Related papers: Operational approach to the Uhlmann holonomy
Koopman operator theory has served as the basis to extract dynamics for nonlinear system modeling and control across settings, including non-holonomic mobile robot control. There is a growing interest in research to derive robustness…
Let $\mathfrak{M}$ be a semifinite von Neumann algebra on a Hilbert space equipped with a faithful normal semifinite trace $\tau$. A closed densely defined operator $x$ affiliated with $\mathfrak{M}$ is called $\tau$-measurable if there…
System identification based on Koopman operator theory has grown in popularity recently. Spectral properties of the Koopman operator of a system were proven to relate to properties like invariant sets, stability, periodicity, etc. of the…
A novel approach for measuring fast oscillations of an absolute value of interferometer optical path difference (OPD) has been developed. The principles of frequency-scanning interferometry are utilized for registration of the…
In this article, we characterize absolutely norm attaining normal operators in terms of the essential spectrum. Later we prove a structure theorem for hyponormal absolutely norm attaining (or $\mathcal{AN}$-operators in short) and deduce…
We argue that in contrast to the classical physics, the measurements in the quantum mechanics should provide simultaneous information about all relevant relative amplitudes (pure states and the transitions between them) and all relevant…
For commuting linear operators $P_0,P_1,..., P_\ell$ we describe a range of conditions which are weaker than invertibility. When any of these conditions hold we may study the composition $P=P_0P_1... P_\ell$ in terms of the component…
In this paper we study the subdifferential set of an operator. We give possible relation of the subdifferential set of an operator to that of its value, at a point where the operator attains its norm.
We propose a new concept for the regularization and discretization of transfer and Koopman operators in dynamical systems. Our approach is based on the entropically regularized optimal transport between two probability measures. In…
We consider the analytic continuation of the transfer function for a 2x2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the…
We find that the perfect distinguishability of two quantum operations by a parallel scheme depends only on an operator subspace generated from their Choi-Kraus operators. We further show that any operator subspace can be obtained from two…
It is the intention of this paper to rigorously clarify the role of the occupation numbers in the current practical applications of the density functional formalism. In these calculations one has to decide how to distribute a given, fixed…
Given a sequence of real numbers, we consider its subsequences converging to possibly different limits and associate to each of them an index of convergence which depends on the density of the associated subsequences. This index turns out…
This paper presents a distributed Koopman operator learning framework for modeling unknown nonlinear dynamics using sequential observations from multiple agents. Each agent estimates a local Koopman approximation based on lifted data and…
In previous work, we showed that an anomaly in the one point function of marginal operators is related by the Wess-Zumino condition to the Euler density anomaly on a two dimensional defect or boundary. Here we analyze in detail the two…
For observers in curved spacetimes, elements of the dual space of the set of linearized Poincar\'e transformations from an observer's tangent space to itself can be naturally interpreted as local linear and angular momenta. We present an…
In this paper we deal with the macroscopic electromagnetic response of a finite size dispersive dielectric object, in unbounded space, in the framework of quantum electrodynamics using the Heisenberg picture. We apply a Hopfield type scheme…
The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalisation yields exact results in the thermodynamic…
An arbitrary polarization state of a single-mode biphoton is considered. The operationalistic criterion is formulated for the orthogonality og these states. It can be used to separate a biphoton with an arbitrary degree of polarization from…
In recent years, deep learning for modeling physical phenomena which can be described by partial differential equations (PDEs) have received significant attention. For example, for learning Hamiltonian mechanics, methods based on deep…