Related papers: Evolution Operators for Linearly Polarized Two-Kil…
We consider the problem of discretizing evolution operators of linear delay equations with the aim of approximating their spectra, which is useful in investigating the stability properties of (nonlinear) equations via the principle of…
The paper deals with the problem of the rigorous description of the evolution of states of large particle quantum systems by means of correlation operators. A nonperturbative solution of the Cauchy problem of the hierarchy of nonlinear…
For a scalar evolution equation $u_t=K(t,x,u,u_x,\ldots, u_n), n\geq 2$ the cohomology spaces $H^{1,s}({\mathcal R}^\infty)$ vanishes for $s\geq 3$ while the space $H^{1,2}({\mathcal R}^\infty)$ is isomorphic to the space of variational…
We present an operator approach to the description of photon polarization, based on Wigner's concept of elementary relativistic systems. The theory of unitary representations of the Poincare group, and of parity, are exploited to construct…
Using the theory of evolutionary equations, we consider abstract differential equations including non-local integral operators. After providing a condition for the well-posedness of the addressed equation we consider a numerical method of…
Given a quantum Hamiltonian and its evolution time, the corresponding unitary evolution operator can be constructed in many different ways, corresponding to different trajectories between the desired end-points and different series…
In the present paper we continue our study of non-commutative operator graphs in infinite-dimensional spaces. We consider examples of the non-commutative operator graphs generated by resolutions of identity corresponding to the…
In this work we begin a theoretical and numerical investigation on the spectra of evolution operators of neutral renewal equations, with the stability of equilibria and periodic orbits in mind. We start from the simplest form of linear…
Optimal realizations of quantum technology tasks lead to the necessity of a detailed analytical study of the behavior of a $d$-level quantum system (qudit) under a time-dependent Hamiltonian. In the present article, we introduce a new…
This work discusses a variational approach to determining the time evolution operator. We directly see a glimpse of how a generalization of the quantum geometric tensor for unitary operators plays a central role in parameter evolution. We…
The relativistic formulation of abstract evolution equations is introduced. The corresponding logarithmic representation is shown to exist without assuming the invertible property of evolution operators. Consequently, by means of the…
We present a general method which expresses a unitary operator by the product of operators allowed by the Hamiltonian of spin-1/2 systems. In this method, the generator of an operator is found first, and then the generator is expanded by…
In this paper, we define an operator function as a series of operators corresponding to the Taylor series representing the function of the complex variable. In previous papers, we considered the case when a function has a decomposition in…
In this work we construct an approximate time evolution operator for a system composed by two coupled Jaynes-Cummings Hamiltonians. We express the full time evolution operator as a product of exponentials and we analyze the validity of our…
Considering evolutionary equations in the sense of Picard, we identify a certain topology for material laws rendering the solution operator continuous if considered as a mapping from the material laws into the set of bounded linear…
Under broad conditions, evolutions due to two different Hamiltonians are shown to lead at some moment to orthogonal states. For two spin-1/2 systems subject to precession by different magnetic fields the achievement of orthogonalization is…
The notion of singular reduction operators, i.e., of singular operators of nonclassical (conditional) symmetry, of partial differential equations in two independent variables is introduced. All possible reductions of these equations to…
In this paper, having introduced a convergence of a series on the root vectors in the Abel-Lidskii sense, we present a valuable application to the evolution equations. The main issue of the paper is an approach allowing us to principally…
We consider Vlasov-type scaling for Markov evolution of birth-and-death type in continuum, which is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of…
We define fully non-perturbative generalizations of the uniform density and comoving curvature perturbations, which are known, in the linear theory, to be conserved on sufficiently large scales for adiabatic perturbations. Our non-linear…