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pro vyhledávání: '"Liu, Wencai"'
This paper investigates uniqueness results for perturbed periodic Schr\"odinger operators on $\mathbb{Z}^d$. Specifically, we consider operators of the form $H = -\Delta + V + v$, where $\Delta$ is the discrete Laplacian, $V: \mathbb{Z}^d \rightarrow
Externí odkaz:
http://arxiv.org/abs/2409.10387
Autor:
Liu, Wencai
Let $\Delta+V$ be the discrete Schr\"odinger operator, where $\Delta$ is the discrete Laplacian on $\mathbb{Z}^d$ and the potential $V:\mathbb{Z}^d\to \mathbb{C}$ is $\Gamma$-periodic with $\Gamma=q_1\mathbb{Z}\oplus q_2 \mathbb{Z}\oplus\cdots\oplus
Externí odkaz:
http://arxiv.org/abs/2306.16412
We present a method to estimate the number of irreducible components of the Fermi varieties of periodic Schr\"odinger operators on graphs in terms of suitable asymptotics. Our main theorem is an abstract bound for the number of irreducible components
Externí odkaz:
http://arxiv.org/abs/2305.06471
Autor:
Liu, Wencai
Let $\Gamma=q_1\mathbb{Z}\oplus q_2 \mathbb{Z}\oplus\cdots\oplus q_d\mathbb{Z}$ with arbitrary positive integers $q_l$, $l=1,2,\cdots,d$. Let $\Delta_{\rm discrete}+V$ be the discrete Schr\"odinger operator on $\mathbb{Z}^d$, where $\Delta_{\rm discr
Externí odkaz:
http://arxiv.org/abs/2302.13103
Autor:
Liu, Wencai
We show that the sublinear bound of the bad Green's functions implies explicit logarithmic bounds of moments for long range operators in arbitrary dimension.
Comment: Dedicated to Abel Klein on the occasion of his 75th birthday
Comment: Dedicated to Abel Klein on the occasion of his 75th birthday
Externí odkaz:
http://arxiv.org/abs/2212.02411
Autor:
Liu, Wencai
For periodic graph operators, we establish criteria to determine the overlaps of spectral band functions based on Bloch varieties. One criterion states that for a large family of periodic graph operators, the irreducibility of Bloch varieties implies
Externí odkaz:
http://arxiv.org/abs/2210.10532
Autor:
Liu, Wencai
Let $\Gamma=q_1\mathbb{Z}\oplus q_2 \mathbb{Z} $ with $q_1\in \mathbb{Z}_+$ and $q_2\in\mathbb{Z}_+$. Let $\Delta+X$ be the discrete periodic Schr\"odinger operator on $\mathbb{Z}^2$, where $\Delta$ is the discrete Laplacian and $X:\mathbb{Z}^2\to \m
Externí odkaz:
http://arxiv.org/abs/2208.06967
Autor:
Liu, Wencai
We discover that the distribution of (frequency and phase) resonances plays a role in determining the spectral type of supercritical quasi-periodic Schr\"odinger operators. In particular, we disprove the second spectral transition line conjecture of
Externí odkaz:
http://arxiv.org/abs/2208.06944
Publikováno v:
Cailiao gongcheng, Vol 52, Iss 2, Pp 16-30 (2024)
Wire arc additive manufacturing (WAAM) has received extensive attention from researchers due to its high deposition rate, high material utilization, low cost, and ability to manufacture large-scale components. It is expected to be widely used in rapi
Externí odkaz:
https://doaj.org/article/31d2ea37662b4be2b8401d2f8293947f
Autor:
Liu, Wencai, Lyu, Kang
In this paper, we introduce a new family of functions to construct Schr\"odinger operators with embedded eigenvalues. This particularly allows us to construct discrete Schr\"odinger operators with arbitrary prescribed sets of eigenvalues.
Externí odkaz:
http://arxiv.org/abs/2207.00194