Related papers: A construction of inductive limit for operator sys…
We introduce the theory of operator monotone functions and employ it to derive a new inequality relating the quantum relative entropy and the quantum conditional entropy. We present applications of this new inequality and in particular we…
This paper shows how the theory of nonlinear adaptive observers can be effectively used in the design of internal models for nonlinear output regulation. The theory substantially enhances the existing results in the context of {\em…
Via operator theoretic methods, we formalize the concentration phenomenon for a given observable `$r$' of a discrete time Markov chain with `$\mu_{\pi}$' as invariant ergodic measure, possibly having support on an unbounded state space. The…
In this paper, we provide a tutorial overview and an extension of a recently developed framework for data-driven control of unknown nonlinear systems with rigorous closed-loop guarantees. The proposed approach relies on the Koopman operator…
We prove that an operator system $\mathcal S$ is nuclear in the category of operator systems if and only if there exist nets of unital completely positive maps $\phi_\lambda : \cl S \to M_{n_\lambda}$ and $\psi_\lambda : M_{n_\lambda} \to…
We consider the construction of integrable quantum field theories in the operator-algebraic approach, which is based on quantum fields localized in infinitely extended wedge regions. This approach has been successful for the construction of…
We consider a superposition operator of the form $$ \int_{[0, 1]} (-\Delta)^s u\, d\mu(s),$$ for a signed measure $\mu$ on the interval of fractional exponents $[0,1]$, joined to a nonlinearity whose term of homogeneity equal to one is…
We propose an extension of minimal intuitionistic predicate logic, based on delimited control operators, that can derive the predicate-logic version of the Double-negation Shift schema, while preserving the disjunction and existence…
The unitary evolution can be represented by a finite product of exponential operators. It leads to a perturbative expression of the density operator of a close system. Based on the perturbative expression scheme, we present a entanglement…
We demonstrate that being a hyperbolicity preserver does not imply monotonicity for infinite order differential operators on $\mathbb{R}[x]$, thereby settling a recent conjecture in the negative. We also give some sufficient conditions for…
The dynamics of an open quantum system can be fully described and tomographically reconstructed if the experimenter has complete control over the system of interest. Most real-world experiments do not fulfill this assumption, and the amount…
We develop a theory of edge states based on the Hermiticity of Hamiltonian operators for tight-binding models defined on lattices with boundaries. We describe Hamiltonians using shift operators which serve as differential operators in…
A modeling methodology and matrix formalism is presented that permits analysis of arbitrarily complex interferometric waveguide systems, including polarization and backreflection effects. Considerable improvement results from separation of…
The mechanical force from light -- radiation pressure -- provides an intrinsic nonlinear interaction. Consequently, optomechanical systems near their steady state, such as the canonical optical spring, can display non-analytic behavior as a…
We construct the most general form of our previously proposed nonlinear extension of quantum mechanics that possesses three basic properties. Unlike the simpler model, the new version is not completely integrable, but it has an underlying…
Non-Hermitian dynamics in quantum systems preserves the rank of the state density operator. Using this insight, we develop a geometric framework to describe its time evolution. In particular, we identify mutually orthogonal coherent and…
We prove a Limiting Absorption Principle for Schr{\"o}dinger operators in tubes about infinite curves embedded in the Euclidian space with different types of boundary conditions. The argument is based on the Mourre theory with conjugate…
Transitive closure logic is a known extension of first-order logic obtained by introducing a transitive closure operator. While other extensions of first-order logic with inductive definitions are a priori parametrized by a set of inductive…
We present a construction of the Steinberg representation admitting an automatic pass to an infinite-dimensional limit.
This paper introduces a systematic method for designing robust linear controllers using output feedback in the presence of operational constraints. The design uses Nagumo's Theorem and the Comparison Lemma to guarantee constraint…