at hand. Here we examine the little-known wave operator…
There is one-to-one correspondence between quadratic operators (mapping $\mathbb R^m$ to itself) and cubic matrices. It is known that any quadratic operator corresponding to a stochastic (in a fixed sense) cubic matrix preserves the…
In this paper we introduce Schwartz operators as a non-commutative analog of Schwartz functions and provide a detailed discussion of their properties. We equip them in particular with a number of different (but equivalent) families of…
In this paper we describe bistochastic Kadison-Schawrz operators on $M_2(\mathbb{C})$. Such a description allows us to find positive, but not Kadison-Schwarz operators. Moreover, by means of that characterization we construct…
The success of quantum physics in description of various physical interaction phenomena relies primarily on the accuracy of analytical methods used. In quantum mechanics, many of such interactions such as those found in quantum…
Using Schroedinger Functional methods, we compute the non-perturbative renormalisation and renormalisation group running of several four-fermion operators, in the framework of lattice simulations with two dynamical Wilson quarks. Two…
The non-cutoff Kac operator is a kinetic model for the non-cutoff radially symmetric Boltzmann operator. For Maxwellian molecules, the linearization of the non-cutoff Kac operator around a Maxwellian distribution is shown to be a function…
We introduce and systematically develop the theory of \emph{quantum doubly stochastic operators}, i.e. positive, trace-preserving maps on non-commutative $L_p$-spaces associated to semifinite von Neumann algebras. After establishing basic…
We introduce a category $\mathcal O$ of representations of the elliptic quantum group associated with $\mathfrak{sl}_2$ with well-behaved $q$-character theory. We derive separation of variables relations for asymptotic representations in…
We investigate the nonperturbative renormalization of composite operators in lattice QCD restricting ourselves to operators that are bilinear in the quark fields. These include operators which are relevant to the calculation of moments of…
Some consequences of promoting the object of noncommutativity ${\mathbf \theta}^{ij}$ to an operator in Hilbert space are explored. Consequently, a consistent algebra involving the enlarged set of canonical operators is obtained, which…
Starting from noncommutative quantum mechanics algebra, we investigate the variances of the deformed two-mode quadrature operators under the evolution of three types of two-mode squeezed states in noncommutative space. A novel conclusion…
We study dynamics of a scalar field in the near-horizon region described by a static Klein-Gordon operator which is the Hamiltonian of the system. The explicite construction of a time operator near-horizon is given and its self-adjointness…