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pro vyhledávání: '"Young, Giorgio"'
In this article, we review some notions of ballistic transport from the mathematics and physics literature, describe their basic interrelations, and contrast them with other commonly studied notions of wave packet spread.
Externí odkaz:
http://arxiv.org/abs/2403.19618
We study the transport properties of Schr\"{o}dinger operators on $\mathbb{R}^d$ and $\mathbb{Z}^d$ with potentials that are periodic in some directions and compactly supported in the others. Such systems are known to produce "surface states" that ar
Externí odkaz:
http://arxiv.org/abs/2311.08612
Autor:
Young, Giorgio
In this paper, we consider the transport properties of the class of limit-periodic continuum Schr\"odinger operators whose potentials are approximated exponentially quickly by a sequence of periodic functions. For such an operator $H$, and $X_H(t)$ t
Externí odkaz:
http://arxiv.org/abs/2109.12096
There is a vast theory of Chebyshev and residual polynomials and their asymptotic behavior. The former ones maximize the leading coefficient and the latter ones maximize the point evaluation with respect to an $L^\infty$ norm. We study Chebyshev and
Externí odkaz:
http://arxiv.org/abs/2101.01744
There is a vast theory of the asymptotic behavior of orthogonal polynomials with respect to a measure on $\mathbb{R}$ and its applications to Jacobi matrices. That theory has an obvious affine invariance and a very special role for $\infty$. We exten
Externí odkaz:
http://arxiv.org/abs/2008.11884
Autor:
Lukić, Milivoje, Young, Giorgio
We consider the Cauchy problem for the KdV hierarchy -- a family of integrable PDEs with a Lax pair representation involving one-dimensional Schr\"odinger operators -- under a local in time boundedness assumption on the solution. For reflectionless i
Externí odkaz:
http://arxiv.org/abs/1910.10237
Akademický článek
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Autor:
Lukić, Milivoje, Young, Giorgio
Publikováno v:
In Journal of Functional Analysis 15 October 2020 279(7)
Akademický článek
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Publikováno v:
Transactions of the American Mathematical Society, Series B; 1/17/2023, Vol. 10, p1-47, 47p