相关论文: Absolute Continuity of the Floquet Spectrum for a …

We show that a large class of limit-periodic Schr\"odinger operators has purely absolutely continuous spectrum in arbitrary dimensions. This result was previously known only in dimension one. The proof proceeds through the non-perturbative…

We prove that the spectrum of a Schrodinger operator that is periodic in certain directions and super-exponentially decaying in the others is purely absolutely continuous.

The nonlinear Schroedinger equation has several families of quasi-periodic travelling waves, each of which can be parametrized up to symmetries by two real numbers: the period of the modulus of the wave profile, and the variation of its…

The absolutely continuous spectrum of one-dimensional Schr\"odinger operators is proved to be stable under perturbation by potentials satisfying mild decay conditions. In particular, the absolutely continuous spectrum of free and periodic…

In this paper we find a new condition on a real periodic potential for which the self-adjoint Schr\"odinger operator may be defined by a quadratic form and the spectrum of the operator is purely absolutely continuous. This is based on…

The Floquet spectrum in an anisotropic tilted Dirac semimetal modulated by linearly polarized light is addressed through the solution of the time-dependent Schr\"odinger equation for the two-dimensional Dirac Hamiltonian via the Floquet…

I prove that quasi-periodic Schr\"odinger operators in arbitrary dimension have some absolutely continuous spectrum.

We eliminate by KAM methods the time dependence in a class of linear differential equations in $\ell^2$ subject to an unbounded, quasi-periodic forcing. This entails the pure-point nature of the Floquet spectrum of the operator $…

We consider a family of operators $-\Delta+ t V$ with a slowly decaying and oscillating potential $V$. We prove that the absolutely continuous spectrum of this operator is essentially supported by $[0,\infty)$ for almost every $t$.

We study the Schr\"odinger operator on $L_2(\mathbb R^3)$ with periodic variable metric, and periodic electric and magnetic fields. It is assumed that the operator is reflection symmetric and the (appropriately defined) flux of the magnetic…

We prove new criteria of stability of the absolutely continuous spectrum of one-dimensional Schr\"odinger operators under slowly decaying perturbations. As applications, we show that the absolutely continuous spectrum of the free and…

How to accurately solve time-dependent Schr\"odinger equation is an interesting and important problem. Here, we propose a novel method to obtain the exact Floquet solutions of the Schr\"odinger equation for periodically driven systems by…

We prove that the $1-d$ quantum harmonic oscillator is stable under spatially localized, time quasi-periodic perturbations on a set of Diophantine frequencies of positive measure. This proves a conjecture raised by Enss-Veselic in their…

We show that the spectrum of a Schr\"odinger operator on $\mathbb{R}^n$, $n\ge 3$, with a periodic smooth Riemannian metric, whose conformal multiple has a product structure with one Euclidean direction, and with a periodic electric…

We consider the Schr\"odinger operator in ${\mathbb R}^n$, $n\geq 3$, with the electric potential $V$ and the magnetic potential $A$ being periodic functions (with a common period lattice) and prove absolute continuity of the spectrum of…

By a straightforward generalisation, we extend the work of Combescure from rank-1 to rank-N perturbations. The requirement for the Floquet operator to be pure point is established and compared to that in Combescure. The result matches that…

In this paper, we prove that for any $d$-frequency analytic quasiperiodic Schr\"odinger operator, if the frequency is weak Liouvillean, and the potential is small enough, then the corresponding operator has absolutely continuous spectrum.…

We consider a family of multi-dimensional Schr\"odinger operators $-\Delta+t V$ with a real $t$. The potential $V$ in our model decays at infinity in a special way, so that it satisfies a certain integral condition. We prove that the…

We prove that 3-dimensional Schrodinger operator with slowly decaying potential has an absolutely continuous spectrum that fills the positive half-line. The asymptotics of Green's function is obtained as well.

Using a perturbative argument, we show that in any finite region containing the lowest transverse eigenmode, the spectrum of a periodically curved smooth Dirichlet tube in two or three dimensions is absolutely continuous provided the tube…