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of 153
pro vyhledávání: '"Hislop, Peter D."'
Autor:
Hislop, Peter D., Soccorsi, Eric
We study the large-time asymptotics of the mean-square displacement for the time-fractional Schrodinger equation in $\mathbb{R}^d$. We define the time-fractional derivative by the Caputo derivative and we consider the initial-value problem for the fr
Externí odkaz:
http://arxiv.org/abs/2401.10918
Autor:
Herschenfeld, Samuel, Hislop, Peter D.
We use the method of eigenvalue level spacing developed by Dietlein and Elgart (arXiv:1712.03925) to prove that the local eigenvalue statistics (LES) for the Anderson model on $Z^d$, with uniform higher-rank $m \geq 2$, single-site perturbations, is
Externí odkaz:
http://arxiv.org/abs/2208.03598
Autor:
Hislop, Peter D., Krishna, M.
We study the local eigenvalue statistics $\xi_{\omega,E}^N$ associated with the eigenvalues of one-dimensional, $(2N+1) \times (2N+1)$ random band matrices with independent, identically distributed, real random variables and band width growing as $N^
Externí odkaz:
http://arxiv.org/abs/2107.01450
Autor:
Brodie, Benjamin, Hislop, Peter D.
We prove that the local eigenvalue statistics for $d=1$ random band matrices with fixed bandwidth and, for example, Gaussian entries, is given by a Poisson point process and we identify the intensity of the process. The proof relies on an extension o
Externí odkaz:
http://arxiv.org/abs/2008.13167
Autor:
Hislop, Peter D., Marx, Christoph A.
We continue our study of the dependence of the density of states measure and related spectral functions of Schr\"odinger operators on the potential. Whereas our earlier work focused on random Schr\"odinger operators, we extend these results to Schr\"
Externí odkaz:
http://arxiv.org/abs/2006.15230
Akademický článek
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Akademický článek
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We prove that the local eigenvalue statistics at energy $E$ in the localization regime for Schr\"odinger operators with random point interactions on $\mathbb{R}^d$, for $d=1,2,3$, is a Poisson point process with the intensity measure given by the den
Externí odkaz:
http://arxiv.org/abs/1905.07889
Publikováno v:
J. Math. Phys. 60, 083303 (2019)
We show that a quantum particle in $\mathbb{R}^d$, for $d \geq 1$, subject to a white-noise potential, moves super-ballistically in the sense that the mean square displacement $\int \|x\|^2 \langle \rho(x,x,t) \rangle ~dx$ grows like $t^{3}$ in any d
Externí odkaz:
http://arxiv.org/abs/1807.08317
Autor:
Hislop, Peter D., Marx, Christoph A.
We prove that the the density of states measure (DOSm) for random Schr\"odinger operators on $\mathbb{Z}^d$ is weak-$^*$ H\"older-continuous in the probability measure. The framework we develop is general enough to extend to a wide range of discrete,
Externí odkaz:
http://arxiv.org/abs/1804.02444