相关论文: A Floquet Operator with Pure Point Spectrum and En…

The spectral properties of a class of non-selfadjoint second order elliptic operators with indefinite weight functions on unbounded domains $\Omega$ are investigated. It is shown that under an abstract regularity assumption the nonreal…

We study the spectral stability of the nonlinear Dirac operator in dimension $1+1$, restricting our attention to nonlinearities of the form $f(\langle\psi,\beta \psi\rangle_{\mathbb{C}^2}) \beta$. We obtain bounds on eigenvalues for the…

In this paper, we study self-adjointness and spectrum of operators of the form $$H=\displaystyle -\frac{d^2}{dx^2}+Fx, F>0 \quad\text{on} \quad \mathcal{H}=L^{2}(-L,L).$$ $H$ is called Stark operator and describes a quantum particle in a…

The spectrum of a one-parameter family of signed transfer operators associated to the Farey map is studied in detail. We show that when acting on a suitable Hilbert space of analytic functions they are self-adjoint and exhibit absolutely…

Floquet topological insulators are noninteracting quantum systems that, when driven by a time-periodic field, are described by effective Hamiltonians whose bands carry nontrivial topological invariants. A longstanding question concerns the…

We find spectrum and eigenfunctions of the operator $(Vf)(x) = \int_0^{x^\alpha} f(t) dt$ in $L_2[0,1]$

In this paper we introduce a notion of $F-$ quadratic stochastic operator. For a wide class of such operators we show that each operator of the class has unique fixed point. Also we prove that any trajectory of the $F$-quadratic stochastic…

Anholonomies in the parametric dependences of the eigenvalues and the eigenvectors of Floquet operators that describe unit time evolutions of periodically driven systems, e.g., kicked rotors, are studied. First, an example of the…

We develop an eigenvalue-based approach for the stability assessment and stabilization of linear systems with multiple delays and periodic coefficient matrices. Delays and period are assumed commensurate numbers, such that the Floquet…

We prove the following. For any complex valued $L^p$-function $b(x)$, $2 \leq p < \infty$ or $L^\infty$-function with the norm $\| b | L^{\infty}\| < 1$, the spectrum of a perturbed harmonic oscillator operator $L = -d^2/dx^2 + x^2 + b(x)$…

In this paper we investigate the action of self-consistent transfer operators (STOs) on Birkhoff cones and give sufficient conditions for stability of their fixed points. Our approach relies on the order preservation properties of STOs that…

The Floquet spectrum of a class of driven SU(2) systems is shown to display a butterfly pattern with multi-fractal properties. The level crossing between Floquet states of the same parity or different parities is studied. The results are…

We complete a full classification of non-degenerate traveling waves of scalar balance laws from the point of view of spectral and nonlinear stability/instability under (piecewise) smooth perturbations. A striking feature of our analysis is…

Floquet engineering provides an optical means to manipulate electronic bandstructures, however, carriers excited by the pump field can lead to an effective heating, and can obscure measurement of the band changes. A recent demonstration of…

We consider the rates of relaxation of a particle in a harmonic well, subject to L\'evy noise characterized by its L\'evy index $\mu$. Using the propagator for this L\'evy Ornstein-Uhlenbeck process (LOUP), we show that the eigenvalue…

We prove a localization theorem for continuous ergodic Schr\"odinger operators $ H_\omega := H_0 + V_\omega $, where the random potential $ V_\omega $ is a nonnegative Anderson-type perturbation of the periodic operator $ H_0$. We consider…

The dynamics of an isolated quantum system is coherent and unitary. Weak coupling to the environment leads to decoherence, which is traditionally modeled with a Lindblad equation for the system's density matrix. Starting from a pure state,…

In this paper, we explore the high-frequency properties of eigenfunctions of point perturbations of the Laplacian on a compact Riemannian manifold. These systems cannot be obtained as the quantization of a classical Hamiltonian, as the…

We consider a singularly perturbed Dirichlet spectral problem for an elliptic operator of second order. The coefficients of the operator are assumed to be locally periodic and oscillating in the scale $\varepsilon$. We describe the leading…

Periodically time-varying media, known as photonic time crystals (PTCs), provide a promising platform for observing unconventional wave phenomena. We analyze the scattering of electromagnetic waves from spatially finite PTCs using the…