Zobrazeno 1 - 10
of 29
pro vyhledávání: '"VandenBoom, Tom"'
Autor:
Forman, Yakir, VandenBoom, Tom
We prove Cantor spectrum and almost-sure Anderson localization for quasiperiodic discrete Schr\"odinger operators $H = \varepsilon\Delta + V$ with potential $V$ sampled with Diophantine frequency $\alpha$ from an asymmetric, smooth, cosine-like funct
Externí odkaz:
http://arxiv.org/abs/2107.05461
We prove a bijective unitary correspondence between 1) the isospectral torus of almost-periodic, absolutely continuous CMV matrices having fixed finite-gap spectrum and 2) special periodic block-CMV matrices satisfying a Magic Formula. This latter cl
Externí odkaz:
http://arxiv.org/abs/1902.05850
Autor:
Bucaj, Valmir, Damanik, David, Fillman, Jake, Gerbuz, Vitaly, VandenBoom, Tom, Wang, Fengpeng, Zhang, Zhenghe
In this short note, we prove positivity of the Lyapunov exponent for 1D continuum Anderson models by leveraging some classical tools from inverse spectral theory. The argument is much simpler than the existing proof due to Damanik--Sims--Stolz, and i
Externí odkaz:
http://arxiv.org/abs/1902.04642
We establish precise spectral criteria for potential functions $V$ of reflectionless Schr\"odinger operators $L_V = -\partial_x^2 + V$ to admit solutions to the Korteweg de-Vries (KdV) hierarchy with $V$ as an initial value. More generally, our metho
Externí odkaz:
http://arxiv.org/abs/1802.00052
We establish concrete criteria for fully supported absolutely continuous spectrum for ergodic CMV matrices and purely absolutely continuous spectrum for limit-periodic CMV matrices. We proceed by proving several variational estimates on the measure o
Externí odkaz:
http://arxiv.org/abs/1712.04620
Autor:
Bucaj, Valmir, Damanik, David, Fillman, Jake, Gerbuz, Vitaly, VandenBoom, Tom, Wang, Fengpeng, Zhang, Zhenghe
We provide a complete and self-contained proof of spectral and dynamical localization for the one-dimensional Anderson model, starting from the positivity of the Lyapunov exponent provided by F\"urstenberg's theorem. That is, a Schr\"odinger operator
Externí odkaz:
http://arxiv.org/abs/1706.06135
Autor:
VandenBoom, Tom
We prove that, if an isospectral torus contains a discrete Schr\"odinger operator with nonconstant potential, the shift dynamics on that torus cannot be minimal. Consequently, we specify a generic sense in which finite unions of nondegenerate closed
Externí odkaz:
http://arxiv.org/abs/1703.01997
Publikováno v:
C. R. Math. Acad. Sci. Soc. R. Can. 40 (2018), 1-28
We study an initial value problem for the Toda lattice with almost periodic initial data. We consider initial data for which the associated Jacobi operator is absolutely continuous and has a spectrum satisfying a Craig-type condition, and show the bo
Externí odkaz:
http://arxiv.org/abs/1603.04905
Publikováno v:
In Journal of Mathematical Analysis and Applications 1 November 2018 467(1):132-147
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