Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Shterenberg, Roman"'
We show that, for one-dimensional discrete Schr\"odinger operators, stability of Anderson localization under a class of rank one perturbations implies absence of intervals in spectra. The argument is based on well-known result of Gordon and Simon, co
Externí odkaz:
http://arxiv.org/abs/2407.00705
Classical Wave methods and modern gauge transforms: Spectral Asymptotics in the one dimensional case
In this article, we consider the asymptotic behaviour of the spectral function of Schr\"odinger operators on the real line. Let $H: L^2(\mathbb{R})\to L^2(\mathbb{R})$ have the form $$ H:=-\frac{d^2}{dx^2}+V, $$ where $V$ is a formally self-adjoint f
Externí odkaz:
http://arxiv.org/abs/2207.08245
Quasi-periodic solutions of the Gross-Pitaevskii equation with a periodic potential in dimension three are studied. It is proven that there is an extensive "non-resonant" set ${\mathcal G} \subset \mathbb{R}^3$ such that for every $\vec k\in \mathcal
Externí odkaz:
http://arxiv.org/abs/2202.06792
One of the main tools used to understand both qualitative and quantitative spectral behaviour of periodic and almost periodic Schr\"odinger operators is the method of gauge transform. In this paper, we extend this method to an abstract setting, thus
Externí odkaz:
http://arxiv.org/abs/2106.01888
We prove the existence of ballistic transport for a Schr\"odinger operator with a generic quasi-periodic potential in any dimension $d>1$.
Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1507.06523
Comment: 16 pages. arXiv admin note: substantial text overlap with arXiv:1507.06523
Externí odkaz:
http://arxiv.org/abs/2102.03677
We consider quasiperiodic operators on $\mathbb Z^d$ with unbounded monotone sampling functions ("Maryland-type"), which are not required to be strictly monotone and are allowed to have flat segments. Under several geometric conditions on the frequen
Externí odkaz:
http://arxiv.org/abs/2102.02839
We consider Schr\"odinger operators $H=-\Delta+V({\mathbf x})$ in ${\mathbb R}^d$, $d\geq2$, with quasi-periodic potentials $V({\mathbf x})$. We prove that the absolutely continuous spectrum of a generic $H$ contains a semi-axis $[\lambda_*,+\infty)$
Externí odkaz:
http://arxiv.org/abs/2010.05881
We consider a class of unbounded quasiperiodic Schr\"odinger-type operators on $\ell^2(\mathbb Z^d)$ with monotone potentials (akin to the Maryland model) and show that the Rayleigh--Schr\"odinger perturbation series for these operators converges in
Externí odkaz:
http://arxiv.org/abs/2006.00346
Publikováno v:
In Advances in Mathematics 19 November 2022 409 Part B
Quasi-periodic solutions of a nonlinear polyharmonic equation for the case $4l>n+1$ in $\R^n$, $n>1$, are studied. This includes Gross-Pitaevskii equation in dimension two ($l=1,n=2$). It is proven that there is an extensive "non-resonant" set ${\mat
Externí odkaz:
http://arxiv.org/abs/1805.03974