Related papers: A Floquet Operator with Pure Point Spectrum and En…

Using the method of similar operators we study an even order differential operator with periodic, semiperiodic, and Dirichlet boundary conditions. We obtain asymptotic formulas for eigenvalues of this operator and estimates for its spectral…

In this paper we provide a complete study of the spectrum of a constant coefficients differential operator on a scale of localized Sobolev spaces, $H^{s}_{loc}(I),$ which are Fr\'echet spaces. This is quite different from what we find in…

We consider a non-self-adjoint third order operator on the interval $[0,2]$ with real 1-periodic coefficients and three-point Dirichlet conditions at the points 0, 1 and 2. The eigenvalues of this operator consist an auxiliary spectrum for…

We investigate the Floquet spectrum of a detuned, driven two-level system and show that it exhibits exact quasienergy crossings when the detuning is an integer multiple of the energy quantum of the driving field. This behavior can be…

For piecewise expanding one-dimensional maps without periodic turning points we prove that isolated eigenvalues of small (random) perturbations of these maps are close to isolated eigenvalues of the unperturbed system. (Here ``eigenvalue''…

Embedded point spectra of rank one singular perturbations of an arbitrary self-adjoint operator A on a Hilbert space H is studied. It is shown that these perturbations can be regarded as self-adjoint extensions of a densely defined closed…

The problem of Anderson localization, as well as the single particle localization-delocalizaton transition of the Aubry-Andr\'e model, is studied employing operator Krylov space methods. It is shown that even when the dynamics is generated…

We study the spectrum of a one-dimensional Schroedinger operator perturbed by a fast oscillating potential. The oscillation period is a small parameter. The essential spectrum is found in an explicit form. The existence and multiplicity of…

We study spectral properties of the Fokker-Planck operator that describes particles diffusing in a quenched random velocity field. This random operator is non-Hermitian and has eigenvalues occupying a finite area in the complex plane. We…

An operator $T\in B(H)$ is said to satisfy property ($UW${\scriptsize \it{E}}) if the complement in the approximate point spectrum of the essential approximate point spectrum coincides with the isolated eigenvalues of the spectrum. Via the…

A recent result characterizes the fully order reversing operators acting on the class of lower semicontinuous proper convex functions in a real Banach space as certain linear deformations of the Legendre-Fenchel transform. Motivated by the…

Finiteness of the point spectrum of linear operators acting in a Banach space is investigated from point of view of perturbation theory. In the first part of the paper we present an abstract result based on analytical continuation of the…

We investigate theoretically a scheme for spectroscopy of electrons emitted by an on-demand single particle source. The total system, with an electron turnstile source and a single level quantum dot spectrometer, is implemented with edge…

In the first part of this manuscript a relationship between the spectrum of self-adjoint operator matrices and the spectra of their diagonal entries is found. This leads to enclosures for spectral points and in particular, enclosures for…

For a simple illustrative model Hamiltonian for Xenon in low frequency linearly polarized laser field we obtain a remarkable agreement between the zero-order energy as well as amplitude and phase of the zero-order Floquet states and the…

The paper deals with the semi-Dirac operator in a half-space arising in the description of quasiparticles in quantum mechanics as well as in semi-metals materials and related structures. It completely shows the self-adjointness, computes…

Protecting superconducting qubits from low-frequency noise is essential for advancing superconducting quantum computation. Based on the application of a periodic drive field, we develop a protocol for engineering dynamical sweet spots which…

Periodically driven many-body systems generally heat towards a featureless 'infinite-temperature' state. As an alternative to uniform heating in a clean system, here we establish a Floquet superheating regime, where fast heating nucleates…

We study the stationary scattering theory for a perturbed 1-body Stark operator. We prove existence and completeness of the stationary wave operators, construct the associated generalized Fourier transforms, and characterize asymptotics of…

We first investigate spectral properties of the Neumann-Poincar\'e (NP) operator for the Lam\'e system of elasto-statics. We show that the elasto-static NP operator can be symmetrized in the same way as that for Laplace operator. We then…