Related papers: Operational approach to the Uhlmann holonomy
Linear optical operations are fundamental and significant for both quantum mechanics and classical technologies. We demonstrate a non-cascaded approach to perform arbitrary unitary and non-unitary linear operations for N-dimensional…
We show that spectral data of transfer operators given by holomorphic data can be approximated using an effective numerical scheme based on Lagrange interpolation. In particular, we show that for one-dimensional systems satisfying certain…
The probability density function for the visible sector of a Riemann-Theta Boltzmann machine can be taken conditional on a subset of the visible units. We derive that the corresponding conditional density function is given by a…
This paper is motivated by recent developments of higher gauge theory. Different from its style of using higher category theory, we try to describe the concept of higher parallel transport within setting of classical principal bundle…
Ruelle's transfer operator plays an important role in understanding thermodynamic and probabilistic properties of dynamical systems. In this work, we develop a method of finding eigenfunctions of transfer operators based on comparing Gibbs…
Realignment operation has a significant role in detecting bound as well as free entanglement. Just like partial transposition, it is also based on permutations of the matrix elements. However, the physical implementation of realignment…
One approach to multivariate operator theory involves concepts and techniques from algebraic and complex geometry and is formulated in terms of Hilbert modules. In these notes we provide an introduction to this approach including many…
This note concerns uniform equicontinuity of families of operators on a separable Hilbert space H, and of families of maps on B(H). It is shown that a one parameter group of automorphisms is uniformly equicontinuous if and only if the group…
We present a decomposition of the Koopman operator based on the sparse structure of the underlying dynamical system, allowing one to consider the system as a family of subsystems interconnected by a graph. Using the intrinsic properties of…
Diffusive transport processes in magnetized plasmas are highly anisotropic, with fast parallel transport along the magnetic field lines sometimes faster than perpendicular transport by orders of magnitude. This constitutes a major challenge…
The goal of this note is to prove a analogue of the Littewood-Paley decomposition for densities of operators and to use it in the context of Lieb-Thirring inequalities.
The topic of this study lies in the intersection of two fields. One is related with analyzing transport phenomena in complicated flows.For this purpose, we use so-called coherent sets: non-dispersing, possibly moving regions in the flow's…
We consider an operator-theoretic approach to linear infinite-dimensional port-Hamiltonian systems. In particular, we use the theory of system nodes by Staffans to formulate a~suitable concept for port-Hamiltonian systems, which allows a…
The Koopman operator, as a linear representation of a nonlinear dynamical system, has been attracting attention in many fields of science. Recently, Koopman operator theory has been combined with another concept that is popular in data…
This paper proposes a robust nonlinear observer synthesis method for a population of systems modelled using the Koopman operator. The Koopman operator allows nonlinear systems to be rewritten as infinite-dimensional linear systems. A…
We analyze geometry of the second order differential operators, having in mind applications to Batalin--Vilkovisky formalism in quantum field theory. As we show, an exhaustive picture can be obtained by considering pencils of differential…
The main purpose of this article is to study estimates for the Tsallis relative operator entropy, by the use of Hermite-Hadamard inequality. Thus, we obtain alternative bounds for the Tsallis relative operator entropy. In the process to…
The purpose of this paper is to study the dynamical behavior of the sequence produced by a forward-backward algorithm involving two random maximal monotone operators and a sequence of decreasing step sizes. Defining a mean monotone operator…
A version of Connes trace formula allows to associate a measure on the essential spectrum of a Schr\"odinger operator with bounded potential. In solid state physics there is another celebrated measure associated with such operators --- the…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…