Xiaoping Yuan

activity

20062026

most citedA KAM theorem with applications to partial equations of higher dimension

26 citations · 85 across the 32 of their papers we have counts for

collaborators

Showing 2013 · math.SPShow all

4 papers · 2 filters

math.SP2013

Absolutely Continuous Spectrum for the Quasi-periodic Schrödinger Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

Avila and Jitomirskaya prove that the quasi-periodic Schrödinger operator $H_{λ v, α, θ}$ has purely absolutely continuous spectrum for $α$ in sub-exponential regime (i.e., $β (α) = 0$ )…

math.SP2013★ 10 cited

Anderson localization for the completely resonant phases

Wencai Liu, Xiaoping Yuan

For the almost Mathieu operator $(H_{λ, α, θ} u) (n) = u (n + 1) + u (n - 1) + λ v (θ + n α) u (n)$ , Avila and Jitomirskaya guess that for every phase $ θ\in \mathscr{R} \triangleq\{θ\in \mathbb{R}\;|…

math.SP2013★ 15 cited

Spectral Gaps of Almost Mathieu Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

For almost Mathieu operator $(H_{λ, α, θ} u)_{n} = u_{n + 1} + u_{n - 1} + 2 λ cos 2 π (θ + n α) u_{n}$ , the dry version of Ten Martini problem predicts that the spectrum $Σ_{λ, α}$ of $H_{λ, α, θ}$ has all…

math.SP2013★ 8 cited

Anderson Localization for the Almost Mathieu Operator in Exponential Regime

Wencai Liu, Xiaoping Yuan

For the almost Mathieu operator $(H_{λ, α, θ} u)_{n} = u_{n + 1} + u_{n - 1} + 2 λ cos 2 π (θ + n α) u_{n}$ , Avila and Jitomirskaya guess that for a.e. $θ$ , $H_{λ, α, θ}$ satisfies Anderson localization if $…