Related papers: The essential spectrum of canonical systems
The Random Transverse Field Ising Chain is the simplest disordered model presenting a quantum phase transition at T=0. We compare analytically its finite-size scaling properties in two different ensembles for the disorder (i) the canonical…
Minimal varying $\Lambda$ theories are defined by an action built from the Einstein-Cartan-Holst first order action for gravity with the cosmological constant $\Lambda$ as an independent scalar field, and supplemented by the Euler and…
The theory of Gaussian quantum fluctuations around classical steady states in nonlinear quantum-optical systems (also known as standard linearization) is a cornerstone for the analysis of such systems. Its simplicity, together with its…
Discrete canonical evolution is a key tool for understanding the dynamics in discrete models of spacetime, in particular those represented by a triangular Regge lattice. We consider a finite-dimensional system whose evolution is realized by…
The functional method, introduced to deal with systems endowed with a continuous spectrum, is used to study the problem of decoherence and correlations in a simple cosmological model.
Beyond the crucial role they play in the foundations of the theory of overconvergent modular forms, canonical subgroups have found new applications to analytic continuation of overconvergent modular forms. For such applications, it is…
We present a derivation of the energy spectrum of the harmonic oscillator by using the alternative approach of topological quantization. The spectrum is derived from the topological invariants of a particular principal fiber bundle which…
The isoperimeric spectrum consists of all real positive numbers $\alpha$ such that $O(n^\alpha)$ is the Dehn function of a finitely presented group. In this note we show how a recent result of Olshanskii completes the description of the…
For many applications, critical information about system dynamics is encoded in associated eigenvalue problems that can be posed as linear Hamiltonian systems with suitable boundary conditions. Motivated by examples from hydrodynamics,…
A Hamiltonian (model operator) $H$ associated to a quantum system describing three particles in interaction, without conservation of the number of particles, is considered. The Faddeev type system of equations for eigenvectors of $H$ is…
Spectrum is an important numerical invariant of an isolated hypersurface singularity, connecting its topological and analytic structures. The well-known Hertling conjecture tells the relation of range and variance of exponents i.e. elements…
We study the concept of canonical characteristic set of a characterizable differential ideal. We propose an efficient algorithm that transforms any characteristic set into the canonical one. We prove the basic properties of canonical…
In the framework of the canonical quantization of the electromagnetic field, we impose as primary condition on the dynamics the positive definiteness of the energy spectrum. This implies that (Glauber) coherent states have to be considered…
A system of functions (signals) on the finite line, called the oscillator system, is described and studied. Applications of this system for discrete radar and digital communication theory are explained. Keywords: Weil representation,…
The spectral characterization of Coulomb systems confined by the homogeneous pseudo-Gaussian oscillator is investigated. This is made using the efficient computational method of generating functional. Also, the method is used for the…
Tunable filters are set to revolutionize many aspects of experimental astrophysics, particularly for applications in observational cosmology. After a summary of the fundamentals of classical spectroscopy, we present a review of the current…
We study the essential spectra of formally self-adjoint elliptic systems on doubly periodic planar domains perturbed by a semi-infinite periodic row of foreign inclusions. We show that the essential spectrum of the problem consists of the…
Based on continued fractions with subtractions, we identify the set of real numbers with the set of infinite integer sequences with all terms but the first one greater or equal to two. Each such sequence produces in a canonical way a unique…
Random variables representing measurements, broadly understood to include any responses to any inputs, form a system in which each of them is uniquely identified by its content (that which it measures) and its context (the conditions under…
We study {\it analytically} the characteristic resonance spectrum of charged massive scalar fields linearly coupled to a spherically symmetric charged reflecting shell. In particular, we use analytical techniques in order to solve the…