Related papers: The essential spectrum of canonical systems

Experimental observation of Bose-Einstein condensation (BEC) of photons inside a microcavity induced an extensive study of the phenomenon. Beyond the purely theoretical interest, this phenomenon is believed to be used to create a novel…

Identifying the Hamiltonian of a quantum system from experimental data is considered. General limits on the identifiability of model parameters with limited experimental resources are investigated, and a specific Bayesian estimation…

We consider a system weakly interacting with a bath as a thermodynamic setting to establish a quantum foundation of statistical physics. It is shown that even if the composite system is initially in an arbitrary nonequilibrium pure quantum…

In this paper, we address the problem of distributed state estimation for a discrete-time, linear time-invariant system. Building on the framework proposed in [2], we exploit the Jordan canonical form of the system matrix to develop a…

The short-time linear canonical transform (STLCT) can be identified as a generalization of the short-time Fourier transform (STFT). It is a novel time-frequency analysis tool. In this paper, we generalize some different uncertainty…

Due to the equivalence of the statistical ensembles thermostatic properties of physical systems with short-range interactions can be calculated in different ensembles leading to the same physics. In particular, the ensemble equivalence…

Coupled quantum harmonic oscillators, studied by many authors using many different techniques over the decades, are frequently used toy-models to study open quantum systems. In this manuscript, we explicitly study the simplest oscillator…

We prove uniqueness problems for meromorphic inner functions on the upper half-plane. In these problems we consider spectral data depending partially or fully on the spectrum, derivative values at the spectrum, Clark measure or the spectrum…

Problems concerning with application of quantum rules on classical phenomena have been widely studied, for which lifted up the idea about quantization and uncertainty principle. Energy quantization on classical example of simple harmonic…

Using an abstract notion of semiclassical quantization for self-adjoint operators, we prove that the joint spectrum of a collection of commuting semiclassical self-adjoint operators converges to the classical spectrum given by the joint…

We study the finite-size spectrum of the O($N$) symmetric Wilson-Fisher conformal field theory (CFT) on the $d=2$ spatial-dimension torus using the expansion in $\epsilon=3-d$. This is done by deriving a set of universal effective…

Kubo's canonical correlation functions (canonical correlators) describe the static response of a system in equilibrium to infinitesimal local perturbations. Knowing their decay properties with respect to spatial distance is important for…

A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…

In this paper, a new class of band matrices is considered where the entries of each non-zero band form a sequence with two limit points. The compact perturbation technique is used to study the spectrum over the $\ell_{p}, (1<p<\infty)$…

We obtain a unified theory of discrete minimal surfaces based on discrete holomorphic quadratic differentials via a Weierstrass representation. Our discrete holomorphic quadratic differential are invariant under M\"{o}bius transformations.…

We study totally ergodic quantum dynamical systems with quasi--discrete spectrum. We investigate the classification problem for such systems in terms of algebraic invariants. The results are noncommutative analogs of (a part of) the theory…

In this paper we investigate system identification for general quantum linear systems. We consider the situation where the input field is prepared as stationary (squeezed) quantum noise. In this regime the output field is characterised by…

An observable canonical form is formulated for the set of rational systems on a variety each of which is a single-input-single-output, affine in the input, and a minimal realization of its response map. The equivalence relation for the…

In 1983, Klaus studied a class of potentials with bumps and computed the essential spectrum of the associated Schr{\"o}dinger operator with the help of some localisations at infinity. A key hypothesis is that the distance between two…

Motivated by an open problem posed by J.P. Hespanha, we extend the notion of Barabanov norm and extremal trajectory to classes of switching signals that are not closed under concatenation. We use these tools to prove that the finiteness of…