Related papers: The essential spectrum of canonical systems
Fix an integer $n\ge 2$. To each non-zero point $\mathbf{u}$ in $\mathbb{R}^n$, one attaches several numbers called exponents of Diophantine approximation. However, as Khintchine first observed, these numbers are not independent of each…
We investigate a hierarchy of arithmetical structures obtained by a transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of…
Using the fact that any minimal strongly regular surface carries locally canonical principal parameters, we obtain a canonical representation of these surfaces, which makes more precise the Weierstrass representation in canonical principal…
We consider equivariant continuous families of discrete one-dimensional operators over arbitrary dynamical systems. We introduce the concept of a pseudo-ergodic element of a dynamical system. We then show that all operators associated to…
In previous papers on this project a general static logical framework for formalizing and mechanizing set theories of different strength was suggested, and the power of some predicatively acceptable theories in that framework was explored.…
According to Jae Suk Park, physicists use "canonical coordinate systems" to compute correlations in perturbative quantum field theories. One may interpret these canonical coordinate systems as equivalences of generalized differential Lie…
We show that minimal models of log canonical pairs exist, assuming the existence of minimal models of smooth varieties.
We investigate the spectral properties of Sturm-Liouville operators with measure potentials. We obtain two-sided estimates for the spectral distribution function of the eigenvalues. As a corollary, we derive a criterion for the discreteness…
The quantization of circular strings in an anti-de Sitter background spacetime is performed, obtaining a discrete spectrum for the string mass. A comparison with a four-dimensional homogeneous and isotropic spacetime coupled to a conformal…
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of…
In this work, we study the Quantum Field Theory version of the higher derivative Pais-Uhlenbeck oscillator. We quantize canonically this system and construct its Fock space, as well as study its path integral. We demonstrate that the…
A practical version of the polynomial canonical formalism is developed for normal mesoscopic systems consisting of N independent electrons. Drastic simplification of calculations is attained by means of proper ordering excited states of the…
Ensemble control, an emerging research field focusing on the study of large populations of dynamical systems, has demonstrated great potential in numerous scientific and practical applications. Striking examples include pulse design for…
We compare the minimal model of a log canonical pair with the minimal model of its reduced boundary. These results are then used to study the existence of the minimal model of a semi-log-canonical pair using its normalization.
Fully oscillating sequences are orthogonal to all topological dynamical systems of quasi-discrete spectrum in the sense of Hahn-Parry. This orthogonality concerns with not only simple but also multiple ergodic means. It is stronger than…
We give a partially alternate proof of the reality of the spectrum of the imaginary cubic oscillator in quantum mechanics.
The spectrum of an arbitrary self-adjoint extension of the minimal linear relation associated with the discrete symplectic system in the limit point case is completely characterized by using the limiting Weyl--Titchmarsh…
We present shadow spectroscopy as a simulator-agnostic quantum algorithm for estimating energy gaps using very few circuit repetitions (shots) and no extra resources (ancilla qubits) beyond performing time evolution and measurements. The…
In this article we prove a generalization of Weyl's criterion for the essential spectrum of a self-adjoint operator on a Hilbert space. We then apply this criterion to the Laplacian on functions over open manifolds and get new results for…
We consider a quantum system consisting of a one-dimensional chain of M identical harmonic oscillators with natural frequency $\omega$, coupled by means of springs. Such systems have been studied before, and appear in various models. In…